Variations in lithospheric thickness on Venus

NASA Technical Reports Server (NTRS)

Johnson, C. L.; Sandwell, David T.

1992-01-01

Recent analyses of Magellan data have indicated many regions exhibiting topograhic flexure. On Venus, flexure is associated predominantly with coronae and the chasmata with Aphrodite Terra. Modeling of these flexural signatures allows the elastic and mechanical thickness of the lithosphere to be estimated. In areas where the lithosphere is flexed beyond its elastic limit the saturation moment provides information on the strength of the lithosphere. Modeling of 12 flexural features on Venus has indicated lithospheric thicknesses comparable with terrestrial values. This has important implications for the venusian heat budget. Flexure of a thin elastic plate due simultaneously to a line load on a continuous plate and a bending moment applied to the end of a broken plate is considered. The mean radius and regional topographic gradient are also included in the model. Features with a large radius of curvature were selected so that a two-dimensional approximation could be used. Comparisons with an axisymmetric model were made for some features to check the validity of the two-dimensional assumption. The best-fit elastic thickness was found for each profile crossing a given flexural feature. In addition, the surface stress and bending moment at the first zero crossing of each profile were also calculated. Flexural amplitudes and elastic thicknesses obtained for 12 features vary significantly. Three examples of the model fitting procedures are discussed.

Elastic And Plastic Deformations In Butt Welds

NASA Technical Reports Server (NTRS)

Verderaime, V.

1992-01-01

Report presents study of mathematical modeling of stresses and strains, reaching beyond limits of elasticity, in bars and plates. Study oriented toward development of capability to predict stresses and resulting elastic and plastic strains in butt welds.

Modeling bicortical screws under a cantilever bending load.

PubMed

James, Thomas P; Andrade, Brendan A

2013-12-01

Cyclic loading of surgical plating constructs can precipitate bone screw failure. As the frictional contact between the plate and the bone is lost, cantilever bending loads are transferred from the plate to the head of the screw, which over time causes fatigue fracture from cyclic bending. In this research, analytical models using beam mechanics theory were developed to describe the elastic deflection of a bicortical screw under a statically applied load. Four analytical models were developed to simulate the various restraint conditions applicable to bicortical support of the screw. In three of the models, the cortical bone near the tip of the screw was simulated by classical beam constraints (1) simply supported, (2) cantilever, and (3) split distributed load. In the final analytical model, the cortices were treated as an elastic foundation, whereby the response of the constraint was proportional to screw deflection. To test the predictive ability of the new analytical models, 3.5 mm cortical bone screws were tested in a synthetic bone substitute. A novel instrument was developed to measure the bending deflection of screws under radial loads (225 N, 445 N, and 670 N) applied by a surrogate surgical plate at the head of the screw. Of the four cases considered, the analytical model utilizing an elastic foundation most accurately predicted deflection at the screw head, with an average difference of 19% between the measured and predicted results. Determination of the bending moments from the elastic foundation model revealed that a maximum moment of 2.3 N m occurred near the middle of the cortical wall closest to the plate. The location of the maximum bending moment along the screw axis was consistent with the fracture location commonly observed in clinical practice.

Geometrically nonlinear analysis of laminated elastic structures

NASA Technical Reports Server (NTRS)

Reddy, J. N.

1984-01-01

Laminated composite plates and shells that can be used to model automobile bodies, aircraft wings and fuselages, and pressure vessels among many other were analyzed. The finite element method, a numerical technique for engineering analysis of structures, is used to model the geometry and approximate the solution. Various alternative formulations for analyzing laminated plates and shells are developed and their finite element models are tested for accuracy and economy in computation. These include the shear deformation laminate theory and degenerated 3-D elasticity theory for laminates.

Evaluation on Bending Properties of Biomaterial GUM Metal Meshed Plates for Bone Graft Applications

NASA Astrophysics Data System (ADS)

Suzuki, Hiromichi; He, Jianmei

2017-11-01

There are three bone graft methods for bone defects caused by diseases such as cancer and accident injuries: Autogenous bone grafts, Allografts and Artificial bone grafts. In this study, meshed GUM Metal plates with lower elasticity, high strength and high biocompatibility are introduced to solve the over stiffness & weight problems of ready-used metal implants. Basic mesh shapes are designed and applied to GUM Metal plates using 3D CAD modeling tools. Bending properties of prototype meshed GUM Metal plates are evaluated experimentally and analytically. Meshed plate specimens with 180°, 120° and 60° axis-symmetrical types were fabricated for 3-point bending tests. The pseudo bending elastic moduli of meshed plate specimens obtained from 3-point bending test are ranged from 4.22 GPa to 16.07 GPa, within the elasticity range of natural cortical bones from 2.0 GPa to 30.0 GPa. Analytical approach method is validated by comparison with experimental and analytical results for evaluation on bending property of meshed plates.

Improving the Diagnostic Specificity of CT for Early Detection of Lung Cancer: 4D CT-Based Pulmonary Nodule Elastometry

DTIC Science & Technology

2013-08-01

transformation models, such as thin - plate spline (1-3) or elastic-body spline (4, 5), is locally controlled. One of the main motivations behind the...research project. References: 1. Bookstein FL. Principal warps: thin - plate splines and the decomposition of deformations. IEEE Transactions on Pattern...Rohr K, Stiehl HS, Sprengel R, Buzug TM, Weese J, Kuhn MH. Landmark-based elastic registration using approximating thin - plate splines . IEEE Transactions

An elastic-perfectly plastic analysis of the bending of the lithosphere at a trench

NASA Technical Reports Server (NTRS)

Turcotte, D. L.; Mcadoo, D. C.; Caldwell, J. G.

1978-01-01

A number of authors have modeled the flexure of the lithosphere at an oceanic trench using a thin elastic plate with a hydrostatic restoring force. In some cases good agreement with observed topography is obtained but in other cases the slope of the lithosphere within the trench is greater than that predicted by the elastic theory. In this paper the bending of a thin plate is considered using an elastic-perfectly plastic rheology. It is found that the lithosphere behaves elastically seaward of the trench, but that plasticity decreases the radius of curvature within the trench. The results are compared with a number of observed trench profiles. The elastic-perfectly plastic profiles are in excellent agreement with those profiles that deviate from elastic behavior.

Laser-Excited Electronic and Thermal Elastic Vibrations in a Semiconductor Rectangular Plate

NASA Astrophysics Data System (ADS)

Todorović, D. M.; Cretin, B.; Vairac, P.; Song, Y. Q.; Rabasović, M. D.; Markushev, D. D.

2013-09-01

Photoacoustic and photothermal effects can be important as driven mechanisms for micro-(opto)-electro-mechanical structures (MOEMS). A new approach for a producing a compact, lightweight, highly sensitive detector is provided by MOEMS technology, which is based on the elastic bending of microstructure generated by absorption of modulated optical power. The electronic and thermal elastic vibrations (the electronic deformation and thermoelastic mechanisms of elastic wave generation) in a semiconductor rectangular simply supported plate (3D geometry), photogenerated by a focused and intensity-modulated laser beam, were studied. The theoretical model for the elastic displacements space and frequency distribution by using the Green function method was given. The amplitude of the elastic bending in the rectangular plate was calculated and analyzed, including the thermalization and surface and volume recombination heat sources. The theoretical results were compared with the experimental data. These investigations are important for many practical experimental situations (atomic force microscopy, thermal microscopy, thermoelastic microscopy, etc.) and sensors and actuators.

Effect of Thermal Gradient on Vibration of Non-uniform Visco-elastic Rectangular Plate

NASA Astrophysics Data System (ADS)

Khanna, Anupam; Kaur, Narinder

2016-04-01

Here, a theoretical model is presented to analyze the effect of bilinear temperature variations on vibration of non-homogeneous visco-elastic rectangular plate with non-uniform thickness. Non-uniformity in thickness of the plate is assumed linear in one direction. Since plate's material is considered as non-homogeneous, authors characterized non-homogeneity in poisson ratio and density of the plate's material exponentially in x-direction. Plate is supposed to be clamped at the ends. Deflection for first two modes of vibration is calculated by using Rayleigh-Ritz technique and tabulated for various values of plate's parameters i.e. taper constant, aspect ratio, non-homogeneity constants and thermal gradient. Comparison of present findings with existing literature is also provided in tabular and graphical manner.

Numerical solution of acoustic scattering by finite perforated elastic plates

PubMed Central

2016-01-01

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates. PMID:27274685

Numerical solution of acoustic scattering by finite perforated elastic plates.

PubMed

Cavalieri, A V G; Wolf, W R; Jaworski, J W

2016-04-01

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k 0 based on the plate length. However, at low k 0 , finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k 0 . The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k 0 for perforated elastic plates.

A Galerkin approximation for linear elastic shallow shells

NASA Astrophysics Data System (ADS)

Figueiredo, I. N.; Trabucho, L.

1992-03-01

This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

Estimation and Control of Distributed Models for Certain Elastic Systems Arising in Large Space Structures.

DTIC Science & Technology

1987-09-30

igennfy by ""aU numiir,) PIAL GROUP Sue. Go. RCI (Cm, inve o owuera Ineeemerv 4R an~ b-, bloca number) The goal of this research was to study...estimation and control of elastic systems compoited of beams and plates. Specifically, the research con- sidered the problem of lcating the optimal placement...estimation and control of elastic systems com- posed of beams and plates. This general goal has served as a guide for our research over the last several

Elastic wave generated by granular impact on rough and erodible surfaces

NASA Astrophysics Data System (ADS)

Bachelet, Vincent; Mangeney, Anne; de Rosny, Julien; Toussaint, Renaud; Farin, Maxime

2018-01-01

The elastic waves generated by impactors hitting rough and erodible surfaces are studied. For this purpose, beads of variable materials, diameters, and velocities are dropped on (i) a smooth PMMA plate, (ii) stuck glass beads on the PMMA plate to create roughness, and (iii) the rough plate covered with layers of free particles to investigate erodible beds. The Hertz model validity to describe impacts on a smooth surface is confirmed. For rough and erodible surfaces, an empirical scaling law that relates the elastic energy to the radius Rb and normal velocity Vz of the impactor is deduced from experimental data. In addition, the radiated elastic energy is found to decrease exponentially with respect to the bed thickness. Lastly, we show that the variability of the elastic energy among shocks increases from some percents to 70% between smooth and erodible surfaces. This work is a first step to better quantify seismic emissions of rock impacts in natural environment, in particular on unconsolidated soils.

Flexural models of trench/outer rise topography of coronae on Venus with axisymmetric spherical shell elastic plates

NASA Technical Reports Server (NTRS)

Moore, W.; Schubert, Gerald; Sandwell, David T.

1992-01-01

Magellan altimetry has revealed that many coronae on Venus have trenches or moats around their peripheries and rises outboard of the trenches. This trench/outer rise topographic signature is generally associated with the tectonic annulus of the corona. Sandwell and Schubert have interpreted the trench/outer rise topography and the associated tectonic annulus around coronae to be the result of elastic bending of the Venus lithosphere (though the tectonic structures are consequences of inelastic deformation of the lithosphere). They used two-dimensional elastic plate flexure theory to fit topographic profiles across a number of large coronae and inferred elastic lithosphere thicknesses between about 15 and 40 km, similar to inferred values of elastic thickness for the Earth's lithosphere at subduction zones around the Pacific Ocean. Here, we report the results of using axisymmetric elastic flexure theory for the deformation of thin spherical shell plates to interpret the trench/outer rise topography of the large coronae modeled by Sandwell and Schubert and of coronae as small as 250 km in diameter. In the case of a corona only a few hundred kilometers in diameter, the model accounts for the small planform radius of the moat and the nonradial orientation of altimetric traces across the corona. By fitting the flexural topography of coronae we determine the elastic thickness and loading necessary to account for the observed flexure. We calculate the associated bending moment and determine whether the corona interior topographic load can provide the required moment. We also calculate surface stresses and compare the stress distribution with the location of annular tectonic features.

The Modeling of Viscoelastic Circular Plates for Use as Waveguide Absorbers

DTIC Science & Technology

1988-09-01

oncituoe Security Ciasstircation) X THE MODELING OF VISCOELASTIC CIRCULAR PLATES FOR USE AS WAVEGUIDE ABSORBERS C 12 PERSONAL AUTmO ?S) -Hettema...33mvU3dT’U Figure 67. Experimental Jmainiey Part ot the Driving Point Jmpedancs of a 6 in Radius Elastic Plate, With and Without aaker and Mount Conecon, In

Thermoelastic stress in oceanic lithosphere due to hotspot reheating

NASA Technical Reports Server (NTRS)

Zhu, Anning; Wiens, Douglas A.

1991-01-01

The effect of hotspot reheating on the intraplate stress field is investigated by modeling the three-dimensional thermal stress field produced by nonuniform temperature changes in an elastic plate. Temperature perturbations are calculated assuming that the lithosphere is heated by a source in the lower part of the thermal lithosphere. A thermal stress model for the elastic lithosphere is calculated by superposing the stress fields resulting from temperature changes in small individual elements. The stress in an elastic plate resulting from a temperature change in each small element is expressed as an infinite series, wherein each term is a source or an image modified from a closed-from half-space solution. The thermal stress solution is applied to midplate swells in oceanic lithosphere with various thermal structures and plate velocities. The results predict a stress field with a maximum deviatoric stress on the order of 100 MPa covering a broad area around the hotspot plume. The predicted principal stress orientations show a complicated geographical pattern, with horizontal extension perpendicular to the hotspot track at shallow depths and compression along the track near the bottom of the elastic lithosphere.

Mathematical Identification of Influential Parameters on the Elastic Buckling of Variable Geometry Plate

PubMed Central

Tepic, Jovan; Kostelac, Milan

2013-01-01

The problem of elastic stability of plates with square, rectangular, and circular holes as well as slotted holes was discussed. The existence of the hole reduces the deformation energy of the plate and it affects the redistribution of stress flow in comparison to a uniform plate which causes a change of the external operation of compressive forces. The distribution of compressive force is defined as the approximate model of plane state of stress. The significant parameters of elastic stability compared to the uniform plate, including the dominant role of the shape, size, and orientation of the hole were identified. Comparative analysis of the shape of the hole was carried out on the data from the literature, which are based on different approaches and methods. Qualitative and quantitative accordance of the results has been found out and it verifies exposed methodology as applicable in the study of the phenomenon of elastic stability. Sensitivity factor is defined that is proportional to the reciprocal value of the buckling coefficient and it is a measure of sensitivity of plate to the existence of the hole. Mechanism of loss of stability is interpreted through the absorption of the external operation, induced by the shape of the hole. PMID:24453821

North America-Pacific plate boundary, an elastic-plastic megashear - Evidence from very long baseline interferometry

NASA Technical Reports Server (NTRS)

Ward, Steven N.

1988-01-01

Data obtained by Mark III VLBI measurements of radio signals from permanent and mobile VLBI sites for 5.5 years of observations, starting in October 1982, were used to derive a picture of the earth crust deformation near the North America-Pacific plate boundary. The data, which included the vector positions of the VLBI sites and their rate of change, were used for comparison with a number of lithospheric deformation models based upon the concept that the motions of points near the North America-Pacific plate boundary are a linear combination of North America and Pacific velocities. The best of these models were found to fit 95 percent of the variance in 139 VLBI length and transverse velocity observations. Instantaneous shear deformation associated with plate tectonics is apparently developing in a zone 450 km wide paralleling the San Andreas Fault; some of this deformation will be recovered through elastic rebound, while the rest will be permanently set through plastic processes. Because the VLBI data have not been collected for a significant fraction of the earthquake cycle, they cannot discriminate between elastic and plastic behaviors.

Dynamic properties and damping predictions for laminated plates: High order theories - Timoshenko beam

NASA Astrophysics Data System (ADS)

Diveyev, Bohdan; Konyk, Solomija; Crocker, Malcolm J.

2018-01-01

The main aim of this study is to predict the elastic and damping properties of composite laminated plates. This problem has an exact elasticity solution for simple uniform bending and transverse loading conditions. This paper presents a new stress analysis method for the accurate determination of the detailed stress distributions in laminated plates subjected to cylindrical bending. Some approximate methods for the stress state predictions for laminated plates are presented here. The present method is adaptive and does not rely on strong assumptions about the model of the plate. The theoretical model described here incorporates deformations of each sheet of the lamina, which account for the effects of transverse shear deformation, transverse normal strain-stress and nonlinear variation of displacements with respect to the thickness coordinate. Predictions of the dynamic and damping values of laminated plates for various geometrical, mechanical and fastening properties are presented. Comparison with the Timoshenko beam theory is systematically made for analytical and approximation variants.

Determination of the elastic and stiffness characteristics of cross-laminated timber plates from flexural wave velocity measurements

NASA Astrophysics Data System (ADS)

Santoni, Andrea; Schoenwald, Stefan; Van Damme, Bart; Fausti, Patrizio

2017-07-01

Cross-laminated timber (CLT) is an engineered wood with good structural properties and it is also economically competitive with the traditional building construction materials. However, due to its low volume density combined with its high stiffness, it does not provide sufficient sound insulation, thus it is necessary to develop specific acoustic treatments in order to increase the noise reduction performance. The material's mechanical properties are required as input data to perform the vibro-acoustic analyses necessary during the design process. In this paper the elastic constants of a CLT plate are derived by fitting the real component of the experimental flexural wave velocity with Mindlin's dispersion relation for thick plates, neglecting the influence of the plate's size and boundary conditions. Furthermore, its apparent elastic and stiffness properties are derived from the same set of experimental data, for the plate considered to be thin. Under this latter assumption the orthotropic behaviour of an equivalent thin CLT plate is described by using an elliptic model and verified with experimental results.

Hierarchic models for laminated plates. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Actis, Ricardo Luis

1991-01-01

Structural plates and shells are three-dimensional bodies, one dimension of which happens to be much smaller than the other two. Thus, the quality of a plate or shell model must be judged on the basis of how well its exact solution approximates the corresponding three-dimensional problem. Of course, the exact solution depends not only on the choice of the model but also on the topology, material properties, loading and constraints. The desired degree of approximation depends on the analyst's goals in performing the analysis. For these reasons models have to be chosen adaptively. Hierarchic sequences of models make adaptive selection of the model which is best suited for the purposes of a particular analysis possible. The principles governing the formulation of hierarchic models for laminated plates are presented. The essential features of the hierarchic models described models are: (1) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness; and (2) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. The formulation is based on one parameter (beta) which characterizes the hierarchic sequence of models, and a set of constants whose influence was assessed by a numerical sensitivity study. The recommended selection of these constants results in the number of fields increasing by three for each increment in the power of beta. Numerical examples analyzed with the proposed sequence of models are included and good correlation with the reference solutions was found. Results were obtained for laminated strips (plates in cylindrical bending) and for square and rectangular plates with uniform loading and with homogeneous boundary conditions. Cross-ply and angle-ply laminates were evaluated and the results compared with those of MSC/PROBE. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity.

Complete volumetric decomposition of individual trabecular plates and rods and its morphological correlations with anisotropic elastic moduli in human trabecular bone.

PubMed

Liu, X Sherry; Sajda, Paul; Saha, Punam K; Wehrli, Felix W; Bevill, Grant; Keaveny, Tony M; Guo, X Edward

2008-02-01

Trabecular plates and rods are important microarchitectural features in determining mechanical properties of trabecular bone. A complete volumetric decomposition of individual trabecular plates and rods was used to assess the orientation and morphology of 71 human trabecular bone samples. The ITS-based morphological analyses better characterize microarchitecture and help predict anisotropic mechanical properties of trabecular bone. Standard morphological analyses of trabecular architecture lack explicit segmentations of individual trabecular plates and rods. In this study, a complete volumetric decomposition technique was developed to segment trabecular bone microstructure into individual plates and rods. Contributions of trabecular type-associated morphological parameters to the anisotropic elastic moduli of trabecular bone were studied. Seventy-one human trabecular bone samples from the femoral neck (FN), tibia, and vertebral body (VB) were imaged using muCT or serial milling. Complete volumetric decomposition was applied to segment trabecular bone microstructure into individual plates and rods. The orientation of each individual trabecula was determined, and the axial bone volume fractions (aBV/TV), axially aligned bone volume fraction along each orthotropic axis, were correlated with the elastic moduli. The microstructural type-associated morphological parameters were derived and compared with standard morphological parameters. Their contributions to the anisotropic elastic moduli, calculated by finite element analysis (FEA), were evaluated and compared. The distribution of trabecular orientation suggested that longitudinal plates and transverse rods dominate at all three anatomic sites. aBV/TV along each axis, in general, showed a better correlation with the axial elastic modulus (r(2) = 0.95 approximately 0.99) compared with BV/TV (r(2) = 0.93 approximately 0.94). The plate-associated morphological parameters generally showed higher correlations with the corresponding standard morphological parameters than the rod-associated parameters. Multiple linear regression models of six elastic moduli with individual trabeculae segmentation (ITS)-based morphological parameters (adjusted r(2) = 0.95 approximately 0.98) performed equally well as those with standard morphological parameters (adjusted r(2) = 0.94 approximately 0.97) but revealed specific contributions from individual trabecular plates or rods. The ITS-based morphological analyses provide a better characterization of the morphology and trabecular orientation of trabecular bone. The axial loading of trabecular bone is mainly sustained by the axially aligned trabecular bone volume. Results suggest that trabecular plates dominate the overall elastic properties of trabecular bone.

Dislocation models of interseismic deformation in the western United States

USGS Publications Warehouse

Pollitz, F.F.; McCrory, P.; Svarc, J.; Murray, J.

2008-01-01

The GPS-derived crustal velocity field of the western United States is used to construct dislocation models in a viscoelastic medium of interseismic crustal deformation. The interseismic velocity field is constrained by 1052 GPS velocity vectors spanning the ???2500-km-long plate boundary zone adjacent to the San Andreas fault and Cascadia subduction zone and extending ???1000 km into the plate interior. The GPS data set is compiled from U.S. Geological Survey campaign data, Plate Boundary Observatory data, and the Western U.S. Cordillera velocity field of Bennett et al. (1999). In the context of viscoelastic cycle models of postearthquake deformation, the interseismic velocity field is modeled with a combination of earthquake sources on ???100 known faults plus broadly distributed sources. Models that best explain the observed interseismic velocity field include the contributions of viscoelastic relaxation from faulting near the major plate margins, viscoelastic relaxation from distributed faulting in the plate interior, as well as lateral variations in depth-averaged rigidity in the elastic lithosphere. Resulting rigidity variations are consistent with reduced effective elastic plate thickness in a zone a few tens of kilometers wide surrounding the San Andreas fault (SAF) system. Primary deformation characteristics are captured along the entire SAF system, Eastern California Shear Zone, Walker Lane, the Mendocino triple junction, the Cascadia margin, and the plate interior up to ???1000 km from the major plate boundaries.

State of stress, faulting, and eruption characteristics of large volcanoes on Mars

NASA Technical Reports Server (NTRS)

Mcgovern, Patrick J.; Solomon, Sean C.

1993-01-01

The formation of a large volcano loads the underlying lithospheric plate and can lead to lithospheric flexure and faulting. In turn, lithospheric stresses affect the stress field beneath and within the volcanic edifice and can influence magma transport. Modeling the interaction of these processes is crucial to an understanding of the history of eruption characteristics and tectonic deformation of large volcanoes. We develop models of time-dependent stress and deformation of the Tharsis volcanoes on Mars. A finite element code is used that simulates viscoelastic flow in the mantle and elastic plate flexural behavior. We calculate stresses and displacements due to a volcano-shaped load emplaced on an elastic plate. Models variously incorporate growth of the volcanic load with time and a detachment between volcano and lithosphere. The models illustrate the manner in which time-dependent stresses induced by lithospheric plate flexure beneath the volcanic load may affect eruption histories, and the derived stress fields can be related to tectonic features on and surrounding martian volcanoes.

A rheological model for immersed corrugated elastic plates.

PubMed

Meier, D; Franklin, H; Predoi, M V; Rousseau, M; Izbicki, J L

2017-03-01

The influence of surface imperfections on the propagation of guided waves in an immersed elastic plate can be interpreted by means of a rheological model. The corrugated surface is modeled by a very thin interface, similar to a Jones spring model, which replaces the continuity boundary conditions at the liquid - corrugated solid-plate interface. As the surrounding liquid is considered to be perfect, only one complex stiffness is used for the model of Jones. The selection of the plate guided mode and the test frequency are motivated by the detectability and non-interference with other modes. The spring stiffness is obtained by a best fit procedure, between the analytical solution and the results obtained by the finite elements method (FEM). One way ensuring the agreement of the two approaches, rheological and FEM, is to consider angular resonances provided by the transmission coefficients. Small changes in the parameters of the roughness keep the positions of the angular resonances of the plate practically unchanged, while at the same time large variations of the half width of the transmission coefficient curve is observed. The effect of corrugation parameters on the guided modes in the plate can be predicted by using the rheological model with the deduced spring complex stiffness. Copyright © 2016. Published by Elsevier B.V.

On the the Contact Lens Problem: Modeling Rigid and Elastic Beams on Thin Films

NASA Astrophysics Data System (ADS)

Trinh, Philippe; Wilson, Stephen; Stone, Howard

2011-11-01

Generally, contact lenses are prescribed by the practitioner to fit each individual patient's eye, but these fitting-philosophies are based on empirical studies and a certain degree of trial-and-error. A badly fitted lens can cause a range of afflictions, which varies from mild dry-eye-discomfort, to more serious corneal diseases. Thus, at this heart of this problem, is the question of how a rigid or elastic plate interacts with the free-surface of a thin viscous film. In this talk, we present several mathematical models for the study of these plate-and-fluid problems. Asymptotic and numerical results are described, and we explain the role of elasticity, surface tension, viscosity, and pressure in determining the equilibrium solutions. Finally, we discuss the implications of our work on the contact lens problem, as well as on other coating processes which involve elastic substrates.

Elastic guided waves in a layered plate with rectangular cross section.

PubMed

Mukdadi, O M; Desai, Y M; Datta, S K; Shah, A H; Niklasson, A J

2002-11-01

Guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) has been studied in this paper. A semianalytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the length of the plate has been used. The method is applicable to arbitrary number of layers and general anisotropic material properties of each layer, and is similar to the stiffness method used earlier to study guided waves in a laminated composite plate of infinite width. Numerical results showing the effect of varying the width of the plate on the dispersion of guided waves are presented and are compared with those for an infinite plate. In addition, effect of thin anisotropic coating or interface layers on the guided waves is investigated.

Effective elastic thicknesses of the lithosphere and mechanisms of isostatic compensation in Australia

NASA Technical Reports Server (NTRS)

Zuber, Maria T.; Bechtel, Timothy D.; Forsyth, Donald W.

1989-01-01

The isostatic compensation of Australia is investigated using an isostatic model for the Australian lithosphere that assumes regional compensation of an elastic plate which undergoes flexure in response to surface and subsurface loading. Using the coherence between Bouguer gravity and topography and two separate gravity/topography data sets, it was found that, for the continent as a whole, loads with wavelengths above 1500 km are locally compensated. Loads with wavelengths in the range 600-1500 km are partially supported by regional stresses, and loads with wavelengths less than 600 km are almost entirely supported by the strength of the lithosphere. It was found that the predicted coherence for a flexural model of a continuous elastic plate does not provide a good fit to the observed coherence of central Australia. The disagreement between model and observations is explained.

Design of a thin-plate based tunable high-quality narrow passband filter for elastic transverse waves propagate in metals

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L. H.; Hu, C. L.; Yan, W. S.; Pennec, Yan; Hu, N.

2018-03-01

For the elastic SV (transverse) waves in metals, a high-quality narrow passband filter that consists of aligned parallel thin plates with small gaps is designed. In order to obtain a good performance, the thin plates should be constituted by materials with a smaller mass density and Young's modulus, such as polymethylmethacrylate (PMMA), compared to the embedded materials in which the elastic SV waves propagate. Both the theoretical model and the full numerical simulation show that the transmission spectrum of the designed filter demonstrates several peaks with flawless transmission within 0 KHz ˜20 KHz frequency range. The peaks can be readily tuned by manipulating the geometrical parameters of the plates. Therefore, the current design works well for both low and high frequencies with a controllable size. Even for low frequencies on the order of kilohertz, the size of this filter can be still limited to the order of centimeters, which significantly benefits the real applications. The investigation also finds that the same filter is valid when using different metals and the reason behind this is explained theoretically. Additionally, the effect of bonding conditions of interfaces between thin plates and the base material is investigated using a spring model.

An Experimental Study of Incremental Surface Loading of an Elastic Plate: Application to Volcano Tectonics

NASA Technical Reports Server (NTRS)

Williams, K. K.; Zuber, M. T.

1995-01-01

Models of surface fractures due to volcanic loading an elastic plate are commonly used to constrain thickness of planetary lithospheres, but discrepancies exist in predictions of the style of initial failure and in the nature of subsequent fracture evolution. In this study, we perform an experiment to determine the mode of initial failure due to the incremental addition of a conical load to the surface of an elastic plate and compare the location of initial failure with that predicted by elastic theory. In all experiments, the mode of initial failure was tension cracking at the surface of the plate, with cracks oriented circumferential to the load. The cracks nucleated at a distance from load center that corresponds the maximum radial stress predicted by analytical solutions, so a tensile failure criterion is appropriate for predictions of initial failure. With continued loading of the plate, migration of tensional cracks was observed. In the same azimuthal direction as the initial crack, subsequent cracks formed at a smaller radial distance than the initial crack. When forming in a different azimuthal direction, the subsequent cracks formed at a distance greater than the radial distance of the initial crack. The observed fracture pattern may explain the distribution of extensional structures in annular bands around many large scale, circular volcanic features.

On the determination of stress fields and displacements in a thin elastoplastic plate containing elastic inclusion - a shim

NASA Astrophysics Data System (ADS)

Kovalev, A. V.; Rusina, E. Y.; Yakovlev, A. Y.

2018-03-01

The paper is devoted to the determination of the stress-strain state of a mechanical structure, which consists of a thin infinite elastoplastic plate with a hole and a continuous fine elastic inclusion. The complexity of this problem lies in the fact that the shape of the boundary between the elastic and plastic zones in the plate is not known in advance. The small parameter method is used as the solution method, while the small parameter characterizes the deviation of the shape of the contour from the circle and the perturbation of external static boundary conditions. As the zero solution, the axisymmetric elastoplastic state of the plate with inclusion is chosen. Two variants of inclusion fixation in a plate are considered: inclusion is enclosed with tension or soldered. As a result of solving the problem within the framework of ideal plasticity, the distribution of the stress and displacement fields and the shape of the elastoplastic boundary are obtained. To illustrate the case of a plane-stressed state, the results of a numerical experiment on the mathematical model obtained are presented.

Inelastic models of lithospheric stress - I. Theory and application to outer-rise plate deformation

USGS Publications Warehouse

Mueller, S.; Choy, G.L.; Spence, W.

1996-01-01

Outer-rise stress distributions determined in the manner that mechanical engineers evaluate inelastic stress distributions within conventional materials are contrasted with those predicted using simple elastic-plate models that are frequently encountered in studies of outer-rise seismicity. This comparison indicates that the latter are inherently inappropriate for studies of intraplate earthquakes, which are a direct manifestation of lithospheric inelasticity. We demonstrate that the common practice of truncating elastically superimposed stress profiles so that they are not permitted to exceed laboratory-based estimates of lithospheric yield strength will result in an accurate characterization of lithospheric stress only under relatively restrictive circumstances. In contrast to elastic-plate models, which predict that lithospheric stress distributions depend exclusively upon the current load, inelastic plate models predict that stress distributions are also significantly influenced by the plate-loading history, and, in many cases, this influence is the dominant factor in determining the style of potential seismicity (e.g. thrust versus normal faulting). Numerous 'intuitive' interpretations of outer-rise earthquakes have been founded upon the implicit assumption that a unique relationship exists between a specified combination of plate curvature and in-plane force, and the resulting lithospheric stress distribution. We demonstrate that the profound influence of deformation history often invalidates such interpretations. Finally, we examine the reliability of 'yield envelope' representations of lithospheric strength that are constructed on the basis of empirically determined frictional sliding relationships and silicate plastic-flow laws. Although representations of this nature underestimate the strength of some major interplate faults, such as the San Andreas, they appear to represent a reliable characterization of the strength of intraplate oceanic lithosphere.

Acoustic Models of Optical Mirrors

ERIC Educational Resources Information Center

Mayer, V. V.; Varaksina, E. I.

2014-01-01

Students form a more exact idea of the action of optical mirrors if they can observe the wave field being formed during reflection. For this purpose it is possible to organize model experiments with flexural waves propagating in thin elastic plates. The direct and round edges of the plates are used as models of plane, convex and concave mirrors.…

An elastic-plastic fracture mechanics analysis of weld-toe surface cracks in fillet welded T-butt joint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, B.

1994-12-31

This paper describes an elastic-plastic fracture mechanics (EPFM) study of shallow weld-toe cracks. Two limiting crack configurations, plane strain edge crack and semi-circular surface crack in fillet welded T-butt plate joint, were analyzed using the finite element method. Crack depth ranging from 2 to 40% of plate thickness were considered. The elastic-plastic analysis, assuming power-law hardening relationship and Mises yield criterion, was based on incremental plasticity theory. Tension and bending loads applied were monotonically increased to a level causing relatively large scale yielding at the crack tip. Effects of weld-notch geometry and ductile material modeling on prediction of fracture mechanicsmore » characterizing parameter were assessed. It was found that the weld-notch effect reduces and the effect of material modeling increases as crack depth increases. Material modeling is less important than geometric modeling in analysis of very shallow cracks but is more important for relatively deeper cracks, e.g. crack depth more than 20% of thickness. The effect of material modeling can be assessed using a simplified structural model. Weld magnification factors derived assuming linear elastic conditions can be applied to EPFM characterization.« less

Complete Volumetric Decomposition of Individual Trabecular Plates and Rods and Its Morphological Correlations With Anisotropic Elastic Moduli in Human Trabecular Bone

PubMed Central

Liu, X Sherry; Sajda, Paul; Saha, Punam K; Wehrli, Felix W; Bevill, Grant; Keaveny, Tony M; Guo, X Edward

2008-01-01

Trabecular plates and rods are important microarchitectural features in determining mechanical properties of trabecular bone. A complete volumetric decomposition of individual trabecular plates and rods was used to assess the orientation and morphology of 71 human trabecular bone samples. The ITS-based morphological analyses better characterize microarchitecture and help predict anisotropic mechanical properties of trabecular bone. Introduction Standard morphological analyses of trabecular architecture lack explicit segmentations of individual trabecular plates and rods. In this study, a complete volumetric decomposition technique was developed to segment trabecular bone microstructure into individual plates and rods. Contributions of trabecular type–associated morphological parameters to the anisotropic elastic moduli of trabecular bone were studied. Materials and Methods Seventy-one human trabecular bone samples from the femoral neck (FN), tibia, and vertebral body (VB) were imaged using μCT or serial milling. Complete volumetric decomposition was applied to segment trabecular bone microstructure into individual plates and rods. The orientation of each individual trabecula was determined, and the axial bone volume fractions (aBV/TV), axially aligned bone volume fraction along each orthotropic axis, were correlated with the elastic moduli. The microstructural type–associated morphological parameters were derived and compared with standard morphological parameters. Their contributions to the anisotropic elastic moduli, calculated by finite element analysis (FEA), were evaluated and compared. Results The distribution of trabecular orientation suggested that longitudinal plates and transverse rods dominate at all three anatomic sites. aBV/TV along each axis, in general, showed a better correlation with the axial elastic modulus (r 2 = 0.95∼0.99) compared with BV/TV (r 2 = 0.93∼0.94). The plate-associated morphological parameters generally showed higher correlations with the corresponding standard morphological parameters than the rod-associated parameters. Multiple linear regression models of six elastic moduli with individual trabeculae segmentation (ITS)-based morphological parameters (adjusted r 2 = 0.95∼0.98) performed equally well as those with standard morphological parameters (adjusted r 2 = 0.94∼0.97) but revealed specific contributions from individual trabecular plates or rods. Conclusions The ITS-based morphological analyses provide a better characterization of the morphology and trabecular orientation of trabecular bone. The axial loading of trabecular bone is mainly sustained by the axially aligned trabecular bone volume. Results suggest that trabecular plates dominate the overall elastic properties of trabecular bone. PMID:17907921

An elastic failure model of indentation damage. [of brittle structural ceramics

NASA Technical Reports Server (NTRS)

Liaw, B. M.; Kobayashi, A. S.; Emery, A. F.

1984-01-01

A mechanistically consistent model for indentation damage based on elastic failure at tensile or shear overloads, is proposed. The model accommodates arbitrary crack orientation, stress relaxation, reduction and recovery of stiffness due to crack opening and closure, and interfacial friction due to backward sliding of closed cracks. This elastic failure model was implemented by an axisymmetric finite element program which was used to simulate progressive damage in a silicon nitride plate indented by a tungsten carbide sphere. The predicted damage patterns and the permanent impression matched those observed experimentally. The validation of this elastic failure model shows that the plastic deformation postulated by others is not necessary to replicate the indentation damage of brittle structural ceramics.

Simulating wave-turbulence on thin elastic plates with arbitrary boundary conditions

NASA Astrophysics Data System (ADS)

van Rees, Wim M.; Mahadevan, L.

2016-11-01

The statistical characteristics of interacting waves are described by the theory of wave turbulence, with the study of deep water gravity wave turbulence serving as a paradigmatic physical example. Here we consider the elastic analog of this problem in the context of flexural waves arising from vibrations of a thin elastic plate. Such flexural waves generate the unique sounds of so-called thunder machines used in orchestras - thin metal plates that make a thunder-like sound when forcefully shaken. Wave turbulence in elastic plates is typically investigated numerically using spectral simulations with periodic boundary conditions, which are not very realistic. We will present the results of numerical simulations of the dynamics of thin elastic plates in physical space, with arbitrary shapes, boundary conditions, anisotropy and inhomogeneity, and show first results on wave turbulence beyond the conventionally studied rectangular plates. Finally, motivated by a possible method to measure ice-sheet thicknesses in the open ocean, we will further discuss the behavior of a vibrating plate when floating on an inviscid fluid.

Deformation of island-arc lithosphere due to steady plate subduction

NASA Astrophysics Data System (ADS)

Fukahata, Yukitoshi; Matsu'ura, Mitsuhiro

2016-02-01

Steady plate subduction elastically brings about permanent lithospheric deformation in island arcs, though this effect has been neglected in most studies based on elastic dislocation theory. We investigate the characteristics of the permanent lithospheric deformation using a kinematic model, in which steady slip motion is given along a plate interface in the elastic lithosphere overlying the viscoelastic asthenosphere under gravity. As a rule of thumb, long-term lithospheric deformation can be understood as a bending of an elastic plate floating on non-viscous fluid, because the asthenosphere behaves like water on the long term. The steady slip below the lithosphere-asthenosphere boundary does not contribute to long-term lithospheric deformation. Hence, the key parameters that control the lithospheric deformation are only the thickness of the lithosphere and the geometry of the plate interface. Slip on a plate interface generally causes substantial vertical displacement, and gravity always tries to retrieve the original gravitational equilibrium. For a curved plate interface gravity causes convex upward bending of the island-arc lithosphere, while for a planar plate interface gravity causes convex downward bending. Larger curvature and thicker lithosphere generally results in larger deformation. When the curvature changes along the plate interface, internal deformation is also involved intrinsically, which modifies the deformation field due to gravity. Because the plate interface generally has some curvature, at least near the trench, convex upward bending of the island-arc lithosphere, which involves uplift of island-arc and subsidence around the trench, is always realized. On the other hand, the deformation field of the island-arc lithosphere sensitively depends on lithospheric thickness and plate interface geometry. These characteristics obtained by the numerical simulation are consistent with observed topography and free-air gravity anomalies in subduction zones: a pair of topography and gravity anomalies, high in the arc and low around the trench, is observed without exceptions all over the world, while there are large variety in the amplitude and horizontal scale of the topography and gravity anomalies.

Elastic-plastic analysis of annular plate problems using NASTRAN

NASA Technical Reports Server (NTRS)

Chen, P. C. T.

1983-01-01

The plate elements of the NASTRAN code are used to analyze two annular plate problems loaded beyond the elastic limit. The first problem is an elastic-plastic annular plate loaded externally by two concentrated forces. The second problem is stressed radially by uniform internal pressure for which an exact analytical solution is available. A comparison of the two approaches together with an assessment of the NASTRAN code is given.

Numerical study of the stress-strain state of reinforced plate on an elastic foundation by the Bubnov-Galerkin method

NASA Astrophysics Data System (ADS)

Beskopylny, Alexey; Kadomtseva, Elena; Strelnikov, Grigory

2017-10-01

The stress-strain state of a rectangular slab resting on an elastic foundation is considered. The slab material is isotropic. The slab has stiffening ribs that directed parallel to both sides of the plate. Solving equations are obtained for determining the deflection for various mechanical and geometric characteristics of the stiffening ribs which are parallel to different sides of the plate, having different rigidity for bending and torsion. The calculation scheme assumes an orthotropic slab having different cylindrical stiffness in two mutually perpendicular directions parallel to the reinforcing ribs. An elastic foundation is adopted by Winkler model. To determine the deflection the Bubnov-Galerkin method is used. The deflection is taken in the form of an expansion in a series with unknown coefficients by special polynomials, which are a combination of Legendre polynomials.

Investigation of free vibration characteristics for skew multiphase magneto-electro-elastic plate

NASA Astrophysics Data System (ADS)

Kiran, M. C.; Kattimani, S.

2018-04-01

This article presents the investigation of skew multiphase magneto-electro-elastic (MMEE) plate to assess its free vibration characteristics. A finite element (FE) model is formulated considering the different couplings involved via coupled constitutive equations. The transformation matrices are derived to transform local degrees of freedom into the global degrees of freedom for the nodes lying on the skew edges. Effect of different volume fraction (Vf) on the free vibration behavior is explicitly studied. In addition, influence of width to thickness ratio, the aspect ratio, and the stacking arrangement on natural frequencies of skew multiphase MEE plate investigated. Particular attention has been paid to investigate the effect of skew angle on the non-dimensional Eigen frequencies of multiphase MEE plate with simply supported edges.

Investigation on the effect of MR elastomer based adaptive vibration absorbers on the radiated sound from circular elastic plates

NASA Astrophysics Data System (ADS)

Hemmatian, M.; Sedaghati, R.

2016-04-01

This study aims to investigate the effect of using magnetorheological elastomer (MRE)-based adaptive tuned vibration absorbers (ATVA) on the sound transmission in an elastic plate. Sound transmission loss (STL) of an elastic circular thin plate is analytically studied. The plate is excited by a plane acoustic wave as an incident sound and the displacement of the plate is calculated using corresponding mode shapes of the system for clamped boundary condition. Rayleigh integral approach is used to express the transmitted sound pressure in terms of the plate's displacement modal amplitude. In order to increase sound transmission loss of the plate, the MRE-based ATVA is considered. The basic idea is to be able to change the stiffness of the ATVA by varying magnetic field in order to reduce the transmitted acoustic energy of the host structure in a wide frequency range. Here, a MRE-based ATVA under the shear mode consisting of an oscillator mass, magnetic conductor, coils and MRE is investigated. In order to predict the viscoelastic characteristics of the field-dependent MRE based on the applied magnetic field, the double pole model is used. Finally, MRE-based ATVAs are integrated with the plate to absorb the plate energy with the aim of decreasing the transmitted sound power. Results show that plate with integrated MRE-based ATVAs suppresses the axisymmetric vibration of the plate and thus considerably improves the STL. Parametric studies on the influence of the position of MRE-based ATVAs and the effects of applied current on their performance are also presented.

Focusing, refraction, and asymmetric transmission of elastic waves in solid metamaterials with aligned parallel gaps.

PubMed

Su, Xiaoshi; Norris, Andrew N

2016-06-01

Gradient index (GRIN), refractive, and asymmetric transmission devices for elastic waves are designed using a solid with aligned parallel gaps. The gaps are assumed to be thin so that they can be considered as parallel cracks separating elastic plate waveguides. The plates do not interact with one another directly, only at their ends where they connect to the exterior solid. To formulate the transmission and reflection coefficients for SV- and P-waves, an analytical model is established using thin plate theory that couples the waveguide modes with the waves in the exterior body. The GRIN lens is designed by varying the thickness of the plates to achieve different flexural wave speeds. The refractive effect of SV-waves is achieved by designing the slope of the edge of the plate array, and keeping the ratio between plate length and flexural wavelength fixed. The asymmetric transmission of P-waves is achieved by sending an incident P-wave at a critical angle, at which total conversion to SV-wave occurs. An array of parallel gaps perpendicular to the propagation direction of the reflected waves stop the SV-wave but let P-waves travel through. Examples of focusing, steering, and asymmetric transmission devices are discussed.

Analytical Round Robin for Elastic-Plastic Analysis of Surface Cracked Plates: Phase I Results

NASA Technical Reports Server (NTRS)

Wells, D. N.; Allen, P. A.

2012-01-01

An analytical round robin for the elastic-plastic analysis of surface cracks in flat plates was conducted with 15 participants. Experimental results from a surface crack tension test in 2219-T8 aluminum plate provided the basis for the inter-laboratory study (ILS). The study proceeded in a blind fashion given that the analysis methodology was not specified to the participants, and key experimental results were withheld. This approach allowed the ILS to serve as a current measure of the state of the art for elastic-plastic fracture mechanics analysis. The analytical results and the associated methodologies were collected for comparison, and sources of variability were studied and isolated. The results of the study revealed that the J-integral analysis methodology using the domain integral method is robust, providing reliable J-integral values without being overly sensitive to modeling details. General modeling choices such as analysis code, model size (mesh density), crack tip meshing, or boundary conditions, were not found to be sources of significant variability. For analyses controlled only by far-field boundary conditions, the greatest source of variability in the J-integral assessment is introduced through the constitutive model. This variability can be substantially reduced by using crack mouth opening displacements to anchor the assessment. Conclusions provide recommendations for analysis standardization.

The effects of pin elasticity, clearance, and friction on the stresses in a pin-loaded orthotropic plate

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Klang, E. C.; Cooper, D. E.

1987-01-01

The effects of pin elasticity, clearance, and friction on the stresses in a pin loaded orthotropic plate are studied. The effects are studied by posing the problem as a planar contact elasticity problem, the pin and the plate being two elastic bodies which interact through contact. Coulomb friction is assumed, the pin loads the plate in one of its principal material directions, and the plate is infinite in extent. A collocation scheme and interaction, in conjunction with a complex variable series solution, are used to obtain numerical results. The contact region between the plate and pin is unknown and must be solved for as part of the solution. The same is true of the region of friction induced no slip. Two pin stiffnesses, two clearance levels, two friction levels and two laminates, a (0/+ or - 45/90)s and a (02/+ or - 45)s, are studied. The effects of pin elasticity, clearance, and friction on the load capacity of the plate are assessed by comparing the load capacity of the plate with the capacity when the pin is rigid, perfectly fitting, and frictionless.

Formation of Island Arc-Trench System due to Plate Subduction on the Basis of Elastic Dislocation Theory

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Matsu'ura, M.

2015-12-01

The most conspicuous cumulative deformation in subduction zones is the formation of island arc-trench system. A pair of anomalies in topography and free-air gravity, high in the arc and low around the trench, is observed without exceptions all over the world. Since the 1960s, elastic dislocation theory has been widely used to interpret coseismic crustal deformation. For the modeling of longer-term crustal deformation, it is necessary to consider viscoelastic properties of the asthenosphere. By simply applying elastic-viscoelastic dislocation theory to plate subduction, Matsu'ura and Sato (1989, GJI) have shown that some crustal deformation remains after the completion of one earthquake cycle, which means that crustal deformation accumulates with time in a long term due to plate subduction. In fact, by constructing a plate interface model in and around Japan, Hashimoto, Fukui and Matsu'ura (2004, PAGEOPH) have demonstrated that the computed vertical displacements due to steady plate subduction well explain the observed free-air gravity anomaly pattern. Recently, we got a lucid explanation of crustal deformation due to plate subduction. In subduction zones, oceanic plates bend and descend into the mantle. Because the bending of oceanic plates is usually not spontaneous, there exists kinematic interaction between the oceanic and overriding plates, which causes cumulative deformation of the overriding plate. This may be understood based on the law of action and reaction: one is bending of an oceanic plate and the other is deformation of the overriding plate. As a special case, it is useful to consider plate subduction along a part of true circle. In this case, crustal deformation due to steady subduction is solely caused by the effect of gravity, because dislocation along a circle does not cause any intrinsic internal deformation. When an oceanic plate is descending along an arcuate plate interface from the right-hand side, according to dislocation theory, the oceanic plate rotates anti-clockwise and the overriding plate rotates clockwise. The gravity, however, requires both plates at a distance from the trench to remain in the original gravitational equilibrium, which results in upward bending of both plates. As subduction proceeds, the deformation of the upward bending accumulates with time.

A Finite Element Model to Predict the Effect of Porosity on Elastic Modulus in Low-Porosity Materials

NASA Astrophysics Data System (ADS)

Morrissey, Liam S.; Nakhla, Sam

2018-07-01

The effect of porosity on elastic modulus in low-porosity materials is investigated. First, several models used to predict the reduction in elastic modulus due to porosity are compared with a compilation of experimental data to determine their ranges of validity and accuracy. The overlapping solid spheres model is found to be most accurate with the experimental data and valid between 3 and 10 pct porosity. Next, a FEM is developed with the objective of demonstrating that a macroscale plate with a center hole can be used to model the effect of microscale porosity on elastic modulus. The FEM agrees best with the overlapping solid spheres model and shows higher accuracy with experimental data than the overlapping solid spheres model.

Hybridization bandgap induced by an electrical resonance in piezoelectric metamaterial plates

NASA Astrophysics Data System (ADS)

Kherraz, N.; Haumesser, L.; Levassort, F.; Benard, P.; Morvan, B.

2018-03-01

We demonstrate numerically and experimentally the opening of a locally resonant bandgap in an active phononic crystal (PC) made of a homogeneous piezoelectric plate covered by a 1D periodic array of thin electrodes connected to inductive shunts. The application of periodic electrical boundary conditions (EBCs) enables an at will tailoring of the dispersion properties of the PC plate, thus leading to a control of the dispersion of the propagating guided elastic waves in the plate. Depending on the nature of the EBCs, several bandgaps open up, the most important being a Hybridization Bandgap (HBG) in the subwavelength regime. The PC behaves as a locally resonant metamaterial. The HBG originates from the interaction of propagating elastic waves (Lamb modes) with an electrical resonant mode whose dispersion can be effectively described through an equivalent transmission line model.

Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

Modeling and simulation of thermally actuated bilayer plates

NASA Astrophysics Data System (ADS)

Bartels, Sören; Bonito, Andrea; Muliana, Anastasia H.; Nochetto, Ricardo H.

2018-02-01

We present a mathematical model of polymer bilayers that undergo large bending deformations when actuated by non-mechanical stimuli such as thermal effects. The simple model captures a large class of nonlinear bending effects and can be discretized with standard plate elements. We devise a fully practical iterative scheme and apply it to the simulation of folding of several practically useful compliant structures comprising of thin elastic layers.

Modeling of composite beams and plates for static and dynamic analysis

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.

1992-01-01

A rigorous theory and the corresponding computational algorithms were developed for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants of a plate. Additionally, the analysis is used to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. It was decided that the variational-asymptotical method (VAM) would serve as a suitable framework in which to solve these types of problems. Work during this reporting period has progressed along two lines: (1) further evaluation of neo-classical plate theory (NCPT) as applied to shear-coupled laminates; and (2) continued modeling of plates with nonuniform thickness.

Numerical modeling of intraplate seismicity with a deformable loading plate

NASA Astrophysics Data System (ADS)

So, B. D.; Capitanio, F. A.

2017-12-01

We use finite element modeling to investigate on the stress loading-unloading cycles and earthquakes occurrence in the plate interiors, resulting from the interactions of tectonic plates along their boundary. We model a visco-elasto-plastic plate embedding a single or multiple faults, while the tectonic stress is applied along the plate boundary by an external loading visco-elastic plate, reproducing the tectonic setting of two interacting lithospheres. Because the two plates deform viscously, the timescale of stress accumulation and release on the faults is self-consistently determined, from the boundary to the interiors, and seismic recurrence is an emerging feature. This approach overcomes the constraints on recurrence period imposed by stress (stress-drop) and velocity boundary conditions, while here it is unconstrained. We illustrate emerging macroscopic characteristics of this system, showing that the seismic recurrence period τ becomes shorter as Γ and Θ decreases, where Γ = ηI/ηL the viscosity ratio of the viscosities of the internal fault-embedded to external loading plates, respectively, and Θ = σY/σL the stress ratio of the elastic limit of the fault to far-field loading stress. When the system embeds multiple, randomly distributed faults, stress transfer results in recurrence period deviations, however the time-averaged recurrence period of each fault show the same dependence on Γ and Θ, illustrating a characteristic collective behavior. The control of these parameters prevails even when initial pre-stress was randomly assigned in terms of the spatial arrangement and orientation on the internal plate, mimicking local fluctuations. Our study shows the relevance of macroscopic rheological properties of tectonic plates on the earthquake occurrence in plate interiors, as opposed to local factors, proposing a viable model for the seismic behavior of continent interiors in the context of large-scale, long-term deformation of interacting tectonic plates.

Nonclassical models of the theory of plates and shells

NASA Astrophysics Data System (ADS)

Annin, Boris D.; Volchkov, Yuri M.

2017-11-01

Publications dealing with the study of methods of reducing a three-dimensional problem of the elasticity theory to a two-dimensional problem of the theory of plates and shells are reviewed. Two approaches are considered: the use of kinematic and force hypotheses and expansion of solutions of the three-dimensional elasticity theory in terms of the complete system of functions. Papers where a three-dimensional problem is reduced to a two-dimensional problem with the use of several approximations of each of the unknown functions (stresses and displacements) by segments of the Legendre polynomials are also reviewed.

Stress and strain relaxation in magnesium AZ31 rolled plate: In-situ neutron measurement and elastic viscoplastic polycrystal modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Huamiao; Clausen, Bjorn; Capolungo, Laurent

Continuous mechanical tests with strain holds (stress relaxation) and with stress holds (strain relaxation) are performed simultaneously with in-situ neutron measurements to analyze the mechanisms of stress and strain relaxation in Mg AZ31 rolled plate. A dislocation activity based constitutive model, accounting for internal stress statistical distributions, is proposed and implemented into an elastic viscoplastic self-consistent (EVPSC) framework to simultaneously describe both stress and strain relaxation. The model captures the experimental data in terms of macroscopic stress strain curves, evolution of stress and strain during holding, as well as evolution of the internal elastic strains. Model results indicate that themore » magnitude of the stress relaxed during strain holding is dependent on both, the magnitude of the flow stress and the spread of the resolved shear stress distribution. The magnitude of strain accumulated during stress holding is, on the other hand, dependent on the magnitude of the hardening rate and on the spread of the resolved shear stress distribution. Furthermore, the internal elastic strains are directly correlated with the stress state, and hence the stress relaxation during strain holds has a greater influence on the lattice strains than strain relaxation during stress holds.« less

Stress and strain relaxation in magnesium AZ31 rolled plate: In-situ neutron measurement and elastic viscoplastic polycrystal modeling

DOE PAGES

Wang, Huamiao; Clausen, Bjorn; Capolungo, Laurent; ...

2015-07-16

Continuous mechanical tests with strain holds (stress relaxation) and with stress holds (strain relaxation) are performed simultaneously with in-situ neutron measurements to analyze the mechanisms of stress and strain relaxation in Mg AZ31 rolled plate. A dislocation activity based constitutive model, accounting for internal stress statistical distributions, is proposed and implemented into an elastic viscoplastic self-consistent (EVPSC) framework to simultaneously describe both stress and strain relaxation. The model captures the experimental data in terms of macroscopic stress strain curves, evolution of stress and strain during holding, as well as evolution of the internal elastic strains. Model results indicate that themore » magnitude of the stress relaxed during strain holding is dependent on both, the magnitude of the flow stress and the spread of the resolved shear stress distribution. The magnitude of strain accumulated during stress holding is, on the other hand, dependent on the magnitude of the hardening rate and on the spread of the resolved shear stress distribution. Furthermore, the internal elastic strains are directly correlated with the stress state, and hence the stress relaxation during strain holds has a greater influence on the lattice strains than strain relaxation during stress holds.« less

Magneto-thermo-elastokinetics of geometrically nonlinear laminated composite plates. Part 2: vibration and wave propagation

NASA Technical Reports Server (NTRS)

Qin, Zhanming; Hasanyan, Davresh; Librescu, Liviu; Ambur, Damodar R.

2005-01-01

In Part 1 of this paper, the governing equations of geometrically nonlinear, anisotropic composite plates incorporating magneto-thermo-elastic effects have been derived. In order to gain insight into the implications of a number of geometrical and physical features of the system. three special cases are investigated: (i) free vibration of a plate strip immersed in a transversal magnetic field; (ii) free vibration of the plate strip immersed in an axial magnetic field; (iii) magneto-elastic wave propagations of an infinite plate. Within each of these cases, a prescribed uniform thermal field is considered. Special coupling characteristics between the magnetic and elastic fields are put into evidence. Extensive numerical investigations are conducted and pertinent conclusions which highlight the various effects induced by the magneto-elastic couplings and the finite electroconductivity, are outlined.

Elastic/viscoplastic behavior of fiber-reinforced thermoplastic composites

NASA Technical Reports Server (NTRS)

Wang, C.; Sun, C. T.; Gates, T. S.

1990-01-01

An elastic/viscoplastic constitutive model was used to characterize the nonlinear and rate dependent behavior of a continuous fiber-reinforced thermoplastic composite. This model was incorporated into a finite element program for the analysis of laminated plates and shells. Details on the finite element formulation with the proposed constitutive model were presented. The numerical results were compared with experimental data for uniaxial tension and three-point bending tests of (+ or - 45 deg)3s APC-2 laminates.

The Hamiltonian Structure of Nonlinear Elasticity: The Convective Representation of Solids, Rods, and Plates,

DTIC Science & Technology

1986-12-01

paper, we consider geometrically exact models, such as the Kirchhoff-Love-Reissner- Antman model for rods and its counterpart for plates and shells. These...equivalent model, formulated as a constrained director theory - the so-called special theory of Cosserat rods - is due to Antman (1974] - see also...Anan and Jordan [1975], Anunan and Kenny [1981]. and Antman [1984] for some applications. The dynamic version along with the parametrization discussed

Size estimates for fat inclusions in an isotropic Reissner-Mindlin plate

NASA Astrophysics Data System (ADS)

Morassi, Antonino; Rosset, Edi; Vessella, Sergio

2018-02-01

In this paper we consider the inverse problem of determining, within an elastic isotropic thick plate modelled by the Reissner-Mindlin theory, the possible presence of an inclusion made of a different elastic material. Under some a priori assumptions on the inclusion, we deduce constructive upper and lower estimates of the area of the inclusion in terms of a scalar quantity related to the work developed in deforming the plate by applying simultaneously a couple field and a transverse force field at the boundary of the plate. The approach allows us to consider plates with a boundary of Lipschitz class. The first author is supported by PRIN 2015TTJN95 ‘Identification and monitoring of complex structural systems’. The second author is supported by FRA 2016 ‘Problemi Inversi, dalla stabilità alla ricostruzione’, Università degli Studi di Trieste. The second and the third authors are supported by Progetto GNAMPA 2017 ‘Analisi di problemi inversi: stabilità e ricostruzione’, Istituto Nazionale di Alta Matematica (INdAM).

MLEP-Fail calibration for 1/8 inch thick cast plate of 17-4 steel.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corona, Edmundo

The purpose of the work presented in this memo was to calibrate the Sierra material model Multilinear Elastic-Plastic Hardening Model with Failure (MLEP-Fail) for 1/8 inch thick cast plate of 17-4 steel. The calibration approach is essentially the same as that recently used in a previous memo using data from smooth and notched tensile specimens. The notched specimens were manufactured with three notch radii R = 1=8, 1/32 and 1/64 inches. The dimensions of the smooth and notched specimens are given in the prints in Appendix A. Two cast plates, Plate 3 and Plate 4, with nominally identical properties weremore » considered.« less

Thickness Measurement of Surface Attachment on Plate with Lamb Wave

NASA Astrophysics Data System (ADS)

Ma, Xianglong; Zhang, Yinghong; Wen, Lichao; He, Yehu

2017-12-01

Aiming at the thickness detection of the plate surface attachment, a nondestructive testing method based on the Lamb wave is presented. This method utilizes Lamb wave propagation characteristics of signals in a bi-layer medium to measure the surface attachment plate thickness. Propagation of Lamb wave in bi-layer elastic is modeled and analyzed. The two-dimensional simulation model of electromagnetic ultrasonic plate - scale is established. The simulation is conducted by software COMSOL for simulation analysis under different boiler scale thickness wave form curve. Through this study, the thickness of the attached material can be judged by analyzing the characteristics of the received signal when the thickness of the surface of the plate is measured.

Mechanisms for creating accommodation space during early Tertiary sedimentation in Tibet.

NASA Astrophysics Data System (ADS)

Studnicki-Gizbert, C.; Burchfiel, B. C.

2003-12-01

The Tibetan plateau is for the most part underlain by rocks of pre-Cenozoic age, a fact that has hindered the identification of Cenozoic shortening structures that can be unequivocally related to the effects of India-Asia collision. Notably, however, the Qiangtang block contains a number of small, short wavelength basins filled with terrestrial sediments of early Tertiary age. Where these basins have been well studied, sedimentation is recognized as having occurred coevally with compressional deformation. The classic treatment of compressional basins appeals to accommodation space created by the flexure of an elastic plate in response to loads created by adjacent thrust fault bound ranges. It is unlikely that the Tertiary basins of the Qiangtang block formed in this manner. The wavelength of a classically modelled flexural basin is a basically a function of the thickness of the elastic plate and the density difference between sedimentary fill and ductile material underlying the plate. Assuming a model of elastic flexure, the very small wavelengths (5 - 30km) characteristic of Qiangtang basins would then imply extremely thin (~ 1-5 km) effective elastic plate thicknesses. These very low values are difficult to reconcile with any reasonable characterization of crustal rheology. Instead, these relatively small basins likely record the creation of accommodation space created by differential uplift across the strike of folds and faults. Stratal geometries and sedimentation rates reflect the kinematics and geometries of local compressional structures and the mechanical basis for the creation of accommodation space remains uncertain. Finally, the origin of these basins makes it unlikely that early Tertiary sedimentation represents a significant fraction of the upper crust of Tibetan plateau.

The effect of plate-scale rheology and plate interactions on intraplate seismicity

NASA Astrophysics Data System (ADS)

So, Byung-Dal; Capitanio, Fabio A.

2017-11-01

We use finite element modeling to investigate on the stress loading-unloading cycles and earthquakes occurrence in the plate interiors, resulting from the interactions of tectonic plates along their boundary. We model a visco-elasto-plastic plate embedding a single or multiple faults, while the tectonic stress is applied along the plate boundary by an external loading visco-elastic plate, reproducing the tectonic setting of two interacting lithospheres. Because the two plates deform viscously, the timescale of stress accumulation and release on the faults is self-consistently determined, from the boundary to the interiors, and seismic recurrence is an emerging feature. This approach overcomes the constraints on recurrence period imposed by stress (stress-drop) and velocity boundary conditions, while here it is unconstrained. We illustrate emerging macroscopic characteristics of this system, showing that the seismic recurrence period τ becomes shorter as Γ and Θ decreases, where Γ =ηI /ηL, the viscosity ratio of the viscosities of the internal fault-embedded to external loading plates, respectively, and Θ =σY /σL the stress ratio of the elastic limit of the fault to far-field loading stress. When the system embeds multiple, randomly distributed faults, stress transfer results in recurrence period deviations, however the time-averaged recurrence period of each fault show the same dependence on Γ and Θ, illustrating a characteristic collective behavior. The control of these parameters prevails even when initial pre-stress was randomly assigned in terms of the spatial arrangement and orientation on the internal plate, mimicking local fluctuations. Our study shows the relevance of macroscopic rheological properties of tectonic plates on the earthquake occurrence in plate interiors, as opposed to local factors, proposing a viable model for the seismic behavior of continent interiors in the context of large-scale, long-term deformation of interacting tectonic plates.

On the contact interaction of two identical stringers with an elastic semi-infinite continuous or vertically cracked plate

NASA Astrophysics Data System (ADS)

Grigoryan, M. S.

2018-04-01

This paper considers two connected contact problems on the interaction of stringers with an elastic semi-infinite plate. In the first problem, an elastic half-infinite continuous plate is reinforced on its boundary by two identical stringers exposed to a tensile external force. In the second problem, in the presence of the same stringers, the plate contains a collinear system of cracks on its vertical axis. The solution of both problems is reduced to the solution of singular integral equations (SIE) that are solved by a known numerical-analytical method.

Instability of fiber-reinforced viscoelastic composite plates to in-plane compressive loads

NASA Technical Reports Server (NTRS)

Chandiramani, N. K.; Librescu, L.

1990-01-01

This study analyzes the stability behavior of unidirectional fiber-reinforced composite plates with viscoelastic material behavior subject to in-plane biaxial compressive edge loads. To predict the effective time-dependent material properties, elastic fibers embedded in a linearly viscoelastic matrix are examined. The micromechanical relations developed for a transversely isotropic medium are discussed along with the correspondence principle of linear viscoelasticity. It is concluded that the stability boundary obtained for a viscoelastic plate is lower (more critical) than its elastic counterpart, and the transverse shear deformation effects are more pronounced in viscoelastic plates than in their elastic counterparts.

Reliability assessment of different plate theories for elastic wave propagation analysis in functionally graded plates.

PubMed

Mehrkash, Milad; Azhari, Mojtaba; Mirdamadi, Hamid Reza

2014-01-01

The importance of elastic wave propagation problem in plates arises from the application of ultrasonic elastic waves in non-destructive evaluation of plate-like structures. However, precise study and analysis of acoustic guided waves especially in non-homogeneous waveguides such as functionally graded plates are so complicated that exact elastodynamic methods are rarely employed in practical applications. Thus, the simple approximate plate theories have attracted much interest for the calculation of wave fields in FGM plates. Therefore, in the current research, the classical plate theory (CPT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) are used to obtain the transient responses of flexural waves in FGM plates subjected to transverse impulsive loadings. Moreover, comparing the results with those based on a well recognized hybrid numerical method (HNM), we examine the accuracy of the plate theories for several plates of various thicknesses under excitations of different frequencies. The material properties of the plate are assumed to vary across the plate thickness according to a simple power-law distribution in terms of volume fractions of constituents. In all analyses, spatial Fourier transform together with modal analysis are applied to compute displacement responses of the plates. A comparison of the results demonstrates the reliability ranges of the approximate plate theories for elastic wave propagation analysis in FGM plates. Furthermore, based on various examples, it is shown that whenever the plate theories are used within the appropriate ranges of plate thickness and frequency content, solution process in wave number-time domain based on modal analysis approach is not only sufficient but also efficient for finding the transient waveforms in FGM plates. Copyright © 2013 Elsevier B.V. All rights reserved.

Titanium Elastic Nail (TEN) versus Reconstruction Plate Repair of Midshaft Clavicular Fractures: A Finite Element Study

PubMed Central

Liu, Yanjie; Zhang, Wen; Pan, Yao; Zhang, Wei; Zhang, Changqing; Zeng, Bingfang; Chen, Yunfeng

2015-01-01

Background The biomechanical characteristics of midshaft clavicular fractures treated with titanium elastic nail (TEN) is unclear. This study aimed to present a biomechanical finite element analysis of biomechanical characteristics involved in TEN fixation and reconstruction plate fixation for midshaft clavicular fractures. Methods Finite element models of the intact clavicle and of midshaft clavicular fractures fixed with TEN and with a reconstruction plate were built. The distal clavicle displacement, peak stress, and stress distribution on the 3 finite element models were calculated under the axial compression and cantilever bending. Results In both loading configurations, TEN generated the highest displacement of the distal clavicle, followed by the intact clavicle and the reconstruction plate. TEN showed higher peak bone and implant stresses, and is more likely to fail in both loading configurations compared with the reconstruction plate. TEN led to a stress distribution similar to that of the intact clavicle in both loading configurations, whereas the stress distribution with the reconstruction plate was nonphysiological in cantilever bending. Conclusions TEN is generally preferable for treating simple displaced fractures of the midshaft clavicle, because it showed a stress distribution similar to the intact clavicle. However, TEN provides less stability, and excessive exercise of and weight bearing on the ipsilateral shoulder should be avoided in the early postoperative period. Fixation with a reconstruction plate was more stable but showed obvious stress shielding. Therefore, for patients with a demand for early return to activity, reconstruction plate fixation may be preferred. PMID:25965409

Quasi-one-dimensional modes in strip plates: Theory and experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arreola, A.; Báez, G.; Méndez-Sánchez, R. A.

2014-01-14

Using acoustic resonance spectroscopy we measure the elastic resonances of a strip rectangular plate with all its ends free. The experimental setup consist of a vector network analyzer, a high-fidelity audio amplifier, and electromagnetic-acoustic transducers. The one-dimensional modes are identified from the measured spectra by comparing them with theoretical predictions of compressional and bending modes of the plate modeled as a beam. The agreement between theory and experiment is excellent.

Solving the Problem of Bending of Multiply Connected Plates with Elastic Inclusions

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

This paper describes a method for determining the strain state of a thin anisotropic plate with elastic arbitrarily arranged elliptical inclusions. Complex potentials are used to reduce the problem to determining functions of generalized complex variables, which, in turn, comes down to an overdetermined system of linear algebraic equations, solved by singular expansions. This paper presents the results of numerical calculations that helped establish the influence of rigidity of elastic inclusions, distances between inclusions, and their geometric characteristics on the bending moments occurring in the plate. It is found that the specific properties of distribution of moments near the apexes of linear elastic inclusions, characterized by moment intensity coefficients, occur only in the case of sufficiently rigid and elastic inclusions.

Three-dimensional flexure modelling of seamounts near the Ogasawara Fracture Zone in the western Pacific

NASA Astrophysics Data System (ADS)

Lee, Tae-Gook; Moon, Jai-Woon; Jung, Mee-Sook

2009-04-01

The geophysical data were obtained in 2000-2003 during a survey of seamounts near the Ogasawara Fracture Zone (OFZ) to the northwest of the Marshall Islands in the western Pacific. The OFZ is unique in that it is a wide rift zone showing 600-km-long right-lateral movement between the Pigafetta Basin (PB) and East Mariana Basin (EMB), and contains many seamounts (e.g. the Magellan Seamounts and the seamounts on the Dutton Ridge). Most seamounts in this study are newly mapped using modern multibeam echosounder (Seabeam 2000) and denoted sequentially by Korea Ocean Research and Development Institute (KORDI). OSM2, OSM4, OSM7, OSM8-1 and OSM8-2 seamounts of the study area are located in the OFZ which formed by the spreading ridge between the Izanagi and Pacific plates, and OSM5-1, Seascan, OSM6-1 and OSM6-2 seamounts in the PB which is a part of the oldest oceanic crust in the Pacific. In this study, the densities of seamounts and the elastic thickness values of lithosphere are estimated by using 3-D flexure and gravity modelling by considering several boundary conditions and a constant sediment layer. The infinite model with two different elastic thickness values is the best-fitting model and it indicates that the OFZ was mechanically coupled with plate of different elastic thickness values, probably after the reorganization of Izanagi-Pacific spreading zone. Very low elastic thickness values (5-10 km), relatively young seamounts, and old lithosphere in the east study area suggest the possibility of the rejuvenation of the lithosphere by widespread volcanism pulses, whereas higher elastic thickness values (15-20 km), relatively younger lithosphere, and old seamounts of the west study area are comparable with a simple cooling plate model. It implies that the west study area is outside the rejuvenation range of the lithosphere. In the flexure and gravity modelling, the different residual pattern of OSM6-1 and OSM6-2, which are joined, suggests that they have different load densities or elastic thickness values. OSM2 and OSM7 may be close to a basaltic volcano with low viscosity because they have high densities and ratios of the basal diameter to the height, whereas OSM4, OSM5-1 and Seascan may be close to an andesitic volcano.

Crustal deformation along the San Andreas, California

NASA Technical Reports Server (NTRS)

Li, Victor C.

1992-01-01

The goal is to achieve a better understanding of the regional and local deformation and crustal straining processes in western North America, particularly the effects of the San Andreas and nearby faults on the spatial and temporal crustal deformation behavior. Construction of theoretical models based on the mechanics of coupled elastic plate, viscoelastic foundation and large scale crack mechanics provide a rational basis for the interpretation of seismic and aseismic anomalies and expedite efforts in forecasting the stability of plate boundary deformation. Special focus is placed on the three dimensional time dependent surface deformation due to localized slippage in a elastic layer coupled to a visco-elastic substrate. The numerical analysis is based on a 3-D boundary element technique. Extension to visco-elastic coupling demands the derivation of 3-D time dependent Green's function. This method was applied to analyze the viscoelastic surface displacements due to a dislocated embedded patch. Surface uplift as a function of time and position are obtained. Comparisons between surface uplift for long and short dislocated patches are made.

Measurements of strain at plate boundaries using space based geodetic techniques

NASA Technical Reports Server (NTRS)

Robaudo, Stefano; Harrison, Christopher G. A.

1993-01-01

We have used the space based geodetic techniques of Satellite Laser Ranging (SLR) and VLBI to study strain along subduction and transform plate boundaries and have interpreted the results using a simple elastic dislocation model. Six stations located behind island arcs were analyzed as representative of subduction zones while 13 sites located on either side of the San Andreas fault were used for the transcurrent zones. The length deformation scale was then calculated for both tectonic margins by fitting the relative strain to an exponentially decreasing function of distance from the plate boundary. Results show that space-based data for the transcurrent boundary along the San Andreas fault help to define better the deformation length scale in the area while fitting nicely the elastic half-space earth model. For subduction type bonndaries the analysis indicates that there is no single scale length which uniquely describes the deformation. This is mainly due to the difference in subduction characteristics for the different areas.

Development of a bending stiffness model for wet process fiberboard

Treesearch

Chris Turk; John F. Hunt

2007-01-01

In traditional mechanics of materials, the stiffness of a beam or plate in bending is described by its cross-sectional shape as well as its material properties, primarily the modulus of elasticity. Previous work at the USDA Forest Products Laboratory, Madison, Wisconsin, has shown that modulus of elasticity has a strong correlation to the density of the fiberboard....

Towards a Model of Reactive-Cracking: the Role of Reactions, Elasticity and Surface Energy Driven Flow in Poro-elastic Media

NASA Astrophysics Data System (ADS)

Evans, O.; Spiegelman, M. W.; Wilson, C. R.; Kelemen, P. B.

2016-12-01

Many critical processes can be described by reactive fluid flow in brittle media, including hydration/alteration of oceanic plates near spreading ridges, chemical weathering, and dehydration/decarbonation of subducting plates. Such hydration reactions can produce volume changes that may induce stresses large enough to drive fracture in the rock, in turn exposing new reactive surface and modifying the permeability. A better understanding of this potentially rich feedback could also be critical in the design of engineered systems for geologic carbon sequestration. To aid understanding of these processes we have developed a macroscopic continuum description of reactive fluid flow in an elastically deformable porous media. We explore the behaviour of this model by considering a simplified hydration reaction (e.g. olivine + H20 -> serpentine + brucite). In a closed system, these hydration reactions will continue to consume available fluids until the permeability reaches zero, leaving behind it a highly stressed residuum. Our model demonstrates this limiting behaviour, and that the elastic stresses generated are large enough to cause failure/fracture of the host rock. Whilst it is understood that `reactive fracture' is an important mechanism for the continued evolution of this process, it is also proposed that imbibition/surface energy driven flow may play a role. Through a simplified set of computational experiments, we investigate the relative roles of elasticity and surface energy in both a non-reactive purely poro-elastic framework, and then in the presence of reaction. We demonstrate that surface energy can drive rapid diffusion of porosity, thus allowing the reaction to propagate over larger areas. As we expect both surface energy and fracture/failure to be of importance in these processes, we plan to integrate the current model into one that allows for fracture once critical stresses are exceeded.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Hannover, Hanover, Federal Republic of Germany, Apr. 8-12, 1990, Reports

NASA Astrophysics Data System (ADS)

Various papers on applied mathematics and mechanics are presented. Among the individual topics addressed are: dynamical systems with time-varying or unsteady structure, micromechanical modeling of creep rupture, forced vibrations of elastic sandwich plates with thick surface layers, postbuckling of a complete spherical shell under a line load, differential-geometric approach to the multibody system dynamics, stability of an oscillator with stochastic parametric excitation, identification strategies for crack-formation in rotors, identification of physical parameters of FEMs, impact model for elastic and partly plastic impacts on objects, varying delay and stability in dynamical systems. Also discussed are: parameter identification of a hybrid model for vibration analysis using the FEM, vibration behavior of a labyrinth seal with through-flow, similarities in the boundary layer of fiber composite materials, distortion parameter in shell theories, elastoplastic crack problem at finite strain, algorithm for computing effective stiffnesses of plates with periodic structure, plasticity of metal-matrix composites in a mixed stress-strain space formation, constitutive equations in directly formulated plate theories, microbuckling and homogenization for long fiber composites.

Modeling of Elastic Collisions between High Energy and Slow Neutral Atoms

DTIC Science & Technology

2015-07-01

cylindrical test cell, and the currents on the four different electrodes-Inner Cylinder , Exit Plate, Back Aperture, and Collector Plat~were measured...Inner Cylinder electrode. Nevertheless, the neutral atom current to the Inner Cylinder electrode predicted by the VHS model is comparable to the...Figure 9. Normalized curre nt at the Inner Cylinder e lectrode. the point of collision. T he discrepancy in the Exit Plate neutral atom current is due to

Web buckling behavior under in-plane compression and shear loads for web reinforced composite sandwich core

NASA Astrophysics Data System (ADS)

Toubia, Elias Anis

Sandwich construction is one of the most functional forms of composite structures developed by the composite industry. Due to the increasing demand of web-reinforced core for composite sandwich construction, a research study is needed to investigate the web plate instability under shear, compression, and combined loading. If the web, which is an integral part of the three dimensional web core sandwich structure, happens to be slender with respect to one or two of its spatial dimensions, then buckling phenomena become an issue in that it must be quantified as part of a comprehensive strength model for a fiber reinforced core. In order to understand the thresholds of thickness, web weight, foam type, and whether buckling will occur before material yielding, a thorough investigation needs to be conducted, and buckling design equations need to be developed. Often in conducting a parametric study, a special purpose analysis is preferred over a general purpose analysis code, such as a finite element code, due to the cost and effort usually involved in generating a large number of results. A suitable methodology based on an energy method is presented to solve the stability of symmetrical and specially orthotropic laminated plates on an elastic foundation. Design buckling equations were developed for the web modeled as a laminated plate resting on elastic foundations. The proposed equations allow for parametric studies without limitation regarding foam stiffness, geometric dimensions, or mechanical properties. General behavioral trends of orthotropic and symmetrical anisotropic plates show pronounced contribution of the elastic foundation and fiber orientations on the buckling resistance of the plate. The effects of flexural anisotropy on the buckling behavior of long rectangular plates when subjected to pure shear loading are well represented in the model. The reliability of the buckling equations as a design tool is confirmed by comparison with experimental results. Comparing to predicted values, the experimental plate shear test results range between 15 and 35 percent, depending on the boundary conditions considered. The compression testing yielded conservative results, and as such, can provide a valuable tool for the designer.

Flexural uplift of rift flanks in central Greece

NASA Astrophysics Data System (ADS)

Poulimenos, George; Doutsos, Theodor

1997-12-01

Uplifts, with elevations of up to 2000 m and short wavelengths (30-35 km), flank three major grabens in central Greece: the Rio, Sparta, and Atalanti grabens. They are bordered on their landward sides by narrow basins oriented parallel to the graben axes: the Manesi and Trichonis basins at the Rio graben and Copais and Istiea basins at the Atalanti graben. The flexural origin of these uplift profiles is investigated here by using thin, broken plate models. It is demonstrated that the observed topography of the graben flanks is consistent with the upward deflection of elastic and viscoelastic plates in response to upward directed forces applied at the graben flanks. In order to evaluate to applicability of each model, their predictions are checked against the observations. The elastic predictive modeling fits well with the observed flexural wavelengths and the flanking seismicity. However, it fails to predict the graben widths and the inferred elastic layer thickness. In contrast, the viscoelastic model successfully explains the graben widths and the "back" basins as flexural hinterland basins and matches the seismological data and the time constraints of rifting. It is therefore suggested that flexural uplift with viscoelastic relaxation accounts for the building of the graben flanks. The invoked viscoelastic models constrain the effective elastic thickness of the plates at 10 km for the Rio graben and 15 km for the Sparta and Atalanti grabens, suggesting a low-viscosity lower crust. Furthermore, they predict low rates of tectonic uplift of the order of 0.1 mm a-1 for the Atalanti graben, intermediate rates of 0.24-0.37 mm a-1 for the Rio graben, and high rates of 0.7-0.9 mm a-1 for the Sparta graben. The latter are quite possibly overestimated since napping events, capable of producing high local relief, are traced normal to the modeled profiles.

Elastic Buckling of Orthotropic Plates Under Varying Axial Stresses

NASA Technical Reports Server (NTRS)

Badir, Ashraf; Hu, Hurang; Diallo, Abdouramane

1997-01-01

The elastic buckling load of simply supported rectangular orthotropic plates subjected to a second degree parabolic variation of axial stresses in the longitudinal direction is calculated using analytical methods. The variation of axial stresses is equilibrated by nonuniform shear stresses along the plate edges and transverse normal stresses. The influence of the aspect ratio is examined, and the results are compared with plates subjected to uniform axial stresses.

Effect of thermal stresses on frequency band structures of elastic metamaterial plates

NASA Astrophysics Data System (ADS)

Wu, Ying; Yu, Kaiping; Yang, Linyun; Zhao, Rui; Shi, Xiaotian; Tian, Kuo

2018-01-01

We investigate the effect of thermal stresses on the band structure of elastic metamaterial plates by developing a useful finite-element based method. The thermal field is assumed to be uniform throughout the whole plate. Specifically, we find that the stiffness matrix of plate element is comprised of elastic and thermal stresses parts, which can be regarded as a linear function of temperature difference. We additionally demonstrate that the relative magnitudes between elastic properties and thermal stresses will lead to nonlinear effects on frequency band structures based on two different types of metamaterial plates made of single and double inclusions of square plates, respectively. Then, we validate the proposed approach by comparing the band structures with the frequency response curves obtained in finite periodic structures. We conduct sensitivity analysis and discuss in-depth the sensitivities of band structures with respect to temperature difference to quantitatively investigate the effect of thermal stresses on each band. In addition, the coupled effects of thermal stresses and temperature-dependent material properties on the band structure of Aluminum/silicone rubber plate have also been discussed. The proposed method and new findings in this paper extends the ability of existing metamaterial plates by enabling tunability over a wide range of frequencies in thermal environments.

Add-on unidirectional elastic metamaterial plate cloak

PubMed Central

Lee, Min Kyung; Kim, Yoon Young

2016-01-01

Metamaterial cloaks control the propagation of waves to make an object invisible or insensible. To manipulate elastic waves in space, a metamaterial cloak is typically embedded in a base system that includes or surrounds a target object. The embedding is undesirable because it structurally weakens or permanently alters the base system. In this study, we propose a new add-on metamaterial elastic cloak that can be placed over and mechanically coupled with a base structure without embedding. We designed an add-on type annular metamaterial plate cloak through conformal mapping, fabricated it and performed cloaking experiments in a thin-plate with a hole. Experiments were performed in a thin plate by using the lowest symmetric Lamb wave centered at 100 kHz. As a means to check the cloaking performance of the add-on elastic plate cloak, possibly as a temporary stress reliever or a so-called “stress bandage”, the degree of stress concentration mitigation and the recovery from the perturbed wave field due to a hole were investigated. PMID:26860896

Add-on unidirectional elastic metamaterial plate cloak

NASA Astrophysics Data System (ADS)

Lee, Min Kyung; Kim, Yoon Young

2016-02-01

Metamaterial cloaks control the propagation of waves to make an object invisible or insensible. To manipulate elastic waves in space, a metamaterial cloak is typically embedded in a base system that includes or surrounds a target object. The embedding is undesirable because it structurally weakens or permanently alters the base system. In this study, we propose a new add-on metamaterial elastic cloak that can be placed over and mechanically coupled with a base structure without embedding. We designed an add-on type annular metamaterial plate cloak through conformal mapping, fabricated it and performed cloaking experiments in a thin-plate with a hole. Experiments were performed in a thin plate by using the lowest symmetric Lamb wave centered at 100 kHz. As a means to check the cloaking performance of the add-on elastic plate cloak, possibly as a temporary stress reliever or a so-called “stress bandage”, the degree of stress concentration mitigation and the recovery from the perturbed wave field due to a hole were investigated.

Furrow Topography and the Elastic Thickness of Ganymede's Dark Terrain Lithosphere

NASA Technical Reports Server (NTRS)

Pappalardo, Robert T.; Nimmo, Francis; Giese, Bernd; Bader, Christina E.; DeRemer, Lindsay C.; Prockter, Louise M.

2003-01-01

The effective elastic thickness of Ganymede's lithosphere tell of the satellite's thermal evolution through time. Generally it has been inferred that dark terrain, which is less tectonically deformed than grooved terrain, represents regions of cooler and thicker lithosphere [1]. The ancient dark terrain is cut by furrows, tectonic troughs about 5 to 20 km in width, which may have formed in response to large ancient impacts [1, 2]. We have applied the methods of [3] to estimate effective elastic thickness based on topographic profiles across tectonic furrows, extracted from a stereo-derived digital elevation model (DEM) of dark terrain in Galileo Regio [4]. Asymmetry in furrow topography and inferred flexure suggests asymmetric furrow fault geometry. We find effective elastic thicknesses 0.4 km, similar to analyzed areas alongside bright grooved terrain. Data and Analysis: A broken-plate elastic model.

Hierarchic models for laminated plates

NASA Technical Reports Server (NTRS)

Szabo, Barna A.; Actis, Ricardo L.

1991-01-01

The research conducted in the formulation of hierarchic models for laminated plates is described. The work is an extension of the work done for laminated strips. The use of a single parameter, beta, is investigated that represents the degree to which the equilibrium equations of three dimensional elasticity are satisfied. The powers of beta identify members in the hierarchic sequence. Numerical examples that were analyzed with the proposed sequence of models are included. The results obtained for square plates with uniform loading and homogeneous boundary conditions are very encouraging. Several cross-ply and angle-ply laminates were evaluated and the results compared with those of the fully three dimensional model, computed using MSC/PROBE, and with previously reported work on laminated strips.

The modeling of piezoceramic patch interactions with shells, plates and beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, R. C.

1992-01-01

General models describing the interactions between a pair of piezoceramic patches and elastic substructures consisting of a cylindrical shell, plate and beam are presented. In each case, the manner in which the patch loads enter both the strong and weak forms of the time-dependent structural equations of motion is described. Through force and moment balancing, these loads are then determined in terms of material properties of the patch and substructure (thickness, elastic properties, Poisson ratios), the geometry of the patch placement, and the voltages into the patches. In the case of the shell, the coupling between banding and inplane deformations, which is due to the curvature, is retained. These models are sufficiently general to allow for potentially different patch voltages which implies that they can be suitably employed when using piezoceramic patches for controlling system dynamics when both extensional and bending vibrations are present.

Lamb wave scattering by a surface-breaking crack in a plate

NASA Technical Reports Server (NTRS)

Datta, S. K.; Al-Nassar, Y.; Shah, A. H.

1991-01-01

An NDE method based on finite-element representation and modal expansion has been developed for solving the scattering of Lamb waves in an elastic plate waveguide. This method is very powerful for handling discontinuities of arbitrary shape, weldments of different orientations, canted cracks, etc. The advantage of the method is that it can be used to study the scattering of Lamb waves in anisotropic elastic plates and in multilayered plates as well.

Formulas for the elastic constants of plates with integral waffle-like stiffening

NASA Technical Reports Server (NTRS)

Dow, Norris R; Libove, Charles; Hubka, Ralph E

1954-01-01

Formulas are derived for the fifteen elastic constants associated with bending, stretching, twisting, and shearing of plates with closely spaced integral ribbing in a variety of configurations and proportions. In the derivation the plates are considered, conceptually, as more uniform orthotropic plates somewhat on the order of plywood. The constants, which include the effectiveness of the ribs for resisting deformations other than bending and stretching in their longitudinal directions, are defined in terms of four coefficients, and theoretical and experimental methods for the evaluation of these coefficients are discussed. Four of the more important elastic constants are predicted by these formulas and are compared with test results. Good correlation is obtained. (author)

An anisotropic elastoplasticity model implemented in FLAG

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buechler, Miles Allen; Canfield, Thomas R.

2017-10-12

Many metals, including Tantalum and Zirconium, exhibit anisotropic elastoplastic behavior at the single crystal level, and if components are manufactured from these metals through forming processes the polycrystal (component) may also exhibit anisotropic elastoplastic behavior. This is because the forming can induce a preferential orientation of the crystals in the polycrystal. One example is a rolled plate of Uranium where the sti /strong orientation of the crystal (c-axis) tends to align itself perpendicular to the rolling direction. If loads are applied to this plate in di erent orientations the sti ness as well as the ow strength of the materialmore » will be greater in the through thickness direction than in other directions. To better accommodate simulations of such materials, an anisotropic elastoplasticity model has been implemented in FLAG. The model includes an anisotropic elastic stress model as well as an anisotropic plasticity model. The model could represent single crystals of any symmetry, though it should not be confused with a high- delity crystal plasticity model with multiple slip planes and evolutions. The model is most appropriate for homogenized polycrystalline materials. Elastic rotation of the material due to deformation is captured, so the anisotropic models are appropriate for arbitrary large rotations, but currently they do not account for signi cant change in material texture beyond the elastic rotation of the entire polycrystal.« less

Estimation of interplate coupling along Nankai trough considering the block motion model based on onland GNSS and seafloor GPS/A observation data using MCMC method

NASA Astrophysics Data System (ADS)

Kimura, H.; Ito, T.; Tadokoro, K.

2017-12-01

Introduction In southwest Japan, Philippine sea plate is subducting under the overriding plate such as Amurian plate, and mega interplate earthquakes has occurred at about 100 years interval. There is no occurrence of mega interplate earthquakes in southwest Japan, although it has passed about 70 years since the last mega interplate earthquakes: 1944 and 1946 along Nankai trough, meaning that the strain has been accumulated at plate interface. Therefore, it is essential to reveal the interplate coupling more precisely for predicting or understanding the mechanism of next occurring mega interplate earthquake. Recently, seafloor geodetic observation revealed the detailed interplate coupling distribution in expected source region of Nankai trough earthquake (e.g., Yokota et al. [2016]). In this study, we estimated interplate coupling in southwest Japan, considering block motion model and using seafloor geodetic observation data as well as onland GNSS observation data, based on Markov Chain Monte Carlo (MCMC) method. Method Observed crustal deformation is assumed that sum of rigid block motion and elastic deformation due to coupling at block boundaries. We modeled this relationship as a non-linear inverse problem that the unknown parameters are Euler pole of each block and coupling at each subfault, and solved them simultaneously based on MCMC method. Input data we used in this study are 863 onland GNSS observation data and 24 seafloor GPS/A observation data. We made some block division models based on the map of active fault tracing and selected the best model based on Akaike's Information Criterion (AIC): that is consist of 12 blocks. Result We find that the interplate coupling along Nankai trough has heterogeneous spatial distribution, strong at the depth of 0 to 20km at off Tokai region, and 0 to 30km at off Shikoku region. Moreover, we find that observed crustal deformation at off Tokai region is well explained by elastic deformation due to subducting Izu Micro Plate. We will present more details of our result, and discuss about not only interplate coupling but also rigid block motion, elastic deformation due to inland fault coupling, and resolution of estimated parameters.

Cymatics for the cloaking of flexural vibrations in a structured plate

PubMed Central

Misseroni, D.; Colquitt, D. J.; Movchan, A. B.; Movchan, N. V.; Jones, I. S.

2016-01-01

Based on rigorous theoretical findings, we present a proof-of-concept design for a structured square cloak enclosing a void in an elastic lattice. We implement high-precision fabrication and experimental testing of an elastic invisibility cloak for flexural waves in a mechanical lattice. This is accompanied by verifications and numerical modelling performed through finite element simulations. The primary advantage of our square lattice cloak, over other designs, is the straightforward implementation and the ease of construction. The elastic lattice cloak, implemented experimentally, shows high efficiency. PMID:27068339

Elastic and plastic buckling of simply supported solid-core sandwich plates in compression

NASA Technical Reports Server (NTRS)

Seide, Paul; Stowell, Elbridge Z

1950-01-01

A solution is presented for the problem of the compressive buckling of simply supported, flat, rectangular, solid-core sandwich plates stressed either in the elastic range or in the plastic range. Charts for the analysis of long sandwich plates are presented for plates having face materials of 24s-t3 aluminum alloy, 76s-t6 alclad aluminum alloy, and stainless steel. A comparison of computed and experimental buckling stresses of square solid-core sandwich plates indicates fair agreement between theory and experiment.

Modified equations of finite-size layered plates made of orthotropic material. Comparison of the results of numerical calculations with analytical solutions

NASA Astrophysics Data System (ADS)

Volchkov, Yu. M.

2017-09-01

This paper describes the modified bending equations of layered orthotropic plates in the first approximation. The approximation of the solution of the equation of the three-dimensional theory of elasticity by the Legendre polynomial segments is used to obtain differential equations of the elastic layer. For the approximation of equilibrium equations and boundary conditions of three-dimensional theory of elasticity, several approximations of each desired function (stresses and displacements) are used. The stresses at the internal points of the plate are determined from the defining equations for the orthotropic material, averaged with respect to the plate thickness. The construction of the bending equations of layered plates for each layer is carried out with the help of the elastic layer equations and the conjugation conditions on the boundaries between layers, which are conditions for the continuity of normal stresses and displacements. The numerical solution of the problem of bending of the rectangular layered plate obtained with the help of modified equations is compared with an analytical solution. It is determined that the maximum error in determining the stresses does not exceed 3 %.

Validation of a 3D computational fluid-structure interaction model simulating flow through an elastic aperture.

PubMed

Quaini, A; Canic, S; Glowinski, R; Igo, S; Hartley, C J; Zoghbi, W; Little, S

2012-01-10

This work presents a validation of a fluid-structure interaction computational model simulating the flow conditions in an in vitro mock heart chamber modeling mitral valve regurgitation during the ejection phase during which the trans-valvular pressure drop and valve displacement are not as large. The mock heart chamber was developed to study the use of 2D and 3D color Doppler techniques in imaging the clinically relevant complex intra-cardiac flow events associated with mitral regurgitation. Computational models are expected to play an important role in supporting, refining, and reinforcing the emerging 3D echocardiographic applications. We have developed a 3D computational fluid-structure interaction algorithm based on a semi-implicit, monolithic method, combined with an arbitrary Lagrangian-Eulerian approach to capture the fluid domain motion. The mock regurgitant mitral valve corresponding to an elastic plate with a geometric orifice, was modeled using 3D elasticity, while the blood flow was modeled using the 3D Navier-Stokes equations for an incompressible, viscous fluid. The two are coupled via the kinematic and dynamic conditions describing the two-way coupling. The pressure, the flow rate, and orifice plate displacement were measured and compared with numerical simulation results. In-line flow meter was used to measure the flow, pressure transducers were used to measure the pressure, and a Doppler method developed by one of the authors was used to measure the axial displacement of the orifice plate. The maximum recorded difference between experiment and numerical simulation for the flow rate was 4%, the pressure 3.6%, and for the orifice displacement 15%, showing excellent agreement between the two. Copyright © 2011 Elsevier Ltd. All rights reserved.

Electrodynamic soil plate oscillator: Modeling nonlinear mesoscopic elastic behavior and hysteresis in nonlinear acoustic landmine detection

NASA Astrophysics Data System (ADS)

Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.

2015-10-01

An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit significant curvature when the soil particle velocity is relatively higher. An oscillator with hysteresis modeled by a distribution of parallel spring elements each with a different threshold slip condition seems to describe fairly linear backbone curve behavior [W. D. Iwan, Transactions of the ASME, J. of Applied Mech., 33,(1966), 893-900], while a single bilinear hysteresis element describes the backbone curvature results in the experiments reported here [T. K. Caughey, Transactions of the ASME, J. of Applied Mech., 27, (1960), 640-643]. When "off target" resonances have a different backbone curvature than "on the mine" backbone curves, then false alarms may be eliminated due to resonances from the natural soil layering. See [R. A. Guyer, J. TenCate, and P. Johnson, "Hysteresis and the Dynamic Elasticity of Consolidated Granular Materials," Phys. Rev. Lett., 82, 16 (1999), 3280-3283] for recent models of nonlinear mesoscopic behavior.

Contact interaction of thin-walled elements with an elastic layer and an infinite circular cylinder under torsion

NASA Astrophysics Data System (ADS)

Kanetsyan, E. G.; Mkrtchyan, M. S.; Mkhitaryan, S. M.

2018-04-01

We consider a class of contact torsion problems on interaction of thin-walled elements shaped as an elastic thin washer – a flat circular plate of small height – with an elastic layer, in particular, with a half-space, and on interaction of thin cylindrical shells with a solid elastic cylinder, infinite in both directions. The governing equations of the physical models of elastic thin washers and thin circular cylindrical shells under torsion are derived from the exact equations of mathematical theory of elasticity using the Hankel and Fourier transforms. Within the framework of the accepted physical models, the solution of the contact problem between an elastic washer and an elastic layer is reduced to solving the Fredholm integral equation of the first kind with a kernel representable as a sum of the Weber–Sonin integral and some integral regular kernel, while solving the contact problem between a cylindrical shell and solid cylinder is reduced to a singular integral equation (SIE). An effective method for solving the governing integral equations of these problems are specified.

Earthquake stress drops, ambient tectonic stresses and stresses that drive plate motions

USGS Publications Warehouse

Hanks, T.C.

1977-01-01

A variety of geophysical observations suggests that the upper portion of the lithosphere, herein referred to as the elastic plate, has long-term material properties and frictional strength significantly greater than the lower lithosphere. If the average frictional stress along the non-ridge margin of the elastic plate is of the order of a kilobar, as suggested by the many observations of the frictional strength of rocks at mid-crustal conditions of pressure and temperature, the only viable mechanism for driving the motion of the elastic plate is a basal shear stress of several tens of bars. Kilobars of tectonic stress are then an ambient, steady condition of the earth's crust and uppermost mantle. The approximate equality of the basal shear stress and the average crustal earthquake stress drop, the localization of strain release for major plate margin earthquakes, and the rough equivalence of plate margin slip rates and gross plate motion rates suggest that the stress drops of major plate margin earthquakes are controlled by the elastic release of the basal shear stress in the vicinity of the plate margin, despite the existence of kilobars of tectonic stress existing across vertical planes parallel to the plate margin. If the stress differences available to be released at the time of faulting are distributed in a random, white fasbion with a mean-square value determined by the average earthquake stress drop, the frequency of occurrence of constant stress drop earthquakes will be proportional to reciprocal faulting area, in accordance with empirically known frequency of occurrence statistics. ?? 1977 Birkha??user Verlag.

Nonlocal integral elasticity in nanostructures, mixtures, boundary effects and limit behaviours

NASA Astrophysics Data System (ADS)

Romano, Giovanni; Luciano, Raimondo; Barretta, Raffaele; Diaco, Marina

2018-02-01

Nonlocal elasticity is addressed in terms of integral convolutions for structural models of any dimension, that is bars, beams, plates, shells and 3D continua. A characteristic feature of the treatment is the recourse to the theory of generalised functions (distributions) to provide a unified presentation of previous proposals. Local-nonlocal mixtures are also included in the analysis. Boundary effects of convolutions on bounded domains are investigated, and analytical evaluations are provided in the general case. Methods for compensation of boundary effects are compared and discussed with a comprehensive treatment. Estimates of limit behaviours for extreme values of the nonlocal parameter are shown to give helpful information on model properties, allowing for new comments on previous proposals. Strain-driven and stress-driven models are shown to emerge by swapping the mechanical role of input and output fields in the constitutive convolution, with stress-driven elastic model leading to well-posed problems. Computations of stress-driven nonlocal one-dimensional elastic models are performed to exemplify the theoretical results.

Line-spring model for surface cracks in a Reissner plate

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissner's plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.

Stochastic Investigation of Natural Frequency for Functionally Graded Plates

NASA Astrophysics Data System (ADS)

Karsh, P. K.; Mukhopadhyay, T.; Dey, S.

2018-03-01

This paper presents the stochastic natural frequency analysis of functionally graded plates by applying artificial neural network (ANN) approach. Latin hypercube sampling is utilised to train the ANN model. The proposed algorithm for stochastic natural frequency analysis of FGM plates is validated and verified with original finite element method and Monte Carlo simulation (MCS). The combined stochastic variation of input parameters such as, elastic modulus, shear modulus, Poisson ratio, and mass density are considered. Power law is applied to distribute the material properties across the thickness. The present ANN model reduces the sample size and computationally found efficient as compared to conventional Monte Carlo simulation.

On the strain energy of laminated composite plates

NASA Technical Reports Server (NTRS)

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.

GPS measurement of relative motion of the Cocos and Caribbean Plates and strain accumulation across the Middle America Trench

NASA Astrophysics Data System (ADS)

Dixon, Timothy H.

1993-10-01

Global Positioning System (GPS) measurements in 1988 and 1991 on Cocos Island (Cocos plate), San Andres Island (Caribbean plate), and Liberia (Caribbean plate, mainland Costa Rica) provide an estimate of relative motion between the Cocos and Caribbean plates. The data for Cocos and San Andres Islands, both located more than 400 km from the Middle America Trench, define a velocity that is equivalent within two standard errors (7 mm/yr rate, 5 degrees azimuth) to the NUVEL-1 plate motion model. The data for Liberia, 120 km from the trench, define a velocity that is similar in azimuth but substantially different in rate from NUVEL-1. The discrepancy can be explained with a simple model of elastic strain accumulation with a subduction zone that is locked to a relatively shallow (20±5 km) depth.

Large-displacement structural durability analyses of simple bend specimen emulating rocket nozzle liners

NASA Technical Reports Server (NTRS)

Arya, Vinod K.; Halford, Gary R.

1994-01-01

Large-displacement elastic and elastic-plastic, finite-element stress-strain analyses of an oxygen-tree high-conductivity (OFHC) copper plate specimen were performed using an updated Lagrangian formulation. The plate specimen is intended for low-cost experiments that emulate the most important thermomechanical loading and failure modes of a more complex rocket nozzle. The plate, which is loaded in bending at 593 C, contains a centrally located and internally pressurized channel. The cyclic crack initiation lives were estimated using the results from the analyses and isothermal strain-controlled low-cycle fatigue data for OFHC copper. A comparison of the predicted and experimental cyclic lives showed that an elastic analysis predicts a longer cyclic life than that observed in experiments by a factor greater than 4. The results from elastic-plastic analysis for the plate bend specimen, however, predicted a cyclic life in close agreement with experiment, thus justifying the need for the more rigorous stress-strain analysis.

Earthquakes in the Laboratory: Continuum-Granular Interactions

NASA Astrophysics Data System (ADS)

Ecke, Robert; Geller, Drew; Ward, Carl; Backhaus, Scott

2013-03-01

Earthquakes in nature feature large tectonic plate motion at large scales of 10-100 km and local properties of the earth on the scale of the rupture width, of the order of meters. Fault gouge often fills the gap between the large slipping plates and may play an important role in the nature and dynamics of earthquake events. We have constructed a laboratory scale experiment that represents a similitude scale model of this general earthquake description. Two photo-elastic plates (50 cm x 25 cm x 1 cm) confine approximately 3000 bi-disperse nylon rods (diameters 0.12 and 0.16 cm, height 1 cm) in a gap of approximately 1 cm. The plates are held rigidly along their outer edges with one held fixed while the other edge is driven at constant speed over a range of about 5 cm. The local stresses exerted on the plates are measured using their photo-elastic response, the local relative motions of the plates, i.e., the local strains, are determined by the relative motion of small ball bearings attached to the top surface, and the configurations of the nylon rods are investigated using particle tracking tools. We find that this system has properties similar to real earthquakes and are exploring these ``lab-quake'' events with the quantitative tools we have developed.

Seismic Velocity and Elastic Properties of Plate Boundary Faults

NASA Astrophysics Data System (ADS)

Jeppson, Tamara N.

The elastic properties of fault zone rock at depth play a key role in rupture nucleation, propagation, and the magnitude of fault slip. Materials that lie within major plate boundary fault zones often have very different material properties than standard crustal rock values. In order to understand the mechanics of faulting at plate boundaries, we need to both measure these properties and understand how they govern the behavior of different types of faults. Mature fault zones tend to be identified in large-scale geophysical field studies as zones with low seismic velocity and/or electrical resistivity. These anomalous properties are related to two important mechanisms: (1) mechanical or diagenetic alteration of the rock materials and/or (2) pore fluid pressure and stress effects. However, in remotely-sensed and large-length-scale data it is difficult to determine which of these mechanisms are affecting the measured properties. The objective of this dissertation research is to characterize the seismic velocity and elastic properties of fault zone rocks at a range of scales, with a focus on understanding why the fault zone properties are different from those of the surrounding rock and the potential effects on earthquake rupture and fault slip. To do this I performed ultrasonic velocity experiments under elevated pressure conditions on drill core and outcrops samples from three plate boundary fault zones: the San Andreas Fault, California, USA; the Alpine Fault, South Island, New Zealand; and the Japan Trench megathrust, Japan. Additionally, I compared laboratory measurements to sonic log and large-scale seismic data to examine the scale-dependence of the measured properties. The results of this study provide the most comprehensive characterization of the seismic velocities and elastic properties of fault zone rocks currently available. My work shows that fault zone rocks at mature plate boundary faults tend to be significantly more compliant than surrounding crustal rocks and quantifies that relationship. The results of this study are particularly relevant to the interpretation of field-scale seismic datasets at major fault zones. Additionally, the results of this study provide constraints on elastic properties used in dynamic rupture models.

Elastic Buckling under Combined Stresses of Flat Plates with Integral Waffle-Like Stiffening

NASA Technical Reports Server (NTRS)

Dow, Norris F.; Levin, L. Ross; Troutman, John L.

1953-01-01

Theory and experiment were compared and found in good agreement for the elastic Buckling under combined stresses of long flat plates with integral waffle-like stiffening in a variety of configurations. For such flat plates, 45deg waffle stiffening was found to be the most effective of the configurations for the proportions considered over the widest range of combinations of compression and shear.

Elastic Buckling Under Combined Stresses of Flat Plates with Integral Waffle-like Stiffening

NASA Technical Reports Server (NTRS)

Dow, Norris F; Levin, L Ross; Troutman, John L

1954-01-01

Theory and experiment were compared and found in good agreement for the elastic buckling under combined stresses of long flat plates with integral waffle-like stiffening in a variety of configurations. For such flat plates, 45 degree waffle stiffening was found to be the most effective of the configurations for the proportions considered over the widest range of combinations of compression and shear.

The relationship between elastic constants and structure of shock waves in a zinc single crystal

NASA Astrophysics Data System (ADS)

Krivosheina, M. N.; Kobenko, S. V.; Tuch, E. V.

2017-12-01

The paper provides a 3D finite element simulation of shock-loaded anisotropic single crystals on the example of a Zn plate under impact using a mathematical model, which allows for anisotropy in hydrostatic stress and wave velocities in elastic and plastic ranges. The simulation results agree with experimental data, showing the absence of shock wave splitting into an elastic precursor and a plastic wave in Zn single crystals impacted in the [0001] direction. It is assumed that the absence of an elastic precursor under impact loading of a zinc single crystal along the [0001] direction is determined by the anomalously large ratio of the c/a-axes and close values of the propagation velocities of longitudinal and bulk elastic waves. It is shown that an increase in only one elastic constant along the [0001] direction results in shock wave splitting into an elastic precursor and a shock wave of "plastic" compression.

Volcano spacing and plate rigidity

USGS Publications Warehouse

ten Brink, Uri S.

1991-01-01

In-plane stresses, which accompany the flexural deformation of the lithosphere under the load of adjacent volcanoes, may govern the spacing of volcanoes in hotspot provinces. Specifically, compressive stresses in the vicinity of a volcano prevent new upwelling in this area, forcing a new volcano to develop at a minimum distance that is equal to the distance in which the radial stresses change from compressional to tensile (the inflection point). If a volcano is modeled as a point load on a thin elastic plate, then the distance to the inflection point is proportional to the thickness of the plate to the power of 3/4. Compilation of volcano spacing in seven volcanic groups in East Africa and seven volcanic groups of oceanic hotspots shows significant correlation with the elastic thickness of the plate and matches the calculated distance to the inflection point. In contrast, volcano spacing in island arcs and over subduction zones is fairly uniform and is much larger than predicted by the distance to the inflection point, reflecting differences in the geometry of the source and the upwelling areas.

Investigation on Tensile Fatigue Characteristics of Meshed GUM Metal Plates for Bone Graft Applications

NASA Astrophysics Data System (ADS)

Sekiguchi, Koki; He, Jianmei

2017-11-01

GUM Metal has characteristics of lower elasticity rigidity, large elastic deformation, higher strength and biocompatibility etc. When it is used for implant applications, there is still problem like overloading on the natural-bone because of its high rigidity compared with the human bones. Therefore, the purpose of this study is to create more flexible meshed plates for implant applications from the viewpoints of elastic rigidity and volume density. Basic mesh shapes are designed, devised and applied for meshed GUM Metal plates using three dimensional (3D) CAD tools. Experimental evaluation on tensile fatigue characteristics of meshed GUM Metal plate specimens are carried out. Analytical approaches on stress evaluation are also executed through finite element method to obtain the S-N curve for fatigue characteristic evaluation.

Plate and butt-weld stresses beyond elastic limit, material and structural modeling

NASA Technical Reports Server (NTRS)

Verderaime, V.

1991-01-01

Ultimate safety factors of high performance structures depend on stress behavior beyond the elastic limit, a region not too well understood. An analytical modeling approach was developed to gain fundamental insights into inelastic responses of simple structural elements. Nonlinear material properties were expressed in engineering stresses and strains variables and combined with strength of material stress and strain equations similar to numerical piece-wise linear method. Integrations are continuous which allows for more detailed solutions. Included with interesting results are the classical combined axial tension and bending load model and the strain gauge conversion to stress beyond the elastic limit. Material discontinuity stress factors in butt-welds were derived. This is a working-type document with analytical methods and results applicable to all industries of high reliability structures.

[Medical image elastic registration smoothed by unconstrained optimized thin-plate spline].

PubMed

Zhang, Yu; Li, Shuxiang; Chen, Wufan; Liu, Zhexing

2003-12-01

Elastic registration of medical image is an important subject in medical image processing. Previous work has concentrated on selecting the corresponding landmarks manually and then using thin-plate spline interpolating to gain the elastic transformation. However, the landmarks extraction is always prone to error, which will influence the registration results. Localizing the landmarks manually is also difficult and time-consuming. We the optimization theory to improve the thin-plate spline interpolation, and based on it, used an automatic method to extract the landmarks. Combining these two steps, we have proposed an automatic, exact and robust registration method and have gained satisfactory registration results.

Convection-driven tectonics on Venus

NASA Astrophysics Data System (ADS)

Phillips, R. J.

1990-02-01

An analysis is presented of convective stress coupling to an elastic lithosphere as applied to Venus. Theoretical solutions are introduced for the response of a mathematically thick elastic plate overlying a Newtonian viscous medium with an exponential depth dependence of viscosity, and a Green's function solution is obtained for the viscous flow driven by a harmonic density distribution at a specified depth. An elastic-plastic analysis is carried out for the deformation of a model Venus lithosphere. The results predict that dynamic uplift of Venusian topography must be accompanied by extensive brittle failure and viscous flow in the lithosphere.

Thick shell tectonics on one-plate planets - Applications to Mars

NASA Technical Reports Server (NTRS)

Banerdt, W. B.; Saunders, R. S.; Phillips, R. J.; Sleep, N. H.

1982-01-01

Using the zero frequency equations of a self-gravitating elastic spherical shell overlying a strengthless fluid, a theory for stress distribution in thick lithospheric shells on one-plate planets is developed. For both the compensated and flexural modes, stress distributions in lithospheres are reviewed. For compensated modes, surface stresses depend only on surface topography, whereas for flexural modes it is shown that, for long wavelengths, stress trajectories are mainly dependent on the lithospheric lateral density distribution and not on elastic properties. Computational analyses are performed for Mars, and it is found that isostatically compensated models correctly predict the graben structure in the immediate Tharsis region and a flexural loading model is satisfactory in explaining the graben in the regions surrounding Tharsis. A three-stage model for the evolution of Tharsis is hypothesized: isostasy with north-south graben formation on Tharsis, followed by flexural loading and radial graben formation on the perimeter of Tharsis, followed by a last stage of loading with little or no regional deformation.

Multiscale modeling and simulation for polymer melt flows between parallel plates

NASA Astrophysics Data System (ADS)

Yasuda, Shugo; Yamamoto, Ryoichi

2010-03-01

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for ωτR≲1 , and the crossover between the liquidlike and solidlike regime takes place around ωτα≃1 (where ω is the angular frequency of the plate and τR and τα are Rouse and α relaxation time, respectively).

Multiscale modeling and simulation for polymer melt flows between parallel plates.

PubMed

Yasuda, Shugo; Yamamoto, Ryoichi

2010-03-01

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for omegatauR < approximately 1 , and the crossover between the liquidlike and solidlike regime takes place around omegataualpha approximately equal 1 (where omega is the angular frequency of the plate and tauR and taualpha are Rouse and alpha relaxation time, respectively).

Various methods of determining the natural frequencies and damping of composite cantilever plates. 1. Exact solution for the binomial model of deformation

NASA Astrophysics Data System (ADS)

Skel'chik, V. S.; Ryabov, V. M.

1996-11-01

On the basis of the classical theory of thin anisotropic laminated plates the article analyzes the free vibrations of rectangular cantilever plates made of fibrous composites. The application of Kantorovich's method for the binomial representation of the shape of the elastic surface of a plate yielded for two unknown functions a system of two connected differential equations and the corresponding boundary conditions at the place of constraint and at the free edge. The exact solution for the frequencies and forms of the free vibrations was found with the use of Laplace transformation with respect to the space variable. The magnitudes of several first dimensionless frequencies of the bending and torsional vibrations of the plate were calculated for a wide range of change of two dimensionless complexes, with the dimensions of the plate and the anisotropy of the elastic properties of the material taken into account. The article shows that with torsional vibrations the warping constraint at the fixed end explains the apparent dependence of the shear modulus of the composite on the length of the specimen that had been discovered earlier on in experiments with a torsional pendulum. It examines the interaction and transformation of the second bending mode and of the first torsional mode of the vibrations. It analyzes the asymptotics of the dimensionless frequencies when the length of the plate is increased, and it shows that taking into account the bending-torsion interaction in strongly anisotropic materials type unidirectional carbon reinforced plastic can reduce substantially the frequencies of the bending vibrations but has no effect (within the framework of the binomial model) on the frequencies of the torsional vibrations.

Generalized Reliability Methodology Applied to Brittle Anisotropic Single Crystals. Degree awarded by Washington Univ., 1999

NASA Technical Reports Server (NTRS)

Salem, Jonathan A.

2002-01-01

A generalized reliability model was developed for use in the design of structural components made from brittle, homogeneous anisotropic materials such as single crystals. The model is based on the Weibull distribution and incorporates a variable strength distribution and any equivalent stress failure criteria. In addition to the reliability model, an energy based failure criterion for elastically anisotropic materials was formulated. The model is different from typical Weibull-based models in that it accounts for strength anisotropy arising from fracture toughness anisotropy and thereby allows for strength and reliability predictions of brittle, anisotropic single crystals subjected to multiaxial stresses. The model is also applicable to elastically isotropic materials exhibiting strength anisotropy due to an anisotropic distribution of flaws. In order to develop and experimentally verify the model, the uniaxial and biaxial strengths of a single crystal nickel aluminide were measured. The uniaxial strengths of the <100> and <110> crystal directions were measured in three and four-point flexure. The biaxial strength was measured by subjecting <100> plates to a uniform pressure in a test apparatus that was developed and experimentally verified. The biaxial strengths of the single crystal plates were estimated by extending and verifying the displacement solution for a circular, anisotropic plate to the case of a variable radius and thickness. The best correlation between the experimental strength data and the model predictions occurred when an anisotropic stress analysis was combined with the normal stress criterion and the strength parameters associated with the <110> crystal direction.

A fluid-structure interaction model of soft robotics using an active strain approach

NASA Astrophysics Data System (ADS)

Hess, Andrew; Lin, Zhaowu; Gao, Tong

2017-11-01

Soft robotic swimmers exhibit rich dynamics that stem from the non-linear interplay of the fluid and immersed soft elastic body. Due to the difficulty of handling the nonlinear two-way coupling of hydrodynamic flow and deforming elastic body, studies of flexible swimmers often employ either one-way coupling strategies with imposed motions of the solid body or some simplified elasticity models. To explore the nonlinear dynamics of soft robots powered by smart soft materials, we develop a computational model to deal with the two-way fluid/elastic structure interactions using the fictitious domain method. To mimic the dynamic response of the functional soft material under external actuations, we assume the solid phase to be neo-Hookean, and employ an active strain approach to incorporate actuation, which is based on the multiplicative decomposition of the deformation gradient tensor. We demonstrate the capability of our algorithm by performing a series of numerical explorations that manipulate an elastic structure with finite thickness, starting from simple rectangular or circular plates to soft robot prototypes such as stingrays and jellyfish.

Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers.

PubMed

Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S

2016-05-01

Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.

Finite plate thickness effects on the Rayleigh-Taylor instability in elastic-plastic materials

NASA Astrophysics Data System (ADS)

Polavarapu, Rinosh; Banerjee, Arindam

2017-11-01

The majority of theoretical studies have tackled the Rayleigh-Taylor instability (RTI) problem in solids using an infinitely thick plate. Recent theoretical studies by Piriz et al. (PRE 95, 053108, 2017) have explored finite thickness effects. We seek to validate this recent theoretical estimate experimentally using our rotating wheel RTI experiment in an accelerated elastic-plastic material. The test section consists of a container filled with air and mayonnaise (a non-Newtonian emulsion) with an initial perturbation between two materials. The plate thickness effects are studied by varying the depth of the soft-solid. A set of experiments is run by employing different initial conditions with different container dimensions. Additionally, the effect of acceleration rate (driving pressure rise time) on the instability threshold with reference to the finite thickness will also be inspected. Furthermore, the experimental results are compared to the analytical strength models related to finite thickness effects on RTI. Authors acknowledge financial support from DOE-SSAA Grant # DE-NA0003195 and LANL subcontract #370333.

Improving the Diagnostic Specificity of CT for Early Detection of Lung Cancer: 4D CT-Based Pulmonary Nodule Elastometry

DTIC Science & Technology

2013-08-01

as thin - plate spline (1-3) or elastic-body spline (4, 5), is locally controlled. One of the main motivations behind the use of B- spline ...FL. Principal warps: thin - plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence...Weese J, Kuhn MH. Landmark-based elastic registration using approximating thin - plate splines . IEEE Transactions on Medical Imaging. 2001;20(6):526-34

Biomechanical implications of cortical elastic properties of the macaque mandible.

PubMed

Dechow, Paul C; Panagiotopoulou, Olga; Gharpure, Poorva

2017-10-01

Knowledge of the variation in the elastic properties of mandibular cortical bone is essential for modeling bone function. Our aim was to characterize the elastic properties of rhesus macaque mandibular cortical bone and compare these to the elastic properties from mandibles of dentate humans and baboons. Thirty cylindrical samples were harvested from each of six adult female rhesus monkey mandibles. Assuming orthotropy, axes of maximum stiffness in the plane of the cortical plate were derived from ultrasound velocity measurements. Further velocity measurements with longitudinal and transverse ultrasonic transducers along with measurements of bone density were used to compute three-dimensional cortical elastic properties using equations based on Hooke's law. Results showed regional variations in the elastic properties of macaque mandibular cortical bone that have both similarities and differences with that of humans and baboons. So far, the biological and structural basis of these differences is poorly understood. Copyright © 2017 Elsevier GmbH. All rights reserved.

Ice Engineering - study of Related Properties of Floating Sea-Ice Sheets and Summary of Elastic and Viscoelastic Analyses

DTIC Science & Technology

1977-12-01

Ice Plate Example. To demonstrate the capability of the visco- elastic finite-element computer code (5), the structural response of an infinite ... sea -ice plate on a fluid foundation is investigated for a simulated aircraft loading condition and, using relaxation functions, is determined

Determination of mass density, dielectric, elastic, and piezoelectric constants of bulk GaN crystal.

PubMed

Soluch, Waldemar; Brzozowski, Ernest; Lysakowska, Magdalena; Sadura, Jolanta

2011-11-01

Mass density, dielectric, elastic, and piezoelectric constants of bulk GaN crystal were determined. Mass density was obtained from the measured ratio of mass to volume of a cuboid. The dielectric constants were determined from the measured capacitances of an interdigital transducer (IDT) deposited on a Z-cut plate and from a parallel plate capacitor fabricated from this plate. The elastic and piezoelectric constants were determined by comparing the measured and calculated SAW velocities and electromechanical coupling coefficients on the Z- and X-cut plates. The following new constants were obtained: mass density p = 5986 kg/m(3); relative dielectric constants (at constant strain S) ε(S)(11)/ε(0) = 8.6 and ε(S)(11)/ε(0) = 10.5, where ε(0) is a dielectric constant of free space; elastic constants (at constant electric field E) C(E)(11) = 349.7, C(E)(12) = 128.1, C(E)(13) = 129.4, C(E)(33) = 430.3, and C(E)(44) = 96.5 GPa; and piezoelectric constants e(33) = 0.84, e(31) = -0.47, and e(15) = -0.41 C/m(2).

Transform push, oblique subduction resistance, and intraplate stress of the Juan de Fuca plate

USGS Publications Warehouse

Wang, K.; He, J.; Davis, E.E.

1997-01-01

The Juan de Fuca plate is a small oceanic plate between the Pacific and North America plates. In the southernmost region, referred to as the Gorda deformation zone, the maximum compressive stress a, constrained by earthquake focal mechanisms is N-S. Off Oregon, and possibly off Washington, NW trending left-lateral faults cutting the Juan de Fuca plate indicate a a, in a NE-SW to E-W direction. The magnitude of differential stress increases from north to south; this is inferred from the plastic yielding and distribution of earthquakes throughout the Gorda deformation zone. To understand how tectonic forces determine the stress field of the Juan de Fuca plate, we have modeled the intraplate stress using both elastic and elastic-perfectly plastic plane-stress finite element models. We conclude that the right-lateral shear motion of the Pacific and North America plates is primarily responsible for the stress pattern of the Juan de Fuca plate. The most important roles are played by a compressional force normal to the Mendocino transform fault, a result of the northward push by the Pacific plate and a horizontal resistance operating against the northward, or margin-parallel, component of oblique subduction. Margin-parallel subduction resistance results in large N-S compression in the Gorda deformation zone because the force is integrated over the full length of the Cascadia subduction zone. The Mendocino transform fault serves as a strong buttress that is very weak in shear but capable of transmitting large strike-normal compressive stresses. Internal failure of the Gorda deformation zone potentially places limits on the magnitude of the fault-normal stresses being transmitted and correspondingly on the magnitude of strike-parallel subduction resistance. Transform faults and oblique subduction zones in other parts of the world can be expected to transmit and create stresses in the same manner. Copyright 1997 by the American Geophysical Union.

Granular dynamics under shear with deformable boundaries

NASA Astrophysics Data System (ADS)

Geller, Drew; Backhaus, Scott; Ecke, Robert

2015-03-01

Granular materials under shear develop complex patterns of stress as the result of granular positional rearrangements under an applied load. We consider the simple planar shear of a quasi two-dimensional granular material consisting of bi-dispersed nylon cylinders confined between deformable boundaries. The aspect ratio of the gap width to total system length is 50, and the ratio of particle diameter to gap width is about 10. This system, designed to model a long earthquake fault with long range elastic coupling through the plates, is an interesting model system for understanding effective granular friction because it essentially self tunes to the jamming condition owing to the hardness of the grains relative to that of the boundary material, a ratio of more than 1000 in elastic moduli. We measure the differential strain displacements of the plates, the inhomogeneous stress distribution in the plates, the positions and angular orientations of the individual grains, and the shear force, all as functions of the applied normal stress. There is significant stick-slip motion in this system that we quantify through our quantitative measurements of both the boundary and the grain motion, resulting in a good characterization of this sheared 2D hard sphere system.

Large deflection random response of cross-ply laminated plates with elastically restrained edges and initial imperfections

NASA Technical Reports Server (NTRS)

Prasad, C. B.; Mei, Chuh

1988-01-01

The large deflection random response of symmetrically laminated cross-ply rectangular thin plates subjected to random excitation is studied. The out-of-plane boundary conditions are such that all the edges are rigidly supported against translation, but elastically restrained against rotation. The plate is also assumed to have a small initial imperfection. The assumed membrane boundary conditions are such that all the edges are free from normal and tangential forces in the plane of the plate. Mean-square deflections and mean-square strains are determined for a three-layered cross-ply laminate.

Elastic plate flexure above mantle plumes explains the upstream offset of volcanic activity at la Réunion and Hawaii

NASA Astrophysics Data System (ADS)

Gerbault, Muriel; Fontaine, Fabrice; Rabinowicz, Michel; Bystricky, Micha

2017-04-01

Surface volcanism at la Réunion and Hawaii occurs with an offset of 150-180 km upstream to the plume axis with respect to the plate motion. This striking observation raises questions about the forcing of plume-lithosphere thermo-mechanical interactions on melt trajectories beneath these islands. Based on visco-elasto-plastic numerical models handled at kilometric resolution, we propose to explain this offset by the development of compressional stresses at the base of the lithosphere, that result from elastic plate bending above the upward load exerted by the plume head. This horizontal compression adopts a disc shape centered around the plume axis, 20 km thick and 150 km in radius, at 50-70 km depth where the temperature varies from 600°C to 750°C. It lasts for 5 to 10 My in an oceanic plate of age greater than 70 My, a timing that is controlled by the visco-elastic relaxation time at 50-70 km depth. This period of time exceeds the time during which both the Somalian/East-African and Pacific plates drift over the Reunion and Hawaii plumes, respectively, thus rendering this basal compression a persistent feature. It is inferred that the buoyant melts percolating in the plume head pond below this zone of compression and eventually spread laterally until the most compressive principal elastic stresses reverse to the vertical, i.e., 150 km away from the plume head. There, melts propagate through dikes upwards to 35 km depth, where the plate curvature reverses and ambient compression diminishes. This 30-35 km depth may thus host magmatic reservoirs where melts pond, until further differentiation can relaunch ascension up to the surface and form a volcanic edifice. In a second stage, as the volcano grows because of melt accumulation at the top of the plate, the lithosphere is flexed downwards, inducing extra tensile stress at 30-35 km depth and compression at 15 km depth. It implies that now the melts pond at 15 km and form another magmatic reservoir lying just underneath the crust. These two processes explain the ponding of primary (shield) melts at 35 km and 15 km depths as partialy recorded below La Reunion, Mauritius or Hawaii volcanoes with seismic tomography.

Dynamic behaviour of thin composite plates for different boundary conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sprintu, Iuliana, E-mail: sprintui@yahoo.com, E-mail: rotaruconstantin@yahoo.com; Rotaru, Constantin, E-mail: sprintui@yahoo.com, E-mail: rotaruconstantin@yahoo.com

2014-12-10

In the context of composite materials technology, which is increasingly present in industry, this article covers a topic of great interest and theoretical and practical importance. Given the complex design of fiber-reinforced materials and their heterogeneous nature, mathematical modeling of the mechanical response under different external stresses is very difficult to address in the absence of simplifying assumptions. In most structural applications, composite structures can be idealized as beams, plates, or shells. The analysis is reduced from a three-dimensional elasticity problem to a oneor two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin.more » This paper aims to validate a mathematical model illustrating how thin rectangular orthotropic plates respond to the actual load. Thus, from the theory of thin plates, new analytical solutions are proposed corresponding to orthotropic rectangular plates having different boundary conditions. The proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis.« less

Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model

NASA Astrophysics Data System (ADS)

Farajpour, A.; Mohammadi, M.; Shahidi, A. R.; Mahzoon, M.

2011-08-01

In this article, the buckling behavior of nanoscale circular plates under uniform radial compression is studied. Small-scale effect is taken into consideration. Using nonlocal elasticity theory the governing equations are derived for the circular single-layered graphene sheets (SLGS). Explicit expressions for the buckling loads are obtained for clamped and simply supported boundary conditions. It is shown that nonlocal effects play an important role in the buckling of circular nanoplates. The effects of the small scale on the buckling loads considering various parameters such as the radius of the plate and mode numbers are investigated.

Three-dimensional elasticity solution of an infinite plate with a circular hole

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. The problem was originally solved by Alblas. The reasons for reconsidering it are to develop a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. The problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Various stress components are tabulated as functions of a/h, z/h, r/a, and nu, a and 2h being the radius of the hole and the plate thickness and nu, the Poisson's ratio. The significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses is discussed.

The role of elasticity in simulating long-term tectonic extension

NASA Astrophysics Data System (ADS)

Olive, Jean-Arthur; Behn, Mark D.; Mittelstaedt, Eric; Ito, Garrett; Klein, Benjamin Z.

2016-05-01

While elasticity is a defining characteristic of the Earth's lithosphere, it is often ignored in numerical models of long-term tectonic processes in favour of a simpler viscoplastic description. Here we assess the consequences of this assumption on a well-studied geodynamic problem: the growth of normal faults at an extensional plate boundary. We conduct 2-D numerical simulations of extension in elastoplastic and viscoplastic layers using a finite difference, particle-in-cell numerical approach. Our models simulate a range of faulted layer thicknesses and extension rates, allowing us to quantify the role of elasticity on three key observables: fault-induced topography, fault rotation, and fault life span. In agreement with earlier studies, simulations carried out in elastoplastic layers produce rate-independent lithospheric flexure accompanied by rapid fault rotation and an inverse relationship between fault life span and faulted layer thickness. By contrast, models carried out with a viscoplastic lithosphere produce results that may qualitatively resemble the elastoplastic case, but depend strongly on the product of extension rate and layer viscosity U × ηL. When this product is high, fault growth initially generates little deformation of the footwall and hanging wall blocks, resulting in unrealistic, rigid block-offset in topography across the fault. This configuration progressively transitions into a regime where topographic decay associated with flexure is fully accommodated within the numerical domain. In addition, high U × ηL favours the sequential growth of multiple short-offset faults as opposed to a large-offset detachment. We interpret these results by comparing them to an analytical model for the fault-induced flexure of a thin viscous plate. The key to understanding the viscoplastic model results lies in the rate-dependence of the flexural wavelength of a viscous plate, and the strain rate dependence of the force increase associated with footwall and hanging wall bending. This behaviour produces unrealistic deformation patterns that can hinder the geological relevance of long-term rifting models that assume a viscoplastic rheology.

Rectangular Shell Plating Under Uniformly Distributed Hydrostatic Pressure

NASA Technical Reports Server (NTRS)

Neubert, M; Sommer, A

1940-01-01

A check of the calculation methods used by Foppl and Henky for investigating the reliability of shell plating under hydrostatic pressure has proved that the formulas yield practical results within the elastic range of the material. Foppl's approximate calculation leaves one on the safe side. It further was found on the basis of the marked ductility of the shell plating under tensile stress that the strength is from 50 to 100 percent higher in the elastic range than expected by either method.

Hydroelastic behaviour of a structure exposed to an underwater explosion

PubMed Central

Colicchio, G.; Greco, M.; Brocchini, M.; Faltinsen, O. M.

2015-01-01

The hydroelastic interaction between an underwater explosion and an elastic plate is investigated num- erically through a domain-decomposition strategy. The three-dimensional features of the problem require a large computational effort, which is reduced through a weak coupling between a one-dimensional radial blast solver, which resolves the blast evolution far from the boundaries, and a three-dimensional compressible flow solver used where the interactions between the compression wave and the boundaries take place and the flow becomes three-dimensional. The three-dimensional flow solver at the boundaries is directly coupled with a modal structural solver that models the response of the solid boundaries like elastic plates. This enables one to simulate the fluid–structure interaction as a strong coupling, in order to capture hydroelastic effects. The method has been applied to the experimental case of Hung et al. (2005 Int. J. Impact Eng. 31, 151–168 (doi:10.1016/j.ijimpeng.2003.10.039)) with explosion and structure sufficiently far from other boundaries and successfully validated in terms of the evolution of the acceleration induced on the plate. It was also used to investigate the interaction of an underwater explosion with the bottom of a close-by ship modelled as an orthotropic plate. In the application, the acoustic phase of the fluid–structure interaction is examined, highlighting the need of the fluid–structure coupling to capture correctly the possible inception of cavitation. PMID:25512585

Crustal deformation in great California earthquake cycles

NASA Technical Reports Server (NTRS)

Li, Victor C.; Rice, James R.

1986-01-01

Periodic crustal deformation associated with repeated strike slip earthquakes is computed for the following model: A depth L (less than or similiar to H) extending downward from the Earth's surface at a transform boundary between uniform elastic lithospheric plates of thickness H is locked between earthquakes. It slips an amount consistent with remote plate velocity V sub pl after each lapse of earthquake cycle time T sub cy. Lower portions of the fault zone at the boundary slip continuously so as to maintain constant resistive shear stress. The plates are coupled at their base to a Maxwellian viscoelastic asthenosphere through which steady deep seated mantle motions, compatible with plate velocity, are transmitted to the surface plates. The coupling is described approximately through a generalized Elsasser model. It is argued that the model gives a more realistic physical description of tectonic loading, including the time dependence of deep slip and crustal stress build up throughout the earthquake cycle, than do simpler kinematic models in which loading is represented as imposed uniform dislocation slip on the fault below the locked zone.

Elastic modulus and thermal stress in coating during heat cycling with different substrate shapes

NASA Astrophysics Data System (ADS)

Gaona, Daniel; Valarezo, Alfredo

2015-09-01

The elastic modulus of a deposit ( E d) can be obtained by monitoring the temperature (Δ T) and curvature (Δ k) of a one-side coated long plate, namely, a onedimensional (1D) deformation model. The aim of this research is to design an experimental setup that proves whether a 1D deformation model can be scaled for complex geometries. The setup includes a laser displacement sensor mounted on a robotic arm capable of scanning a specimen surface and measuring its deformation. The reproducibility of the results is verified by comparing the present results with Stony Brook University Laboratory's results. The Δ k-Δ T slope error is less than 8%, and the E d estimation error is close to 2%. These values reveal the repeatability of the experiments. Several samples fabricated with aluminum as the substrate and 100MXC nanowire (Fe and Cr alloy) as the deposit are analyzed and compared with those in finite element (FE) simulations. The linear elastic behavior of 1D (flat long plate) and 2D (squared plate) specimens during heating/cooling cycles is demonstrated by the high linearity of all Δ k-Δ T curves (over 97%). The E d values are approximately equal for 1D and 2D analyses, with a median of 96 GPa and standard deviation of 2 GPa. The correspondence between the experimental and simulated results for the 1D and 2D specimens reveals that deformation and thermal stress in coated specimens can be predicted regardless of specimen geometry through FE modeling and by using the experimental value of E d. An example of a turbine-bladeshaped substrate is presented to validate the approach.

Experiments on elastic cloaking in thin plates.

PubMed

Stenger, Nicolas; Wilhelm, Manfred; Wegener, Martin

2012-01-06

Following a theoretical proposal [M. Farhat et al., Phys. Rev. Lett. 103, 024301 (2009)], we design, fabricate, and characterize a cloaking structure for elastic waves in 1 mm thin structured polymer plates. The cloak consists of 20 concentric rings of 16 different metamaterials, each being a tailored composite of polyvinyl chloride and polydimethylsiloxane. By using stroboscopic imaging with a camera from the direction normal to the plate, we record movies of the elastic waves for monochromatic plane-wave excitation. We observe good cloaking behavior for carrier frequencies in the range from 200 to 400 Hz (one octave), in good agreement with a complete continuum-mechanics numerical treatment. This system is thus ideally suited for demonstration experiments conveying the ideas of transformation optics.

Nanoindentation of virus capsids in a molecular model

NASA Astrophysics Data System (ADS)

Cieplak, Marek; Robbins, Mark O.

2010-01-01

A molecular-level model is used to study the mechanical response of empty cowpea chlorotic mottle virus (CCMV) and cowpea mosaic virus (CPMV) capsids. The model is based on the native structure of the proteins that constitute the capsids and is described in terms of the Cα atoms. Nanoindentation by a large tip is modeled as compression between parallel plates. Plots of the compressive force versus plate separation for CCMV are qualitatively consistent with continuum models and experiments, showing an elastic region followed by an irreversible drop in force. The mechanical response of CPMV has not been studied, but the molecular model predicts an order of magnitude higher stiffness and a much shorter elastic region than for CCMV. These large changes result from small structural changes that increase the number of bonds by only 30% and would be difficult to capture in continuum models. Direct comparison of local deformations in continuum and molecular models of CCMV shows that the molecular model undergoes a gradual symmetry breaking rotation and accommodates more strain near the walls than the continuum model. The irreversible drop in force at small separations is associated with rupturing nearly all of the bonds between capsid proteins in the molecular model, while a buckling transition is observed in continuum models.

A Biomechanical Comparison of Three 1.5-mm Plate and Screw Configurations and a Single 2.0-mm Plate for Internal Fixation of a Mandibular Condylar Fracture

PubMed Central

Aquilina, Peter; Parr, William C.H.; Chamoli, Uphar; Wroe, Stephen; Clausen, Philip

2014-01-01

The most stable pattern of internal fixation for mandibular condyle fractures is an area of ongoing discussion. This study investigates the stability of three patterns of plate fixation using readily available, commercially pure titanium implants. Finite element models of a simulated mandibular condyle fracture were constructed. The completed models were heterogeneous in bone material properties, contained approximately 1.2 million elements and incorporated simulated jaw adducting musculature. Models were run assuming linear elasticity and isotropic material properties for bone. No human subjects were involved in this investigation. The stability of the simulated condylar fracture reduced with the different implant configurations, and the von Mises stresses of a 1.5-mm X-shaped plate, a 1.5-mm rectangular plate, and a 1.5-mm square plate (all Synthes (Synthes GmbH, Zuchwil, Switzerland) were compared. The 1.5-mm X plate was the most stable of the three 1.5-mm profile plate configurations examined and had comparable mechanical performance to a single 2.0-mm straight four-hole plate. This study does not support the use of rectangular or square plate patterns in the open reduction and internal fixation of mandibular condyle fractures. It does provide some support for the use of a 1.5-mm X plate to reduce condylar fractures in selected clinical cases. PMID:25136411

Time-dependent inversions of slow slip at the Hikurangi subduction zone, New Zealand, using numerical Green's functions

NASA Astrophysics Data System (ADS)

Williams, C. A.; Wallace, L. M.; Bartlow, N. M.

2017-12-01

Slow slip events (SSEs) have been observed throughout the world, and the existence of these events has fundamentally altered our understanding of the possible ranges of slip behavior at subduction plate boundaries. In New Zealand, SSEs occur along the Hikurangi Margin, with shallower events in the north and deeper events to the south. In a recent study, Williams and Wallace (2015) found that static SSE inversions that consider elastic property variations provided significantly different results than those based on an elastic half-space. For deeper events, the heterogeneous models predicted smaller amounts of slip, while for shallower events the heterogeneous model predicted larger amounts of slip. In this study, we extend our initial work to examine the temporal variations in slip. We generate Green's functions using the PyLith finite element code (Aagaard et al., 2013) to allow consideration of elastic property variations provided by the New Zealand-wide seismic velocity model (Eberhart-Phillips et al., 2010). These Green's functions are then integrated to provide Green's functions compatible with the Network Inversion Filter (NIF, Segall and Matthews,1997; McGuire and Segall, 2003; Miyazaki et al.,2006). We examine 12 SSEs occurring along the Hikurangi Margin during 2010 and 2011, and compare the results using heterogeneous Green's functions with those of Bartlow et al. (2014), who examined the same set of SSEs with the NIF using a uniform elastic half-space model. The use of heterogeneous Green's functions should provide a more accurate picture of the slip distribution and evolution of the SSEs. This will aid in understanding the correlations between SSEs and seismicity and/or tremor and the role of SSEs in the accommodation of plate motion budgets in New Zealand.

Flexural modeling of the elastic lithosphere at an ocean trench: A parameter sensitivity analysis using analytical solutions

NASA Astrophysics Data System (ADS)

Contreras-Reyes, Eduardo; Garay, Jeremías

2018-01-01

The outer rise is a topographic bulge seaward of the trench at a subduction zone that is caused by bending and flexure of the oceanic lithosphere as subduction commences. The classic model of the flexure of oceanic lithosphere w (x) is a hydrostatic restoring force acting upon an elastic plate at the trench axis. The governing parameters are elastic thickness Te, shear force V0, and bending moment M0. V0 and M0 are unknown variables that are typically replaced by other quantities such as the height of the fore-bulge, wb, and the half-width of the fore-bulge, (xb - xo). However, this method is difficult to implement with the presence of excessive topographic noise around the bulge of the outer rise. Here, we present an alternative method to the classic model, in which lithospheric flexure w (x) is a function of the flexure at the trench axis w0, the initial dip angle of subduction β0, and the elastic thickness Te. In this investigation, we apply a sensitivity analysis to both methods in order to determine the impact of the differing parameters on the solution, w (x). The parametric sensitivity analysis suggests that stable solutions for the alternative approach requires relatively low β0 values (<15°), which are consistent with the initial dip angles observed in seismic velocity-depth models across convergent margins worldwide. The predicted flexure for both methods are compared with observed bathymetric profiles across the Izu-Mariana trench, where the old and cold Pacific plate is characterized by a pronounced outer rise bulge. The alternative method is a more suitable approach, assuming that accurate geometric information at the trench axis (i.e., w0 and β0) is available.

Flexure and the role of inplane force around coronae on Venus

NASA Technical Reports Server (NTRS)

Brown, C. David; Grimm, Robert E.

1993-01-01

Large coronae on Venus, such as Artemis and Latona, are rimmed by conspicuous trenches and associated outer rises. Sandwell and Schubert have observed that these systems resemble terrestrial subduction zones in planform and have succeeded in fitting an elastic plate bending equation to the inferred flexural topography. However, the first zero crossing bending moments required are -2.5 x 10(exp 17) N for Artemis and -5.0 x 10(exp 16) N for Latona. Since these moments are similar in magnitude to those of subducting slabs on Earth, a rollback subduction mechanism was proposed to explain the flexure around the largest coronae, although a differential thermal subsidence model is sufficient to account for the topography around some coronae. The purpose is to investigate the effect of inplane force as a possible alternative to large applied moments in producing flexure at Artemis and Latona. The close correlation of gravity to topography on Venus implies the absence of a low viscosity zone and the strong coupling of the lithosphere to mantle convection. If coronae are the surface manifestations of mantle plumes, they may be the sites of active convective stress coupling. As the upwelling reaches the lithosphere, it spreads radially outward, inducing shear tractions on the base of the plate. In addition, the hot, expanding corona may load the surrounding plate horizonally. Both the basal shear stresses and radial loading can be treated as an equivalent compressive inplane force in the mechanical lithosphere, which contributes to the bending of the outlying plate. Using a model that relates inplane force to the measured gravity anomalies, a rough value of the inplane force at Artemis was calculated. Recent Pioneer Venus spherical harmonic gravity models indicate a geoid anomaly of about 75 m over Artemis, which corresponds to an estimated inplane force on the order of -1x10(exp 13) N/m. The gravity model is unable to resolve Latona, but an inplane force of similar dimensions is assumed. The maximum possible inplane force based on the expected rheology can be constrained by using the approximate 5 K/km thermal gradient inferred from the best fit 30 km elastic plate at Artemis and Latona. For a dry olivine flow law in the upper mantle, the compressional load limit of the 60 km thick mechanical lithosphere is -4 x 10(exp 13) N/m. This value is equivalent to a load of -8 x 10(exp 13) N/m on a 30 km thick elastic plate.

Aspects of modelling the tectonics of large volcanoes on the terrestrial planets

NASA Technical Reports Server (NTRS)

Mcgovern, Patrick J.; Solomon, Sean C.

1993-01-01

Analytic solutions for the responses of planetary lithospheres to volcanic loads have been used to model faulting and infer elastic plate thicknesses. Predictions of the distribution of faulting around volcanic loads, based on the application of Anderson's criteria for faulting to the results of the models, do not agree well with observations. Such models do not give the stress state in the load itself, but only suggest a state of horizontal compressive stress there. Further, these models have considered only the effect of an instantaneously emplaced load. They do not address the time evolution of stresses, nor do they consider the effect of a load which grows. A finite element approach allows us to assign elements to the load itself, and thus permits calculation of the stress state and stress history within the edifice. The effects of episodic load growth can also be treated. When these effects are included, models give much better agreement with observations. We use the finite element code TECTON to construct axisymmetric models of volcanoes resting on an elastic lithospheric plate overlying a viscoelastic asthenosphere. We have implemented time-dependent material properties in order to simulate incremental volcano growth. The viscoelastic layer was taken to extend to a sufficient depth so that a rigid lower boundary has no significant influence on the results. The code first calculates elastic deformations and stresses and then determines the time-dependent viscous deformations and stresses. Time in the model scales as the Maxwell time tau(m) in the asthenosphere. We consider a volcano 25 km in height and 200 km in radius on an elastic lithosphere 40 km thick (parameters approximately appropriate to Ascraeus Mons). The volcano consists of three load increments applied at intervals of 1000 tau(m). Contours of maximum deviatoric stress in the fully-grown edifice at the conclusion of flexure (t = 3000 tau(m)) are shown.

The stress distribution in pin-loaded orthotropic plates

NASA Technical Reports Server (NTRS)

Klang, E. C.; Hyer, M. W.

1985-01-01

The performance of mechanically fastened composite joints was studied. Specially, a single-bolt connector was modeled as a pin-loaded, infinite plate. The model that was developed used two dimensional, complex variable, elasticity techniques combined with a boundary collocation procedure to produce solutions for the problem. Through iteration, the boundary conditions were satisfied and the stresses in the plate were calculated. Several graphite epoxy laminates were studied. In addition, parameters such as the pin modulus, coefficient of friction, and pin-plate clearance were varied. Conclusions drawn from this study indicate: (1) the material properties (i.e., laminate configuration) of the plate alter the stress state and, for highly orthotropic materials, the contact stress deviates greatly from the cosinusoidal distribution often assumed; (2) friction plays a major role in the distribution of stresses in the plate; (3) reversing the load direction also greatly effects the stress distribution in the plate; (4) clearance (or interference) fits change the contact angle and thus the location of the peak hoop stress; and (5) a rigid pin appears to be a good assumption for typical material systems.

How wing compliance drives the efficiency of self-propelled flapping flyers.

PubMed

Thiria, Benjamin; Godoy-Diana, Ramiro

2010-07-01

Wing flexibility governs the flying performance of flapping-wing flyers. Here, we use a self-propelled flapping-wing model mounted on a "merry go round" to investigate the effect of wing compliance on the propulsive efficiency of the system. Our measurements show that the elastic nature of the wings can lead not only to a substantial reduction in the consumed power, but also to an increment of the propulsive force. A scaling analysis using a flexible plate model for the wings points out that, for flapping flyers in air, the time-dependent shape of the elastic bending wing is governed by the wing inertia. Based on this prediction, we define the ratio of the inertial forces deforming the wing to the elastic restoring force that limits the deformation as the elastoinertial number N(ei). Our measurements with the self-propelled model confirm that it is the appropriate structural parameter to describe flapping flyers with flexible wings.

Analysis on spectra of hydroacoustic field in sonar cavity of the sandwich elastic wall structure

NASA Astrophysics Data System (ADS)

Xuetao, W.; Rui, H.; Weike, W.

2017-09-01

In this paper, the characteristics of the mechanical self - noise in sonar array cavity are studied by using the elastic flatbed - filled rectangular cavity parameterization model. Firstly, the analytic derivation of the vibration differential equation of the single layer, sandwich elastic wall plate structure and internal fluid coupling is carried out, and the modal method is used to solve it. Finally, the spectral characteristics of the acoustic field of rectangular cavity of different elastic wallboard materials are simulated and analyzed, which provides a theoretical reference for the prediction and control of sonar mechanical self-noise. In this paper, the sandwich board as control inside the dome background noise of a potential means were discussed, the dome background noise of qualitative prediction analysis and control has important theoretical significance.

A nonlinear theory for elastic plates with application to characterizing paper properties

Treesearch

M. W. Johnson; Thomas J. Urbanik

1984-03-01

A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...

Micromechanical models for textile structural composites

NASA Technical Reports Server (NTRS)

Marrey, Ramesh V.; Sankar, Bhavani V.

1995-01-01

The objective is to develop micromechanical models for predicting the stiffness and strength properties of textile composite materials. Two models are presented to predict the homogeneous elastic constants and coefficients of thermal expansion of a textile composite. The first model is based on rigorous finite element analysis of the textile composite unit-cell. Periodic boundary conditions are enforced between opposite faces of the unit-cell to simulate deformations accurately. The second model implements the selective averaging method (SAM), which is based on a judicious combination of stiffness and compliance averaging. For thin textile composites, both models can predict the plate stiffness coefficients and plate thermal coefficients. The finite element procedure is extended to compute the thermal residual microstresses, and to estimate the initial failure envelope for textile composites.

A nonlinear fracture mechanics approach to the growth of small cracks

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.

1983-01-01

An analytical model of crack closure is used to study the crack growth and closure behavior of small cracks in plates and at notches. The calculated crack opening stresses for small and large cracks, together with elastic and elastic plastic fracture mechanics analyses, are used to correlate crack growth rate data. At equivalent elastic stress intensity factor levels, calculations predict that small cracks in plates and at notches should grow faster than large cracks because the applied stress needed to open a small crack is less than that needed to open a large crack. These predictions agree with observed trends in test data. The calculations from the model also imply that many of the stress intensity factor thresholds that are developed in tests with large cracks and with load reduction schemes do not apply to the growth of small cracks. The current calculations are based upon continuum mechanics principles and, thus, some crack size and grain structure exist where the underlying fracture mechanics assumptions become invalid because of material inhomogeneity (grains, inclusions, etc.). Admittedly, much more effort is needed to develop the mechanics of a noncontinuum. Nevertheless, these results indicate the importance of crack closure in predicting the growth of small cracks from large crack data.

Simulation of the main physical processes in remote laser penetration with large laser spot size

DOE PAGES

Khairallah, S. A.; Anderson, A.; Rubenchik, A. M.; ...

2015-04-10

A 3D model is developed to simulate remote laser penetration of a 1mm Aluminum metal sheet with large laser spot size (~3x3cm²), using the ALE3D multi-physics code. The model deals with the laser-induced melting of the plate and the mechanical interaction between the solid and the melted part through plate elastic-plastic response. The effect of plate oscillations and other forces on plate rupture, the droplet formation mechanism and the influence of gravity and high laser power in further breaking the single melt droplet into many more fragments are analyzed. In the limit of low laser power, the numerical results matchmore » the available experiments. The numerical approach couples mechanical and thermal diffusion to hydrodynamics melt flow and accounts for temperature dependent material properties, surface tension, gravity and vapor recoil pressure.« less

Present-day Kinematics of Papua New Guinea from GPS campaign measurements

NASA Astrophysics Data System (ADS)

Koulali Idrissi, A.; McClusky, S.; Tregoning, P.

2013-12-01

Papua New Guinea (PNG) is a complex tectonic region located in the convergence zone between the Australian and Pacific Plate. It occupies arguably one of the most tectonically complicated regions of the world, and its geodynamic evolution involves micro-plate rotation, lithospheric rupture forming ocean basins, arc-continent collision, subduction polarity reversal, collisional orogenesis, ophiolite obduction, and exhumation of high-pressure metamorphic (ultramafic) rocks. In this study we present a GPS derived velocity field based on 1993-2008 survey mode observations at 30 GPS sites. We combine our results with previously published GPS velocities to investigate the deformation in northern and northwestern Papua New Guinea. We use an elastic block model to invert the regional GPS velocities as well as earthquake slip vectors for poles of rotation of several micro-plates. The micro-plate block boundary fault geometry is based on geological mapping and regional seismicity. The results show that fault system north of the Highlands fold and thrust belt is the major boundary between the rigid Australian Plate and the north Highlands block, with convergence occurring at rates of between ~ 6 and 11.5 mm/yr. The relative motion across the northern Highlands block increases to the north to ~ 21-24 mm/yr, meaning that the New Guinea trench is likely accumulating elastic strain and confirming that the new Guinea Trench is an active inter-plate boundary. Our results also show, that the north New Guinea Highlands and the Papuan peninsula are best modelled as two blocks separated by a boundary through the Aure Fold belt Belt complex. This block boundary today is accommodating an estimated 4-5 mm/yr dextral motion. Our model also confirms previous results showing that the Ramu-Markham fault accommodates the deformation associated with the Finisterre arc-continent collision. This new GPS velocity field provides fresh insights into the details of the kinematics of the PNG present-day deformation.

Ultrasonic input-output for transmitting and receiving longitudinal transducers coupled to same face of isotropic elastic plate

NASA Technical Reports Server (NTRS)

Williams, J. H., Jr.; Karagulle, H.; Lee, S. S.

1982-01-01

The quantitative understanding of ultrasonic nondestructive evaluation parameters such as the stress wave factor were studied. Ultrasonic input/output characteristics for an isotropic elastic plate with transmitting and receiving longitudinal transducers coupled to the same face were analyzed. The asymptotic normal stress is calculated for an isotropic elastic half space subjected to a uniform harmonic normal stress applied to a circular region at the surface. The radiated stress waves are traced within the plate by considering wave reflections at the top and bottom faces. The output voltage amplitude of the receiving transducer is estimated by considering only longitudinal waves. Agreement is found between the output voltage wave packet amplitudes and times of arrival due to multiple reflections of the longitudinal waves.

Hydroelastic slamming response in the evolution of a flip-through event during shallow-liquid sloshing

NASA Astrophysics Data System (ADS)

Lugni, C.; Bardazzi, A.; Faltinsen, O. M.; Graziani, G.

2014-03-01

The evolution of a flip-through event [6] upon a vertical, deformable wall during shallow-water sloshing in a 2D tank is analyzed, with specific focus on the role of hydroelasticity. An aluminium plate, whose dimensions are Froude-scaled in order to reproduce the first wet natural frequency associated with the typical structural panel of a Mark III containment system, is used. (Mark III Containment System is a membrane-type tank used in the Liquefied Natural Gas (LNG) carrier to contain the LNG. A typical structural panel is composed by two metallic membranes and two independent thermal insulation layers. The first membrane contains the LNG, the second one ensures redundancy in case of leakage.) Such a system is clamped to a fully rigid vertical wall of the tank at the vertical ends while being kept free on its lateral sides. Hence, in a 2D flow approximation the system can be suitably modelled, as a double-clamped Euler beam, with the Euler beam theory. The hydroelastic effects are assessed by cross-analyzing the experimental data based both on the images recorded by a fast camera, and on the strain measurements along the deformable panel and on the pressure measurements on the rigid wall below the elastic plate. The same experiments are also carried out by substituting the deformable plate with a fully stiff panel. The pressure transducers are mounted at the same positions of the strain gauges used for the deformable plate. The comparison between the results of rigid and elastic case allows to better define the role of hydroelasticity. The analysis has identified three different regimes characterizing the hydroelastic evolution: a quasi-static deformation of the beam (regime I) precedes a strongly hydroelastic behavior (regime II), for which the added mass effects are relevant; finally, the free-vibration phase (regime III) occurs. A hybrid method, combining numerical modelling and experimental data from the tests with fully rigid plate is proposed to examine the hydroelastic effects. Within this approach, the measurements provide the experimental loads acting on the rigid plate, while the numerical solution enables a more detailed analysis, by giving additional information not available from the experimental tests. More in detail, an Euler beam equation is used to model numerically the plate with the added-mass contribution estimated in time. In this way the resulting hybrid method accounts for the variation of the added mass associated with the instantaneous wetted length of the beam, estimated from the experimental images. Moreover, the forcing hydrodynamic load is prescribed by using the experimental pressure distribution measured in the rigid case. The experimental data for the elastic beam are compared with the numerical results of the hybrid model and with those of the standard methods used at the design stage. The comparison against the experimental data shows an overall satisfactory prediction of the hybrid model. The maximum peak pressure predicted by the standard methods agrees with the result of the hybrid model only when the added mass effect is considered. However, the standard methods are not able to properly estimate the temporal evolution of the plate deformation.

Deformation of the Japanese Islands and seismic coupling: an interpretation based on GSI permanent GPS observations

NASA Astrophysics Data System (ADS)

Le Pichon, Xavier; Mazzotti, Stéphane; Henry, Pierre; Hashimoto, Manabu

1998-08-01

The entire area of the Japanese Islands has been covered by the permanent GPS observation network of the Geographical Survey Institute since 1994. In this paper we use a solution for the vectors of motion during 1995 for a selection of 116 stations to discuss the origin of the observed deformation field. We refer the displacement field to Eurasia using the VLBI-determined motion of Kashima and demonstrate that other choices such as the Okhotsk or North American plates for north Japan are not compatible with the data. 1 yr GPS velocities are much higher than geological constraints would allow because these short-term measurements include transient elastic deformation. However, the good qualitative agreement between the observed geodetic deformation tensors and those inferred from active faults and earthquakes suggests that the Quaternary permanent deformation is essentially the result of the transfer of part of the subduction-induced elastic deformation into permanent plastic deformation. We then compute the elastic deformation of the Japanese Islands caused by interseismic loading of the Pacific and Philippine subduction planes. The geometry of the coupled zone and its downward extension are determined from the distribution of earthquakes for the Pacific slab. For the Philippine slab we use the geometry proposed by Hyndman et al. (1995). These elastic models account for most of the observed velocity field if the subduction movement of the Philippine Sea Plate is 100 per cent locked and if that of the Pacific Plate is 75-85 per cent locked. We note that the boundaries of the areas where significant elastic deformation is predicted (more than 10 mm yr-1 of motion with respect to Eurasia) coincide with the main zones of permanent deformation: the Eastern Japan Sea deformation zone for the Pacific subduction elastic deformation field and the Setouchi/MTL deformation zone for the Nankai field. Each zone probably accommodates 10-15 mm yr-1 of motion in the long term (convergence in the Eastern Japan Sea; strike-slip in the Setouchi/MTL zone). To account for this deformation, the effect of elastic loading from the trench must be combined with 5-10 mm yr-1 of motion of the Amur Plate with respect to Eurasia. Because loading during the subduction earthquake cycle causes an increase in stress in the Eastern Japan Sea and Setouchi/MTL deformation zones, the probability of earthquake occurrence in these zones may be higher near the end of the cycle.

Deformation and instability of underthrusting lithospheric plates

NASA Technical Reports Server (NTRS)

Liu, H.

1972-01-01

Models of the underthrusting lithosphere are constructed for the calculation of displacement and deflection. First, a mathematical theory is developed that rigorously demonstrates the elastic instability in the decending lithosphere. The theory states that lithospheric thrust beneath island arcs becomes unstable and suffers deflection as the compression increases. Thus, in the neighborhood of the edges where the lithospheric plate plunges into the asthenosphere and mesosphere its shape will be contorted. Next, the lateral displacement is calculated, and it is shown that, before contortion, the plate will thicken and contract at different positions with the variation in thickness following a parabolic profile. Finally, the depth distribution of the intermediate and deep focus earthquakes is explained in terms of plate buckling and contortion.

Gravity anomalies, flexure and mantle rheology seaward of circum-Pacific trenches

NASA Astrophysics Data System (ADS)

Hunter, J.; Watts, A. B.

2016-10-01

We have used ensemble averages of satellite-derived free-air gravity anomaly data, together with inverse modelling techniques, to determine the effective elastic thickness, Te, of circum-Pacific subducting oceanic lithosphere and its relationship to plate age. Synthetic modelling tests show that Te can be recovered best using gravity anomaly, rather than bathymetry, data and profiles that are at least 750 km long. Inverse modelling based on a uniform Te elastic plate suggests that Te increases with age of the subducting oceanic lithosphere and is given approximately by the depth to the 390 ± 10 °C oceanic isotherm based on a cooling plate model. Misfits between the observed and calculated gravity anomalies are significantly improved if a mechanically weak zone is included between the trench axis and the outer rise. This weak zone is coincident with observations of bend-faulting and seismicity. Inverse modelling shows that Te landward of the outer rise is generally 40-65 per cent less than the Te seaward of the outer rise. Both landward and seaward Te increases with age of the lithosphere and are given by the depth to the 342-349 °C and 671-714 °C oceanic isotherm, respectively. A dependence of Te on age is consistent with models for the cooling of oceanic lithosphere as it moves away from a mid-ocean ridge and the temperature-dependent ductile creep of oceanic lithospheric minerals such as olivine. By comparing the observed Te to the predicted Te based on laboratory-derived yield strength envelopes and an assumption of elastic-perfectly plastic deformation, we have attempted to constrain the rheology of oceanic lithosphere. Regardless of the assumed friction coefficient, the dry-olivine low-temperature plasticity flow laws of Goetze, Evans & Goetze, Raterron et al. and Mei et al. all provide quite a good fit to the observed Te at circum-Pacific subduction zones. This result contrasts with the Hawaiian Islands, where these flow laws are generally too strong to fit the observations. The discrepancy in rheology within Pacific plate may be caused by differences in the timescale of loading and therefore the amount of viscoelastic stress relaxation that has occurred. Other possibilities include thermal rejuvenation and magma-assisted flexure at the Hawaiian Islands.

An exact solution for the history-dependent material and delamination behavior of laminated plates subjected to cylindrical bending

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Todd O

2009-01-01

The exact solution for the history-dependent behavior of laminated plates subjected to cylindrical bending is presented. The solution represents the extension of Pagano's solution to consider arbitrary types of constitutive behaviors for the individual lamina as well as arbitrary types of cohesive zones models for delamination behavior. Examples of the possible types of material behavior are plasticity, viscoelasticity, viscoplasticity, and damaging. Examples of possible CZMs that can be considered are linear, nonlinear hardening, as well as nonlinear with softening. The resulting solution is intended as a benchmark solution for considering the predictive capabilities of different plate theories. Initial results aremore » presented for several types of history-dependent material behaviors. It is shown that the plate response in the presence of history-dependent behaviors can differ dramatically from the elastic response. These results have strong implications for what constitutes an appropriate plate theory for modeling such behaviors.« less

Estimates of effective elastic thickness at subduction zones

NASA Astrophysics Data System (ADS)

Yang, An; Fu, Yongtao

2018-06-01

The effective elastic thickness (Te) is an important parameter that characterizes the long-term strength of the lithosphere. Estimates of Te at subduction zones have important tectonic and geodynamic implications, providing constraints for the strength of the oceanic lithosphere at a short-term scale. We estimated Te values in several subduction zones worldwide by using models including both surface and subsurface loads from the analysis of free-air gravity anomaly and bathymetric data, together with a moving window admittance technique (MWAT). Tests with synthetic gravity and bathymetry data show that this method is a reliable way to recover Te of oceanic lithosphere. Our results show that there is a noticeable reduction in the effective elastic thickness of the subducting plate from the outer rise to the trench axis for most studied subduction zones, suggesting plate weakening at the trench-outer rise of the subduction zones. These subduction zones have Te range of 6-60 km, corresponding to a wide range of isotherms from 200 to 800 °C. Different trenches show distinct patterns. The Caribbean, Kuril-Japan, Mariana and Tonga subduction zones show predominantly high Te. By contrast, the Middle America and Java subduction zones have a much lower Te. The Peru-Chile, Aleutian and Philippine subduction zones show considerable scatter. The large variation of the isotherm for different trenches does not show clear relationship with plate weakening at the outer rise.

Determination of elastic constants of a generally orthotropic plate by modal analysis

NASA Astrophysics Data System (ADS)

Lai, T. C.; Lau, T. C.

1993-01-01

This paper describes a method of finding the elastic constants of a generally orthotropic composite thin plate through modal analysis based on a Rayleigh-Ritz formulation. The natural frequencies and mode shapes for a plate with free-free boundary conditions are obtained with chirp excitation. Based on the eigenvalue equation and the constitutive equations of the plate, an iteration scheme is derived using the experimentally determined natural frequencies to arrive at a set of converged values for the elastic constants. Four sets of experimental data are required for the four independent constants: namely the two Young's moduli E1 and E2, the in-plane shear modulus G12, and one Poisson's ratio nu12. The other Poisson's ratio nu21 can then be determined from the relationship among the constants. Comparison with static test results indicate good agreement. Choosing the right combinations of natural modes together with a set of reasonable initial estimates for the constants to start the iteration has been found to be crucial in achieving convergence.

Pressures in Tumuli: A Study of Tumuli Formation

NASA Technical Reports Server (NTRS)

Hansen, James E.

2005-01-01

Tumuli form via localized inflation in surface lava flows. These domed features have widths of 10-20 m, lengths of 10-150 m, and heights of 1-9 m. The axial fracture exposes a brittle crust overlying a ductilely deformed layer. The total crustal thickness is typically less than lm. Tumuli are observed on both terrestrial and martian lava flow surfaces, and provide insight on the flow formation processes and rates. Past studies have estimated the inflation pressure using a bending model for a circular, thin elastic plate, assuming small deflection (Rossi and Gudmundson, 1996). This formulation results in unrealistic pressures for some tumuli. We thus examine alternative models, including those with different shapes, bending of the ductile crust, large deflection, plastic deformation, and thick plate bending. Using the thickness of the ductile crust in the equations for thin, circular plates reduces most pressures to reasonable values. Alternative plate shapes do not cause a significant reduction in inflation pressure. Although the large deflection equations should be applicable based on the plate thickness to tumuli height ratios, they give even less realistic pressures. Tumuli with unrealistic pressures appear to have exceeded the critical bending moment, and have relatively thick crusts, requiring thick plate bending models.

The Effect of Applied Tensile Stress on Localized Corrosion in Sensitized AA5083

DTIC Science & Technology

2015-09-01

of stainless steel 4-point bending rig used to apply elastic stress to aluminum plate samples. (Bottom) Stress- strain data based on displacement and...ASTM-G39, from [25]. ..........................20 Figure 13. Photograph of stainless steel 4-point bending rig used to apply elastic stress to...aluminum plate samples, from [8]. ....................................................20 Figure 14. Photograph of stainless steel 4-point bending rig

Modeling of composite beams and plates for static and dynamic analysis

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Sutyrin, Vladislav G.; Lee, Bok Woo

1993-01-01

The main purpose of this research was to develop a rigorous theory and corresponding computational algorithms for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants for a plate and to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. This also requires the development of finite deformation plate equations which are compatible with the through-the-thickness analyses. After about one year's work, we settled on the variational-asymptotical method (VAM) as a suitable framework in which to solve these types of problems. VAM was applied to laminated plates with constant thickness in the work of Atilgan and Hodges. The corresponding geometrically nonlinear global deformation analysis of plates was developed by Hodges, Atilgan, and Danielson. A different application of VAM, along with numerical results, was obtained by Hodges, Lee, and Atilgan. An expanded version of this last paper was submitted for publication in the AIAA Journal.

Elastic stability of biaxially loaded longitudinally stiffened composite structures.

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Tamekuni, M.; Tripp, L. L.

1973-01-01

A linear analysis method is presented for the elastic stability of structures of uniform cross section, that may be idealized as an assemblage of laminated plate-strips, flat and curved, and beams. Each plate-strip and beam covers the entire length of the structure and is simply supported on the edges normal to the longitudinal axis. Arbitrary boundary conditions may be specified on any external longitudinal side of plate-strips. The structure or selected plate-strips may be loaded in any desired combination of inplane biaxial loads. The analysis simultaneously considers all modes of instability and is applicable for the buckling of laminated composite structures. Some numerical results are presented to indicate possible applications.

Probing elastically or plastically induced structural heterogeneities in bulk metallic glasses by nanoindentation pop-in tests

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Tingkun; Gao, Yanfei; Bei, Hongbin

Shear banding dynamics in bulk metallic glasses (BMGs) is manifested by the spatiotemporal evolution of strain fields which in turn depend on structural heterogeneities. The spacing of these heterogeneities, as a characteristic length scale, was determined from the analysis of nanoindentation pop-in tests using a stochastic model. Furthermore, the pre-stress by elastic bending and residual stress by plastic bending of BMG plates were found to dramatically decrease such spacings, thus increasing heterogeneity density and mechanically rejuvenating the glass structure.

Probing elastically or plastically induced structural heterogeneities in bulk metallic glasses by nanoindentation pop-in tests

DOE PAGES

Liu, Tingkun; Gao, Yanfei; Bei, Hongbin

2017-07-21

Shear banding dynamics in bulk metallic glasses (BMGs) is manifested by the spatiotemporal evolution of strain fields which in turn depend on structural heterogeneities. The spacing of these heterogeneities, as a characteristic length scale, was determined from the analysis of nanoindentation pop-in tests using a stochastic model. Furthermore, the pre-stress by elastic bending and residual stress by plastic bending of BMG plates were found to dramatically decrease such spacings, thus increasing heterogeneity density and mechanically rejuvenating the glass structure.

First evidence of non-locality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model

PubMed Central

Barbagallo, Gabriele; d’Agostino, Marco Valerio; Placidi, Luca; Neff, Patrizio

2016-01-01

In this paper, we propose the first estimate of some elastic parameters of the relaxed micromorphic model on the basis of real experiments of transmission of longitudinal plane waves across an interface separating a classical Cauchy material (steel plate) and a phononic crystal (steel plate with fluid-filled holes). A procedure is set up in order to identify the parameters of the relaxed micromorphic model by superimposing the experimentally based profile of the reflection coefficient (plotted as function of the wave-frequency) with the analogous profile obtained via numerical simulations. We determine five out of six constitutive parameters which are featured by the relaxed micromorphic model in the isotropic case, plus the determination of the micro-inertia parameter. The sixth elastic parameter, namely the Cosserat couple modulus μc, still remains undetermined, since experiments on transverse incident waves are not yet available. A fundamental result of this paper is the estimate of the non-locality intrinsically associated with the underlying microstructure of the metamaterial. We show that the characteristic length Lc measuring the non-locality of the phononic crystal is of the order of 13 of the diameter of its fluid-filled holes. PMID:27436984

First evidence of non-locality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model.

PubMed

Madeo, Angela; Barbagallo, Gabriele; d'Agostino, Marco Valerio; Placidi, Luca; Neff, Patrizio

2016-06-01

In this paper, we propose the first estimate of some elastic parameters of the relaxed micromorphic model on the basis of real experiments of transmission of longitudinal plane waves across an interface separating a classical Cauchy material (steel plate) and a phononic crystal (steel plate with fluid-filled holes). A procedure is set up in order to identify the parameters of the relaxed micromorphic model by superimposing the experimentally based profile of the reflection coefficient (plotted as function of the wave-frequency) with the analogous profile obtained via numerical simulations. We determine five out of six constitutive parameters which are featured by the relaxed micromorphic model in the isotropic case, plus the determination of the micro-inertia parameter. The sixth elastic parameter, namely the Cosserat couple modulus μ c , still remains undetermined, since experiments on transverse incident waves are not yet available. A fundamental result of this paper is the estimate of the non-locality intrinsically associated with the underlying microstructure of the metamaterial. We show that the characteristic length L c measuring the non-locality of the phononic crystal is of the order of [Formula: see text] of the diameter of its fluid-filled holes.

Hydroelastic behaviour of a structure exposed to an underwater explosion.

PubMed

Colicchio, G; Greco, M; Brocchini, M; Faltinsen, O M

2015-01-28

The hydroelastic interaction between an underwater explosion and an elastic plate is investigated num- erically through a domain-decomposition strategy. The three-dimensional features of the problem require a large computational effort, which is reduced through a weak coupling between a one-dimensional radial blast solver, which resolves the blast evolution far from the boundaries, and a three-dimensional compressible flow solver used where the interactions between the compression wave and the boundaries take place and the flow becomes three-dimensional. The three-dimensional flow solver at the boundaries is directly coupled with a modal structural solver that models the response of the solid boundaries like elastic plates. This enables one to simulate the fluid-structure interaction as a strong coupling, in order to capture hydroelastic effects. The method has been applied to the experimental case of Hung et al. (2005 Int. J. Impact Eng. 31, 151-168 (doi:10.1016/j.ijimpeng.2003.10.039)) with explosion and structure sufficiently far from other boundaries and successfully validated in terms of the evolution of the acceleration induced on the plate. It was also used to investigate the interaction of an underwater explosion with the bottom of a close-by ship modelled as an orthotropic plate. In the application, the acoustic phase of the fluid-structure interaction is examined, highlighting the need of the fluid-structure coupling to capture correctly the possible inception of cavitation. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Modeling the impact behavior of high strength ceramics. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajendran, A.M.

1993-12-01

An advanced constitutive model is used to describe the shock and high strain rate behaviors of silicon carbide (SC), boron carbide B4C, and titanium diboride (TiB2) under impact loading conditions. The model's governing equations utilize a set of microphysically-based constitutive relationships to model the deformation and damage processes in a ceramic. The total strain is decomposed into elastic, plastic, and microcracking components. The plastic strain component was calculated using conventional viscoplastic equations. The strain components due to microcracking utilized relationships derived for a penny-shaped crack containing elastic solids. The main features of the model include degradation of strength and stiffnessmore » under both compressive and tensile loading conditions. When loaded above the Hugoniot elastic limit (HEL), the strength is limited by the strain rate dependent strength equation. However, below the HEL, the strength variation with respect to strain rate and pressure is modeled through microcracking relationships assuming no plastic flow. The ceramic model parameters were determined using a set of VISAR data from the plate impact experiments.« less

Numerical simulation of present day tectonic stress across the Indian subcontinent

NASA Astrophysics Data System (ADS)

Yadav, R.; Tiwari, V. M.

2018-04-01

In situ measurements of maximum horizontal stress (S Hmax) in the Indian subcontinent are limited and do not present regional trends of intraplate stress orientation. The observed orientations of S Hmax vary considerably and often differ from the plate velocity direction. We have simulated orientation and magnitude of S Hmax through finite element modeling incorporating heterogeneities in elastic property of the Indian continent and plain stress approximation to understand the variability of S Hmax. Four different scenarios are tested in simulation: (1) homogeneous plate with fixed plate boundary (2) homogeneous plate with boundary forces (3) heterogeneous plate with fixed boundary (4) heterogeneous plate with boundary forces. The estimated orientation and magnitude of S Hmax with a heterogeneous plate with boundary forces in the Himalayan region and an eastern plate boundary comprising the Indo-Burmese arc and Andaman subduction zone are consistent with measured maximum horizontal stress. This study suggests that plate boundary force varies along the northern Indian plate margin and also provides a constraint on the intraplate stress field in the Indian subcontinent.

Implications of new gravity data for Baikal Rift zone structure

NASA Technical Reports Server (NTRS)

Ruppel, C.; Kogan, M. G.; Mcnutt, M. K.

1993-01-01

Newly available, 2D Bouguer gravity anomaly data from the Baikal Rift zone, Siberia, indicate that this discrete, intracontinental rift system is regionally compensated by an elastic plate about 50 km thick. However, spectral and spatial domain analyses and isostatic anomaly calculations show that simple elastic plate theory does not offer an adequate explanation for compensation in the rift zone, probably because of significant lateral variations in plate strength and the presence of subsurface loads. Our results and other geophysical observations support the interpretation that the Baikal Rift zone is colder than either the East African or Rio Grande rift.

Elastic flexure controls magma trajectories and explains the offset of primary volcanic activity upstream of mantle plume axis at la Réunion and Hawaii hotspot islands

NASA Astrophysics Data System (ADS)

Gerbault, Muriel; Fontaine, Fabrice J.; Rabinowicz, Michel; Bystricky, Misha

2017-03-01

Surface volcanism at la Réunion and Hawaii occurs with an offset of 150-180 km upstream to the plume axis with respect to the plate motion. This striking observation raises questions about the forcing of plume-lithosphere thermo-mechanical interactions on melt trajectories beneath these islands. Based on visco-elasto-plastic numerical models handled at kilometric resolution, we propose to explain this offset by the development of compressional stresses at the base of the lithosphere, that result from elastic plate bending above the upward load exerted by the plume head. This horizontal compression adopts a disc shape centered around the plume axis: (i) it is 20 km thick, (ii) it has a 150 km radius, (iii) it lays at the base of the elastic part of the lithosphere, i.e., around ∼50-70 km depth where the temperature varies from ∼600 °C to ∼750 °C, (iv) it lasts for 5 to 10 My in an oceanic plate of age greater than 70 My, and (vi) it is controlled by the visco-elastic relaxation time at ∼50-70 km depth. This period of time exceeds the time during which both the Somalian/East-African and Pacific plates drift over the Reunion and Hawaii plumes, respectively. This indicates that this basal compression is actually a persistent feature. It is inferred that the buoyant melts percolating in the plume head pond below this zone of compression and eventually spread laterally until the most compressive principal elastic stresses reverse to the vertical, i.e., ∼150 km away from the plume head. There, melts propagate through dikes upwards to ∼35 km depth, where the plate curvature reverses and ambient compression diminishes. This 30-35 km depth may thus host a magmatic reservoir where melts transported by dykes pond. Only after further magmatic differentiation can dykes resume their ascension up to the surface and begin forming a volcanic edifice. As the volcano grows because of melt accumulation at the top of the plate, the lithosphere is flexed downwards, inducing extra tensile stress at 30-35 km depth and compression at ∼15 km depth (induced by the edifice load). It implies that now the melts pond at ∼15 km and form another magmatic reservoir lying just underneath the crust. These processes explain the ponding of primary (shield) melts at ∼35 km and ∼15 km depths as recorded below La Reunion, Mauritius or Hawaii volcanoes, all shifted by ∼150 km with respect to the plume axis.

Three-dimensional solutions for the free vibrations and buckling of thermally stressed multilayered angle-ply composite plates

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Burton, W. S.

1992-01-01

Analytic three-dimensional elasticity solutions are developed for the free vibration and buckling of thermally stressed rectangular multilayered angle-ply anisotropic plates which are assumed to have an antisymmetric lamination with respect to the middle plane. Sensitivity derivatives are evaluated and used to investigate the sensitivity of the vibration and buckling responses to variations in the different lamination and material parameters of the plate. A Duhamel-Neumann-type constitutive model is used, and the material properties are assumed to be independent of temperature. Numerical results are presented, showing the effects of variations in the material characteristics and fiber orientation of different layers, as well as the effect of initial thermal deformation on the vibrational and buckling responses of the plate.

Observations and models of Co- and Post-Seismic Deformation Due to the 2015 Mw 7.8 Gorkha (Nepal) Earthquake

NASA Astrophysics Data System (ADS)

Wang, K.; Fialko, Y. A.

2016-12-01

The 2015 Mw 7.8 Gorkha (Nepal) earthquake occurred along the central Himalayan arc, a convergent boundary between India and Eurasian plates. We use space geodetic data to investigate co- and post-seismic deformation due to the Gorkha earthquake. Because the epicentral area of the earthquake is characterized by strong variations in surface relief and material properties, we developed finite element models that explicitly account for topography and 3-D elastic structure. Compared with slip models obtained using homogenous elastic half-space models, the model including elastic heterogeneity and topography exhibits greater (up to 10%) slip amplitude. GPS observations spanning more than 1 year following the earthquake show overall southward movement and uplift after the Gorkha earthquake, qualitatively similar to the coseismic deformation pattern. Kinematic inversions of GPS data, and forward modeling of stress-driven creep indicate that the observed post-seismic transient is consistent with afterslip on a down-dip extention of the seismic rupture. The Main Himalayan Thrust (MHT) has negligible creep updip of the 2015 rupture, reiterating a future seismic hazard. A poro-elastic rebound may contribute to the observed uplift southward motion, but the predicted surface displacements are small (on the order of 1 cm or less). We also tested a wide range of visco-elastic relaxation models, including 1-D and 3-D variations in the viscosity structure. All tested visco-elastic models predict the opposite signs of horizontal and vertical displacements compared to those observed. Available surface deformation data allow one to rule out a model of a low viscosity channel beneath Tibetan Plateau invoked to explain variations in surface relief at the plateau margins.

Elastic effects on vibration of bilayer graphene sheets incorporating integrated VdWs interactions

NASA Astrophysics Data System (ADS)

Kamali, Kamran; Nazemnezhad, Reza; Zare, Mojtaba

2018-03-01

The following study addresses the free vibration analysis of a bilayer graphene sheet (BLGS) embedded in an elastic medium in the presence of shear and tensile-compressive effects of van der Waals (vdWs) interactions. To ascertain the contribution of each force, the effects are considered separately and simultaneously. To model the geometry of the BLGS, the sandwich plate theory and the Hamilton’s principle are considered to derive the governing equations of motion. The Harmonic differential quadrature method is applied to solve the coupled equations and obtain the natural frequencies and related mode shapes. The results reveal that the contribution of tensile-compressive modulus of elastic medium is the most in changing the frequency of BLGSs.

Effect of Substrate Compliance on Measuring Delamination Properties of Elastic Thin Foil

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, C.

Through the analysis of a model problem, a thin elastic plate bonded to an elastic foundation, we address several issues related to the miniature bulge test for measuring the energy-release rate associated with the interfacial fracture of a bimaterial system, where one of the constituents is a thin foil. These issues include the effect of the substrate compliance on the interpretation of the energy release rate, interfacial strength, and the identification of the boundary of the deforming bulge or the location of the interfacial crack front. The analysis done also suggests a way for measuring the so-called foundation modulus, whichmore » characterizes the property of the substrate. An experimental example, a stainless steel thin foil bonded to an aluminum substrate through hot-isostatic-pressing (HIP), is used to illustrate and highlight some of the conclusions of the model analysis.« less

Effect of Substrate Compliance on Measuring Delamination Properties of Elastic Thin Foil

DOE PAGES

Liu, C.

2018-03-20

Through the analysis of a model problem, a thin elastic plate bonded to an elastic foundation, we address several issues related to the miniature bulge test for measuring the energy-release rate associated with the interfacial fracture of a bimaterial system, where one of the constituents is a thin foil. These issues include the effect of the substrate compliance on the interpretation of the energy release rate, interfacial strength, and the identification of the boundary of the deforming bulge or the location of the interfacial crack front. The analysis done also suggests a way for measuring the so-called foundation modulus, whichmore » characterizes the property of the substrate. An experimental example, a stainless steel thin foil bonded to an aluminum substrate through hot-isostatic-pressing (HIP), is used to illustrate and highlight some of the conclusions of the model analysis.« less

Drainage fracture networks in elastic solids with internal fluid generation

NASA Astrophysics Data System (ADS)

Kobchenko, Maya; Hafver, Andreas; Jettestuen, Espen; Galland, Olivier; Renard, François; Meakin, Paul; Jamtveit, Bjørn; Dysthe, Dag K.

2013-06-01

Experiments in which CO2 gas was generated by the yeast fermentation of sugar in an elastic layer of gelatine gel confined between two glass plates are described and analyzed theoretically. The CO2 gas pressure causes the gel layer to fracture. The gas produced is drained on short length scales by diffusion and on long length scales by flow in a fracture network, which has topological properties that are intermediate between river networks and hierarchical-fracture networks. A simple model for the experimental system with two parameters that characterize the disorder and the intermediate (river-fracture) topology of the network was developed and the results of the model were compared with the experimental results.

Hydrodynamic instability of elastic-plastic solid plates at the early stage of acceleration.

PubMed

Piriz, A R; Sun, Y B; Tahir, N A

2015-03-01

A model is presented for the linear Rayleigh-Taylor instability taking place at the early stage of acceleration of an elastic-plastic solid, when the shock wave is still running into the solid and is driven by a time varying pressure on the interface. When the the shock is formed sufficiently close to the interface, this stage is considered to follow a previous initial phase controlled by the Ritchmyer-Meshkov instability that settles new initial conditions. The model reproduces the behavior of the instability observed in former numerical simulation results and provides a relatively simpler physical picture than the currently existing one for this stage of the instability evolution.

The influence of primary and secondary orientations on the elastic response of a nickel-base single-crystal superalloy

NASA Technical Reports Server (NTRS)

Abdul-Aziz, Ali; Kalluri, Sreeramesh; Mcgaw, Michael A.

1993-01-01

The influence of primary orientation on the elastic response of a (001)-oriented nickel-base single-crystal superalloy, PWA 1480, was investigated under mechanical, thermal, and combined thermal and mechanical loading conditions using finite element techniques. Elastic stress analyses were performed using the MARC finite element code on a square plate of PWA 1480 material. Primary orientation of the single crystal superalloy was varied in increments of 2 deg, from 0 to 10 deg, from the (001) direction. Two secondary orientations (0 and 45 deg) were considered, with respect to the global coordinate system, as the primary orientation angle was varied. The stresses developed within the single crystal plate were determined for each loading condition. In this paper, the influence of the angular offset between the primary crystal orientation and the loading direction on the elastic stress response of the PWA 1480 plate is presented for different loading conditions. The influence of primary orientation angle, when constrained between the bounds considered, was not found to be as significant as the influence of the secondary orientation angle, which is not typically controlled.

Elastic-plastic models for multi-site damage

NASA Technical Reports Server (NTRS)

Actis, Ricardo L.; Szabo, Barna A.

1994-01-01

This paper presents recent developments in advanced analysis methods for the computation of stress site damage. The method of solution is based on the p-version of the finite element method. Its implementation was designed to permit extraction of linear stress intensity factors using a superconvergent extraction method (known as the contour integral method) and evaluation of the J-integral following an elastic-plastic analysis. Coarse meshes are adequate for obtaining accurate results supported by p-convergence data. The elastic-plastic analysis is based on the deformation theory of plasticity and the von Mises yield criterion. The model problem consists of an aluminum plate with six equally spaced holes and a crack emanating from each hole. The cracks are of different sizes. The panel is subjected to a remote tensile load. Experimental results are available for the panel. The plasticity analysis provided the same limit load as the experimentally determined load. The results of elastic-plastic analysis were compared with the results of linear elastic analysis in an effort to evaluate how plastic zone sizes influence the crack growth rates. The onset of net-section yielding was determined also. The results show that crack growth rate is accelerated by the presence of adjacent damage, and the critical crack size is shorter when the effects of plasticity are taken into consideration. This work also addresses the effects of alternative stress-strain laws: The elastic-ideally-plastic material model is compared against the Ramberg-Osgood model.

Static response of deformable microchannels

NASA Astrophysics Data System (ADS)

Christov, Ivan C.; Sidhore, Tanmay C.

2017-11-01

Microfluidic channels manufactured from PDMS are a key component of lab-on-a-chip devices. Experimentally, rectangular microchannels are found to deform into a non-rectangular cross-section due to fluid-structure interactions. Deformation affects the flow profile, which results in a nonlinear relationship between the volumetric flow rate and the pressure drop. We develop a framework, within the lubrication approximation (l >> w >> h), to self-consistently derive flow rate-pressure drop relations. Emphasis is placed on handling different types of elastic response: from pure plate-bending, to half-space deformation, to membrane stretching. The ``simplest'' model (Stokes flow in a 3D rectangular channel capped with a linearly elastic Kirchhoff-Love plate) agrees well with recent experiments. We also simulate the static response of such microfluidic channels under laminar flow conditions using ANSYSWorkbench. Simulations are calibrated using experimental flow rate-pressure drop data from the literature. The simulations provide highly resolved deformation profiles, which are difficult to measure experimentally. By comparing simulations, experiments and our theoretical models, we show good agreement in many flow/deformation regimes, without any fitting parameters.

The role of surface elasticity in liquid film formation

NASA Astrophysics Data System (ADS)

Champougny, Lorene; Scheid, Benoit; Restagno, Frederic; Rio, Emmanuelle; Laboratoire de Physique des Solides Team; TIPS-Fluid Physics Unit Team

2014-11-01

The formation of thin liquid films, either free standing (soap films) or deposited on a solid substrate (coated films), is of utmost importance for many applications, ranging from the control of foam stability to surface functionalization. In this work, the behavior of thin liquid films during their generation from a surfactant solution is investigated through comparison between a hydrodynamic model including surface elasticity and experiments. ``Twin'' models are proposed to describe the coating of films onto a solid plate (Landau-Levich-Derjaguin configuration) as well as soap film pulling (Frankel configuration) in a single framework. Experimental data are successfully fitted using the models, surface elasticity being the only adjustable parameter. For a given surfactant solution, the analyses of soap and coated films both yield the same value for the effective surface elasticity, showing that it is an intrinsic parameter of a surfactant solution. Conversely, we demonstrate that Frankel- or Landau-Levich-like experiments can be used in practice as surface rheometers to determine the numerical value of the (effective) surface elasticity of a solution, especially for values lower than those measurable by classical devices. L.C. was supported by ANR F2F. B.S. thanks the F.R.S.-FNRS for funding as well as the IAP-MicroMAST project.

Critical Compressive Stress for Flat Rectangular Plates Supported Along All Edges and Elastically Restrained Against Rotation along the Unloaded Edges

NASA Technical Reports Server (NTRS)

Lundquist, Eugene E; Stowell, Elbridge Z

1942-01-01

A chart is presented for the values of the coefficient in the formula for the critical compressive stress at which buckling may be expected to occur in flat rectangular plates supported along all edges and, in addition, elastically restrained against rotation along the unloaded edges. The mathematical derivations of the formulas required in the construction of the chart are given.

Elastic plate spallation

NASA Technical Reports Server (NTRS)

Oline, L.; Medaglia, J.

1972-01-01

The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.

A finite difference analysis of the field present behind an acoustically impenetrable two-layer barrier.

PubMed

Hurrell, Andrew M

2008-06-01

The interaction of an incident sound wave with an acoustically impenetrable two-layer barrier is considered. Of particular interest is the presence of several acoustic wave components in the shadow region of this barrier. A finite difference model capable of simulating this geometry is validated by comparison to the analytical solution for an idealized, hard-soft barrier. A panel comprising a high air-content closed cell foam backed with an elastic (metal) back plate is then examined. The insertion loss of this panel was found to exceed the dynamic range of the measurement system and was thus acoustically impenetrable. Experimental results from such a panel are shown to contain artifacts not present in the diffraction solution, when acoustic waves are incident upon the soft surface. A finite difference analysis of this experimental configuration replicates the presence of the additional field components. Furthermore, the simulated results allow the additional components to be identified as arising from the S(0) and A(0) Lamb modes traveling in the elastic plate. These Lamb mode artifacts are not found to be present in the shadow region when the acoustic waves are incident upon the elastic surface.

Spatiotemporal stick-slip phenomena in a coupled continuum-granular system

NASA Astrophysics Data System (ADS)

Ecke, Robert

In sheared granular media, stick-slip behavior is ubiquitous, especially at very small shear rates and weak drive coupling. The resulting slips are characteristic of natural phenomena such as earthquakes and well as being a delicate probe of the collective dynamics of the granular system. In that spirit, we developed a laboratory experiment consisting of sheared elastic plates separated by a narrow gap filled with quasi-two-dimensional granular material (bi-dispersed nylon rods) . We directly determine the spatial and temporal distributions of strain displacements of the elastic continuum over 200 spatial points located adjacent to the gap. Slip events can be divided into large system-spanning events and spatially distributed smaller events. The small events have a probability distribution of event moment consistent with an M - 3 / 2 power law scaling and a Poisson distributed recurrence time distribution. Large events have a broad, log-normal moment distribution and a mean repetition time. As the applied normal force increases, there are fractionally more (less) large (small) events, and the large-event moment distribution broadens. The magnitude of the slip motion of the plates is well correlated with the root-mean-square displacements of the granular matter. Our results are consistent with mean field descriptions of statistical models of earthquakes and avalanches. We further explore the high-speed dynamics of system events and also discuss the effective granular friction of the sheared layer. We find that large events result from stored elastic energy in the plates in this coupled granular-continuum system.

Polynomial decay rate of a thermoelastic Mindlin-Timoshenko plate model with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-02-01

In this article, we are concerned with the polynomial stabilization of a two-dimensional thermoelastic Mindlin-Timoshenko plate model with no mechanical damping. The model is subject to Dirichlet boundary conditions on the elastic as well as the thermal variables. The work complements our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 64:1305-1325, 2013) on the polynomial stabilization of a Mindlin-Timoshenko model in a radially symmetric domain under Dirichlet boundary conditions on the displacement and thermal variables and free boundary conditions on the shear angle variables. In particular, our aim is to investigate the effect of the Dirichlet boundary conditions on all the variables on the polynomial decay rate of the model. By once more applying a frequency domain method in which we make critical use of an inequality for the trace of Sobolev functions on the boundary of a bounded, open connected set we show that the decay is slower than in the model considered in the cited work. A comparison of our result with our polynomial decay result for a magnetoelastic Mindlin-Timoshenko model subject to Dirichlet boundary conditions on the elastic variables in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) also indicates a correlation between the robustness of the coupling between parabolic and hyperbolic dynamics and the polynomial decay rate in the two models.

Investigations of thickness-shear mode elastic constant and damping of shunted piezoelectric materials with a coupling resonator

NASA Astrophysics Data System (ADS)

Hu, Ji-Ying; Li, Zhao-Hui; Sun, Yang; Li, Qi-Hu

2016-12-01

Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode (TSM) elastic constant and the mechanical loss factor can change correspondingly when piezoelectric materials are shunted to different electrical circuits. This phenomenon makes it possible to control the performance of a shear-mode piezoelectric damping system through designing the shunt circuit. However, due to the difficulties in directly measuring the TSM elastic constant and the mechanical loss factor of piezoelectric materials, the relationships between those parameters and the shunt circuits have rarely been investigated. In this paper, a coupling TSM electro-mechanical resonant system is proposed to indirectly measure the variations of the TSM elastic constant and the mechanical loss factor of piezoelectric materials. The main idea is to transform the variations of the TSM elastic constant and the mechanical loss factor into the changes of the easily observed resonant frequency and electrical quality factor of the coupling electro-mechanical resonator. Based on this model, the formular relationships are set up theoretically with Mason equivalent circuit method and they are validated with finite element (FE) analyses. Finally, a prototype of the coupling electro-mechanical resonator is fabricated with two shear-mode PZT5A plates to investigate the TSM elastic constants and the mechanical loss factors of different circuit-shunted cases of the piezoelectric plate. Both the resonant frequency shifts and the bandwidth changes observed in experiments are in good consistence with the theoretical and FE analyses under the same shunt conditions. The proposed coupling resonator and the obtained relationships are validated with but not limited to PZT5A. Project supported by the National Defense Foundation of China (Grant No. 9149A12050414JW02180).

Experimental investigation of Rayleigh Taylor instability in elastic-plastic materials

NASA Astrophysics Data System (ADS)

Haley, Aaron Alan; Banerjee, Arindam

2010-11-01

The interface of an elastic-plastic plate accelerated by a fluid of lower density is Rayleigh Taylor (RT) unstable, the growth being mitigated by the mechanical strength of the plate. The instability is observed when metal plates are accelerated by high explosives, in explosive welding, and in volcanic island formation due to the strength of the inner crust. In contrast to the classical case involving Newtonian fluids, RT instability in accelerated solids is not well understood. The difficulties for constructing a theory for the linear growth phase in solids is essentially due to the character of elastic-plastic constitutive properties which has a nonlinear dependence on the magnitude of the rate of deformation. Experimental investigation of the phenomena is difficult due to the exceedingly small time scales (in high energy density experiments) and large measurement uncertainties of material properties. We performed experiments on our Two-Wheel facility to study the linear stage of the incompressible RT instability in elastic-plastic materials (yogurt) whose properties were well characterized. Rotation of the wheels imparted a constant centrifugal acceleration on the material interface that was cut with a small sinusoidal ripple. The controlled initial conditions and precise acceleration amplitudes are levied to investigate transition from elastic to plastic deformation and allow accurate and detailed measurements of flow properties.

The elasticity and failure of fluid-filled cellular solids: Theory and experiment

NASA Astrophysics Data System (ADS)

Warner, M.; Thiel, B. L.; Donald, A. M.

2000-02-01

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials.

The elasticity and failure of fluid-filled cellular solids: theory and experiment.

PubMed

Warner, M; Thiel, B L; Donald, A M

2000-02-15

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials.

The elasticity and failure of fluid-filled cellular solids: Theory and experiment

PubMed Central

Warner, M.; Thiel, B. L.; Donald, A. M.

2000-01-01

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials. PMID:10660680

Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology. Appendix C -- Finite Element Models Solution Database File, Appendix D -- Benchmark Finite Element Models Solution Database File

NASA Technical Reports Server (NTRS)

Allen, Phillip A.; Wells, Douglas N.

2013-01-01

No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.

Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology

NASA Technical Reports Server (NTRS)

Allen, P. A.; Wells, D. N.

2013-01-01

No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.

Active vibration control of thin-plate structures with partial SCLD treatment

NASA Astrophysics Data System (ADS)

Lu, Jun; Wang, Pan; Zhan, Zhenfei

2017-02-01

To effectively suppress the low-frequency vibration of a thin-plate, the strategy adopted is to develop a model-based approach to the investigation on the active vibration control of a clamped-clamped plate with partial SCLD treatment. Firstly, a finite element model is developed based on the constitutive equations of elastic, piezoelectric and viscoelastic materials. The characteristics of viscoelastic materials varying with temperature and frequency are described by GHM damping model. A low-dimensional real modal control model which can be used as the basis for active vibration control is then obtained from the combined reduction. The emphasis is placed on the feedback control system to attenuate the vibration of plates with SCLD treatments. A modal controller in conjunction with modal state estimator is designed to solve the problem of full state feedback, making it much more feasible to real-time control. Finally, the theoretical model is verified by modal test, and an active vibration control is validated by hardware-in-the-loop experiment under different external excitations. The numerical and experimental study demonstrate how the piezoelectric actuators actively control the lower modes (first bending and torsional modes) using modal controller, while the higher frequency vibration attenuated by viscoelastic passive damping layer.

Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

NASA Astrophysics Data System (ADS)

McGee, O. G.; Kim, J. W.

2010-02-01

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of " edge functions" that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1- c/ a), and the notch angle is defined as (360°- α). For a very small notch angle (1° or less), the notch may be regarded as a "sharp radial crack." Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°- α), depths (1- c/ a), and thickness ratios ( a/ h for plates and h/ a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and segmented plates and cylinders are also reported herein as interesting special cases. A generalization of the elasticity-based Ritz analysis and findings applicable here is an arbitrarily shaped V-notched cylindrical solid, being a surface traced out by a family of generatrix, which pass through the circumference of an arbitrarily shaped V-notched directrix curve, r( θ), several of which are described for future investigations and close extensions of this work.

Greenland GPS network: Measurements and Models of 3D Elastic deformation

NASA Astrophysics Data System (ADS)

Khan, S. A.; van Dam, T. M.; Bevis, M. G.; Sasgen, I.; Bamber, J. L.; Helm, V.; Bjork, A. A.; Liu, L.; Kjaer, K. H.; Knudsen, P.; Kjeldsen, K. K.

2017-12-01

The Greenland GPS Network (GNET) uses the Global Positioning System (GPS) to measure the displacement of bedrock exposed near the margins of the Greenland ice sheet. The entire network is uplifting in response to past and present-day changes in ice mass. Here, we focus on present-day changes and compare measurements with models. To retrieve 3D elastic displacements from GPS time series, we correct our observations for glacial-isostatic adjustment and tectonic plate motion, and study the effect of the underlying mantle viscosity, ice load history and Euler parameters. To model 3D elastic displacements, we first estimate mass loss using 1995-2014 NASA's Airborne Topographic Mapper (ATM) flights derived altimetry, supplemented with laser altimetry observations from the Ice, Cloud, and Land Elevation Satellite (ICESat) during 2003-2009; the airborne Land, Vegetation, and Ice Sensor (LVIS) instrument during 2007-2013; radar altimetry from the CryoSat-2 satellite during 2010-2017; and European Remote-Sensing Satellite-1 (ERS-1) and ERS-2 data during 1995-2003. We converted the volume loss rate into a mass loss rate accounting for firn compaction as described by Kuipers Munneke et al. (2015). We predict the elastic displacements by convolving mass loss estimates with Green's functions for vertical and horizontal displacements. We use a variety of elastic Green's functions and mass change grid resolutions, respectively, to study the sensitivity of 3D elastic deformation on Earth model parameters different from the Preliminary Reference Earth Reference Model (PREM; Dziewonski & Anderson 1981) and the forcing ice load.

Stress and strain concentration at a circular hole in an infinite plate

NASA Technical Reports Server (NTRS)

Stowell, Elbridge Z

1950-01-01

The theory of elasticity shows that the maximum stress at a circular hole in an infinite plate in tension is three times the applied stress when the material remains elastic. The effect of plasticity of the material is to lower this ratio. This paper considers the theoretical problem of the stress distribution in an infinitely large sheet with a circular hole for the general case where the material may have any stress-strain curve. The plate is assumed to be under uniform tension at a large distance from the hole. The material is taken to be isotropic and incompressible. (author)

A coupled-mode model for the hydroelastic analysis of large floating bodies over variable bathymetry regions

NASA Astrophysics Data System (ADS)

Belibassakis, K. A.; Athanassoulis, G. A.

2005-05-01

The consistent coupled-mode theory (Athanassoulis & Belibassakis, J. Fluid Mech. vol. 389, 1999, p. 275) is extended and applied to the hydroelastic analysis of large floating bodies of shallow draught or ice sheets of small and uniform thickness, lying over variable bathymetry regions. A parallel-contour bathymetry is assumed, characterized by a continuous depth function of the form h( {x,y}) {=} h( x ), attaining constant, but possibly different, values in the semi-infinite regions x {<} a and x {>} b. We consider the scattering problem of harmonic, obliquely incident, surface waves, under the combined effects of variable bathymetry and a floating elastic plate, extending from x {=} a to x {=} b and {-} infty {<} y{<}infty . Under the assumption of small-amplitude incident waves and small plate deflections, the hydroelastic problem is formulated within the context of linearized water-wave and thin-elastic-plate theory. The problem is reformulated as a transition problem in a bounded domain, for which an equivalent, Luke-type (unconstrained), variational principle is given. In order to consistently treat the wave field beneath the elastic floating plate, down to the sloping bottom boundary, a complete, local, hydroelastic-mode series expansion of the wave field is used, enhanced by an appropriate sloping-bottom mode. The latter enables the consistent satisfaction of the Neumann bottom-boundary condition on a general topography. By introducing this expansion into the variational principle, an equivalent coupled-mode system of horizontal equations in the plate region (a {≤} x {≤} b) is derived. Boundary conditions are also provided by the variational principle, ensuring the complete matching of the wave field at the vertical interfaces (x{=}a and x{=}b), and the requirements that the edges of the plate are free of moment and shear force. Numerical results concerning floating structures lying over flat, shoaling and corrugated seabeds are presented and compared, and the effects of wave direction, bottom slope and bottom corrugations on the hydroelastic response are presented and discussed. The present method can be easily extended to the fully three-dimensional hydroelastic problem, including bodies or structures characterized by variable thickness (draught), flexural rigidity and mass distributions.

Towards a Millennial Time-scale Vertical Deformation Field in Taiwan

NASA Astrophysics Data System (ADS)

Bordovaos, P. A.; Johnson, K. M.

2015-12-01

Pete Bordovalos and Kaj M. Johnson To better understand the feedbacks between erosion and deformation in Taiwan, we need constraints on the millennial time-scale vertical field. Dense GPS and leveling data sets in Taiwan provide measurements of the present-day vertical deformation field over the entire Taiwan island. However, it is unclear how much of this vertical field is transient (varies over earthquake cycle) or steady (over millennial time scale). A deformation model is required to decouple transient from steady deformation. This study takes a look at how the 82 mm/yr of convergence motion between the Eurasian plate and the Philippine Sea plate is distributed across the faults on Taiwan. We build a plate flexure model that consists of all known active faults and subduction zones cutting through an elastic plate supported by buoyancy. We use horizontal and vertical GPS data, leveling data, and geologic surface uplift rates with a Monte Carlo probabilistic inversion method to infer fault slip rates and locking depths on all faults. Using our model we examine how different fault geometries influence the estimates of distribution of slip along faults and deformation patterns.

Aeroelastic Studies of a Rectangular Wing with a Hole: Correlation of Theory and Experiment

NASA Technical Reports Server (NTRS)

Conyers, Howard J.; Dowell, Earl H.; Hall, Kenneth C.

2010-01-01

Two rectangular wing models with a hole have been designed and tested in the Duke University wind tunnel to better understand the effects of damage. A rectangular hole is used to simulate damage. The wing with a hole is modeled structurally as a thin elastic plate using the finite element method. The unsteady aerodynamics of the plate-like wing with a hole is modeled using the doublet lattice method. The aeroelastic equations of motion are derived using Lagrange's equation. The flutter boundary is found using the V-g method. The hole's location effects the wing's mass, stiffness, aerodynamics and therefore the aeroelastic behavior. Linear theoretical models were shown to be capable of predicting the critical flutter velocity and frequency as verified by wind tunnel tests.

Tensile behaviors of three-dimensionally free-formable titanium mesh plates for bone graft applications

NASA Astrophysics Data System (ADS)

He, Jianmei

2017-11-01

Present metal artificial bones for bone grafts have the problems like too heavy and excessive elastic modulus compared with natural bones. In this study, three-dimensionally (3D) free-formable titanium mesh plates for bone graft applications was introduced to improve these problems. Fundamental mesh shapes and patterns were designed under different base shapes and design parameters through three dimensional CAD tools from higher flexibility and strength points of view. Based on the designed mesh shape and patterns, sample specimens of titanium mesh plates with different base shapes and design variables were manufactured through laser processing. Tensile properties of the sample titanium mesh plates like volume density, tensile elastic modulus were experimentally and analytically evaluated. Experimental results showed that such titanium mesh plates had much higher flexibility and their mechanical properties could be controlled to close to the natural bones. More details on the mechanical properties of titanium mesh plates including compression, bending, torsion and durability will be carried out in future study.

A variable-order laminated plate theory based on the variational-asymptotical method

NASA Technical Reports Server (NTRS)

Lee, Bok W.; Sutyrin, Vladislav G.; Hodges, Dewey H.

1993-01-01

The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.

Analysis of a monolithic crystal plate acoustic wave filter.

PubMed

He, Huijing; Liu, Jinxi; Yang, Jiashi

2011-12-01

We study thickness-shear and thickness-twist vibrations of a finite, monolithic, AT-cut quartz plate crystal filter with two pairs of electrodes. The equations of anisotropic elasticity are used with the omission of the small elastic constant c(56). An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and the vibration confinement due to the electrode inertia are calculated and examined. Copyright © 2011 Elsevier B.V. All rights reserved.

A Proposal of Monitoring and Forecasting Method for Crustal Activity in and around Japan with 3-dimensional Heterogeneous Medium Using a Large-scale High-fidelity Finite Element Simulation

NASA Astrophysics Data System (ADS)

Hori, T.; Agata, R.; Ichimura, T.; Fujita, K.; Yamaguchi, T.; Takahashi, N.

2017-12-01

Recently, we can obtain continuous dense surface deformation data on land and partly on the sea floor, the obtained data are not fully utilized for monitoring and forecasting of crustal activity, such as spatio-temporal variation in slip velocity on the plate interface including earthquakes, seismic wave propagation, and crustal deformation. For construct a system for monitoring and forecasting, it is necessary to develop a physics-based data analysis system including (1) a structural model with the 3D geometry of the plate inter-face and the material property such as elasticity and viscosity, (2) calculation code for crustal deformation and seismic wave propagation using (1), (3) inverse analysis or data assimilation code both for structure and fault slip using (1) & (2). To accomplish this, it is at least necessary to develop highly reliable large-scale simulation code to calculate crustal deformation and seismic wave propagation for 3D heterogeneous structure. Unstructured FE non-linear seismic wave simulation code has been developed. This achieved physics-based urban earthquake simulation enhanced by 1.08 T DOF x 6.6 K time-step. A high fidelity FEM simulation code with mesh generator has also been developed to calculate crustal deformation in and around Japan with complicated surface topography and subducting plate geometry for 1km mesh. This code has been improved the code for crustal deformation and achieved 2.05 T-DOF with 45m resolution on the plate interface. This high-resolution analysis enables computation of change of stress acting on the plate interface. Further, for inverse analyses, waveform inversion code for modeling 3D crustal structure has been developed, and the high-fidelity FEM code has been improved to apply an adjoint method for estimating fault slip and asthenosphere viscosity. Hence, we have large-scale simulation and analysis tools for monitoring. We are developing the methods for forecasting the slip velocity variation on the plate interface. Although the prototype is for elastic half space model, we are applying it for 3D heterogeneous structure with the high-fidelity FE model. Furthermore, large-scale simulation codes for monitoring are being implemented on the GPU clusters and analysis tools are developing to include other functions such as examination in model errors.

Numerical investigation of the effects of compressibility on the flutter of a cantilevered plate in an inviscid, subsonic, open flow

NASA Astrophysics Data System (ADS)

Colera, Manuel; Pérez-Saborid, Miguel

2018-06-01

We have carried out a numerical study of the influence of the upstream Mach number on the flutter of a two-dimensional, cantilevered, flexible plate subject to a subsonic, inviscid, open flow. We have assumed a linear elastic model for the plate and that the fluid flow is governed by the linearized potential theory. The fluid equations are solved with a novel frequency-domain, finite differences method to obtain the generalized aerodynamic forces as a function of the plate displacements. Then, these generalized forces are coupled to the equation of motion of the plate and an eigenvalue analysis is performed to find the flutter point. The obtained results are in good agreement with those of related theoretical and experimental studies found in the literature. To the best of our knowledge, the analysis performed here is the first self-consistent, parametric study of the influence of the compressibility on the flutter point of a two-dimensional cantilevered plate in subsonic flow.

A simple nonlinear element model

NASA Astrophysics Data System (ADS)

Mikhailov, S. G.; Rudenko, O. V.

2017-05-01

We study experimentally the behavior of a nonlinear element, a light plate pressed to the opening in the cavity of an acoustic resonator. Measurements of field oscillations inside and outside the cavity have shown that for large amplitudes, they become essentially anharmonic. The time dependences of displacement of the plate with increasing amplitude of the exciting voltage demonstrates a gradual change in the shape of vibrations from harmonic to half-period oscillation. A constant component appears in the cavity: rarefaction or outflow of the medium through the orifice. We construct a theory for nonlinear oscillations of a plate taking into account its different elastic reactions to compression and rarefaction with allowance for monopole radiation by the small-wave-size plate or radiation of a plane wave by the plate. We calculate the amplitudes of the harmonics and solve the problem of low-frequency stationary noise acting on the plate. We obtain expressions for the correlation function and mean power at the output given a normal random process at the input.

Development an efficient calibrated nonlocal plate model for nonlinear axial instability of zirconia nanosheets using molecular dynamics simulation.

PubMed

Sahmani, S; Fattahi, A M

2017-08-01

New ceramic materials containing nanoscaled crystalline phases create a main object of scientific interest due to their attractive advantages such as biocompatibility. Zirconia as a transparent glass ceramic is one of the most useful binary oxides in a wide range of applications. In the present study, a new size-dependent plate model is constructed to predict the nonlinear axial instability characteristics of zirconia nanosheets under axial compressive load. To accomplish this end, the nonlocal continuum elasticity of Eringen is incorporated to a refined exponential shear deformation plate theory. A perturbation-based solving process is put to use to derive explicit expressions for nonlocal equilibrium paths of axial-loaded nanosheets. After that, some molecular dynamics (MD) simulations are performed for axial instability response of square zirconia nanosheets with different side lengths, the results of which are matched with those of the developed nonlocal plate model to capture the proper value of nonlocal parameter. It is demonstrated that the calibrated nonlocal plate model with nonlocal parameter equal to 0.37nm has a very good capability to predict the axial instability characteristics of zirconia nanosheets, the accuracy of which is comparable with that of MD simulation. Copyright © 2017 Elsevier Inc. All rights reserved.

Micromechanics of Ultrafine Particle Adhesion—Contact Models

NASA Astrophysics Data System (ADS)

Tomas, Jürgen

2009-06-01

Ultrafine, dry, cohesive and compressible powders (particle diameter d<10 μm) show a wide variety of flow problems that cause insufficient apparatus and system reliability of processing plants. Thus, the understanding of the micromechanics of particle adhesion is essential to assess the product quality and to improve the process performance in particle technology. Comprehensive models are shown that describe the elastic-plastic force-displacement and frictional moment-angle behavior of adhesive contacts of isotropic smooth spheres. By the model stiff particles with soft contacts, a sphere-sphere interaction of van der Waals forces without any contact deformation describes the stiff attractive term. But, the soft micro-contact response generates a flattened contact, i.e. plate-plate interaction, and increasing adhesion. These increasing adhesion forces between particles directly depend on this frozen irreversible deformation. Thus, the adhesion force is found to be load dependent. It contributes to the tangential forces in an elastic-plastic frictional contact with partially sticking and micro-slip within the contact plane. The load dependent rolling resistance and torque of mobilized frictional contact rotation (spin around its principal axis) are also shown. This reasonable combination of particle contact micromechanics and powder continuum mechanics is used to model analytically the macroscopic friction limits of incipient powder consolidation, yield and cohesive steady-state shear flow on physical basis.

A Linear Theory for Inflatable Plates of Arbitrary Shape

NASA Technical Reports Server (NTRS)

McComb, Harvey G., Jr.

1961-01-01

A linear small-deflection theory is developed for the elastic behavior of inflatable plates of which Airmat is an example. Included in the theory are the effects of a small linear taper in the depth of the plate. Solutions are presented for some simple problems in the lateral deflection and vibration of constant-depth rectangular inflatable plates.

On the Behavior of Pliable Plate Dynamics in Wind: Application to Vertical Axis Wind Turbines

NASA Astrophysics Data System (ADS)

Cosse, Julia Theresa

Numerous studies have shown that flexible materials improve resilience and durability of a structure. Several studies have investigated the behavior of elastic plates under the influence of a free stream, such as studies of the fluttering flag and others of shape reconfiguration, due to a free stream. The principle engineering contribution of this thesis is the design and development of a vertical axis wind turbine that features pliable blades which undergo various modes of behavior, ultimately leading to rotational propulsion of the turbine. The wind turbine design was tested in a wind tunnel and at the Caltech Laboratory for Optimized Wind Energy. Ultimately, the flexible blade vertical axis wind turbine proved to be an effective way of harnessing the power of the wind. In addition, this body of work builds on the current knowledge of elastic cantilever plates in a free stream flow by investigating the inverted flag. While previous studies have focused on the fluid structure interaction of a free stream on elastic cantilever plates, none had studied the plate configuration where the trailing edge was clamped, leaving the leading edge free to move. Furthermore, the studies presented in this thesis establish the geometric boundaries of where the large-amplitude flapping occurs.

Lithospheric Structure and Isostasy of Central Andes: Implication for plate Coupling

NASA Astrophysics Data System (ADS)

Mahatsente, R.; Rutledge, S.

2017-12-01

A significant section of the Peru-Chile convergent zone is building up stresses. The interseismic coupling in northern and southern Peru is significantly high indicating, elastic energy accumulation since the 1746 and 1868 earthquakes of magnitude 8.6 and 8.8 , respectively. Similar seismic patterns have also been observed in Central Chile. The plate interface beneath Central Chile is highly coupled, and the narrow zones of low coupling separate seismic gaps. The reasons for the seismic gaps and plate coupling are yet unknown, but the configuration of the slab is thought to be the main factor. Here, we assessed the locking mechanism and isostatic state of the Central Andes based on gravity models of the crust and upper mantle structure. The density models are based on satellite gravity data and are constrained by velocity models and earthquake hypocenters. The gravity models indicate a high-density batholithic structure in the fore-arc, overlying the subducting Nazca plate. This high-density body pushes downward on the slab, causing the slab to lock with the overlying continental plate. The increased compressive stress closer to the trench, due to the increased contact area between the subducting and overriding plates, may have increased the plate coupling in the Central Andes. Thus, trench parallel crustal thickness and density variations along the Central Andes and buoyancy force on the subducting Nazca plate may control plate coupling and asperity generation. The western part of the Central Andes may be undercompensated. There is a residual topography of 800 m in the western part of the Central Andes that cannot be explained by the observed crustal thicknesses. Thus, part of the observed topography in the western part of the Central Andes may be dynamically supported by mantle wedge flow below the overriding plate.

A study of elastic and plastic stress concentration factors due to notches and fillets in flat plates

NASA Technical Reports Server (NTRS)

Hardrath, Herbert F; Ohman, Lachlan

1953-01-01

Six large 24s-t3 aluminum-alloy-sheet specimens containing various notches or fillets were tested in tension to determine their stress concentration factors in both the elastic and plastic ranges. The elastic stress concentration factors were found to be slightly higher than those calculated by Neuber's method and those obtained photoelastically by Frocht. The results showed further that the stress concentration factor decreases as strains at the discontinuity enter the plastic range. A generalization of Stowell's relation for the plastic stress concentration factor at a circular hole in an infinite plate was applied to the specimen shapes tested and gave good agreement with test results.

Nonlinear dispersion effects in elastic plates: numerical modelling and validation

NASA Astrophysics Data System (ADS)

Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.

Effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures: A paradigm in three dimensions

PubMed Central

Ovtchinnikov, Evgueni E.; Xanthis, Leonidas S.

2000-01-01

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickness is small. In this paper we show an effective way of resolving this difficulty by invoking a special preconditioning technique associated with the effective dimensional reduction algorithm (EDRA). As an example, we present an algorithm for computing the minimal eigenvalue of a thin elastic plate and we show both theoretically and numerically that it is robust with respect to both the thickness and discretization parameters, i.e. the convergence does not deteriorate with diminishing thickness or mesh refinement. This robustness is sine qua non for the efficient computation of large-scale eigenvalue problems for thin elastic structures. PMID:10655469

A Low Frequency FBG Accelerometer with Symmetrical Bended Spring Plates.

PubMed

Liu, Fufei; Dai, Yutang; Karanja, Joseph Muna; Yang, Minghong

2017-01-22

To meet the requirements for low-frequency vibration monitoring, a new type of FBG (fiber Bragg grating) accelerometer with a bended spring plate is proposed. Two symmetrical bended spring plates are used as elastic elements, which drive the FBG to produce axial strains equal in magnitude but opposite in direction when exciting vibrations exist, leading to doubling the wavelength shift of the FBG. The mechanics model and a numerical method are presented in this paper, with which the influence of the structural parameters on the sensitivity and the eigenfrequency are discussed. The test results show that the sensitivity of the accelerometer is more than 1000 pm/g when the frequency is within the 0.7-20 Hz range.

Star-Shaped Crack Pattern of Broken Windows

NASA Astrophysics Data System (ADS)

Vandenberghe, Nicolas; Vermorel, Romain; Villermaux, Emmanuel

2013-04-01

Broken thin brittle plates like windows and windshields are ubiquitous in our environment. When impacted locally, they typically present a pattern of cracks extending radially outward from the impact point. We study the variation of the pattern of cracks by performing controlled transverse impacts on brittle plates over a broad range of impact speed, plate thickness, and material properties, and we establish from experiments a global scaling law for the number of radial cracks incorporating all these parameters. A model based on Griffith’s theory of fracture combining bending elastic energy and fracture energy accounts for our observations. These findings indicate how the postmortem shape of broken samples are related to material properties and impact parameters, a procedure relevant to forensic science, archaeology, or astrophysics.

Accelerated plate tectonics.

PubMed

Anderson, D L

1975-03-21

The concept of a stressed elastic lithospheric plate riding on a viscous asthenosphere is used to calculate the recurrence interval of great earthquakes at convergent plate boundaries, the separation of decoupling and lithospheric earthquakes, and the migration pattern of large earthquakes along an arc. It is proposed that plate motions accelerate after great decoupling earthquakes and that most of the observed plate motions occur during short periods of time, separated by periods of relative quiescence.

Nonlinear dynamics and control of a vibrating rectangular plate

NASA Technical Reports Server (NTRS)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

Statistical analysis of vibration in tyres

NASA Astrophysics Data System (ADS)

Le Bot, Alain; Bazari, Zakia; Klein, Philippe; Lelong, Joël

2017-03-01

The vibration in tyres submitted to random forces in the contact zone is investigated with the model of prestressed orthotropic plate on visco-elastic foundation. It is shown that beyond a cut-on frequency a single wave propagates whose speed is directional-dependent. A systematic numerical exploration of the governing equation solutions shows that three regimes may exist in such plates. These are modal field, diffuse field and free field. For actual tyres which present a high level of damping, the passage from low to high frequencies generally explores the modal and free field regimes but not the diffuse field regime.

The effects of tibia profile, distraction angle, and knee load on wedge instability and hinge fracture: A finite element study.

PubMed

Weng, Pei-Wei; Chen, Chia-Hsien; Luo, Chu-An; Sun, Jui-Sheng; Tsuang, Yang-Hwei; Cheng, Cheng-Kung; Lin, Shang-Chih

2017-04-01

Several plate systems for high tibial osteotomy (HTO) have been developed to stabilize the opening wedge of an osteotomized tibia. Among them, the TomoFix system, having a quasi-straight and T-shaped design, has been widely adopted in the literature. However, this system is implemented by inserting a lag (i.e., cortical) screw through the proximal combi-hole, to deform the plate and pull the distal tibia toward the plate. This process potentially induces plate springback and creates an elastic preload on the osteotomized tibia, especially at the lateral hinge of the distracted wedge. Using the finite-element method, this study aims to investigate the contoured effect of lag-screw application on the biomechanical behavior of the tibia-plate construct. Two tibial profiles (normal and more concave), three distraction angles (6°, 9°, and 12°), and three knee loads (intraoperative: contouring plate; postoperative: weight and nonweight bearing) are systematically varied in this study. The wedge instability and fracture risk at the lateral hinge are chosen as the comparison indices. The results show the necessity of preoperative planning for a precontoured procedure, rather than elastic deformation using a lag screw. Within the intraoperative period, a more concave tibial profile and/or reduced distraction angle (i.e., 6° or 9°) necessitate a higher compressive load to elastically deform the plate, thereby deteriorating the lateral-hinge fracture risk. A precontoured plate is recommended in the case that the proximal tibia is highly concave and the distraction angle is insufficient to stretch the tibial profile. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Theoretical model of impact damage in structural ceramics

NASA Technical Reports Server (NTRS)

Liaw, B. M.; Kobayashi, A. S.; Emery, A. G.

1984-01-01

This paper presents a mechanistically consistent model of impact damage based on elastic failures due to tensile and shear overloading. An elastic axisymmetric finite element model is used to determine the dynamic stresses generated by a single particle impact. Local failures in a finite element are assumed to occur when the primary/secondary principal stresses or the maximum shear stress reach critical tensile or shear stresses, respectively. The succession of failed elements thus models macrocrack growth. Sliding motions of cracks, which closed during unloading, are resisted by friction and the unrecovered deformation represents the 'plastic deformation' reported in the literature. The predicted ring cracks on the contact surface, as well as the cone cracks, median cracks, radial cracks, lateral cracks, and damage-induced porous zones in the interior of hot-pressed silicon nitride plates, matched those observed experimentally. The finite element model also predicted the uplifting of the free surface surrounding the impact site.

Multigrid finite element method in stress analysis of three-dimensional elastic bodies of heterogeneous structure

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2016-11-01

To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.

Dynamic Stabilization of Simple Fractures With Active Plates Delivers Stronger Healing Than Conventional Compression Plating

PubMed Central

Tsai, Stanley; Bliven, Emily K.; von Rechenberg, Brigitte; Kindt, Philipp; Augat, Peter; Henschel, Julia; Fitzpatrick, Daniel C.; Madey, Steven M.

2017-01-01

Objectives: Active plates dynamize a fracture by elastic suspension of screw holes within the plate. We hypothesized that dynamic stabilization with active plates delivers stronger healing relative to standard compression plating. Methods: Twelve sheep were randomized to receive either a standard compression plate (CP) or an active plate (ACTIVE) for stabilization of an anatomically reduced tibial osteotomy. In the CP group, absolute stabilization was pursued by interfragmentary compression with 6 cortical screws. In the ACTIVE group, dynamic stabilization after bony apposition was achieved with 6 elastically suspended locking screws. Fracture healing was analyzed weekly on radiographs. After sacrifice 9 weeks postsurgery, the torsional strength of healed tibiae and contralateral tibiae was measured. Finally, computed tomography was used to assess fracture patterns and healing modes. Results: Healing in both groups included periosteal callus formation. ACTIVE specimens had almost 6 times more callus area by week 9 (P < 0.001) than CP specimens. ACTIVE specimens recovered on average 64% of their native strength by week 9, and were over twice as strong as CP specimens, which recovered 24% of their native strength (P = 0.008). Microcomputed tomography demonstrated that compression plating induced a combination of primary bone healing and gap healing. Active plating consistently stimulated biological bone healing by periosteal callus formation. Conclusions: Compared with compression plating, dynamic stabilization of simple fractures with active plates delivers significantly stronger healing. PMID:27861456

Large amplitude flexural vibration of thin elastic flat plates and shells

NASA Technical Reports Server (NTRS)

Pandalia, K. A. V.

1972-01-01

The general equations governing the large amplitude flexural vibration of any thin elastic shell using curvilinear orthogonal coordinates are derived and consist of two coupled, nonlinear, partial differential equations in the normal displacement w and the stress function F. From these equations, the governing equations for the case of shells of revolution or flat plates can be readily obtained as special cases. The material of the shell or plate is isotropic and homogeneous and Hooke's law for the two-dimensional case is valid. It is suggested that the difference between the hardening type of nonlinearity in the case of flat plates and straight beams and the softening type of nonlinearity in the case of shells and rings can, in general, be traced to the amount of curvature present in the underformed median surface of the structure concerned.

New System for Measuring Impact Vibration on Floor Decking Sheets

PubMed Central

Moron, Carlos; Garcia, Alfonso; Ferrandez, Daniel

2015-01-01

Currently, there is a narrow range of materials that are used as attenuators of impact noise and building vibrations. Materials used in construction, such as elastic materials, must meet the requirement of having very low elastic modulus values. For the determination of the material's elastic modulus and the acoustic insulation of the same, costly and difficult to execute testing is required. The present paper exposes an alternative system that is simpler and more economic, consisting of a predefined striking device and a sensor able to determine, once the strike is produced, the energy absorbed by the plate. After the impact is produced, the plate undergoes a deformation, which absorbs part of the energy, the remaining part being transmitted to the slab and, at the same time, causing induced airborne noise in the adjoining room. The plate absorbs the power through its own deformation, which is measured with the help of a capacitive sensor. This way, it would be possible to properly define the geometry of the plates, after the execution of the test, and we will try to establish a relationship between the values proposed in this research and the acoustic behavior demanded by the Spanish standards. PMID:25558998

On mixed and displacement finite element models of a refined shear deformation theory for laminated anisotropic plates

NASA Technical Reports Server (NTRS)

Reddy, J. N.

1986-01-01

An improved plate theory that accounts for the transverse shear deformation is presented, and mixed and displacement finite element models of the theory are developed. The theory is based on an assumed displacement field in which the inplane displacements are expanded in terms of the thickness coordinate up to the cubic term and the transverse deflection is assumed to be independent of the thickness coordinate. The governing equations of motion for the theory are derived from the Hamilton's principle. The theory eliminates the need for shear correction factors because the transverse shear stresses are represented parabolically. A mixed finite element model that uses independent approximations of the displacements and moments, and a displacement model that uses only displacements as degrees of freedom are developed. A comparison of the numerical results for bending with the exact solutions of the new theory and the three-dimensional elasticity theory shows that the present theory (and hence the finite element models) is more accurate than other plate-theories of the same order.

Analytical Round Robin for Elastic-Plastic Analysis of Surface Cracked Plates, Phase II Results

NASA Technical Reports Server (NTRS)

Allen, P. A.; Wells, D. N.

2017-01-01

The second phase of an analytical round robin for the elastic-plastic analysis of surface cracks in flat plates was conducted under the auspices of ASTM Interlaboratory Study 732. The interlaboratory study (ILS) had 10 participants with a broad range of expertise and experience, and experimental results from a surface crack tension test in 4142 steel plate loaded well into the elastic-plastic regime provided the basis for the study. The participants were asked to evaluate a surface crack tension test according to the version of the surface crack initiation toughness testing standard published at the time of the ILS, E2899-13. Data were provided to each participant that represent the fundamental information that would be provided by a mechanical test laboratory prior to evaluating the test result. Overall, the participant’s test analysis results were in good agreement and constructive feedback was received that has resulted in an improved published version of the standard E2899-15.

Boundary conditions traps when modeling interseismic deformation at subduction zones

NASA Astrophysics Data System (ADS)

Contreras, Marcelo; Gerbault, Muriel; Tassara, Andres; Bataille, Klaus; Araya, Rodolfo

2017-04-01

In order to gain insight on the controling factors for elastic strain build-up in subduction zones, such as those triggering the Mw 8. 2010 Maule earthquake, we published a modeling study to test the influence of the subducting plate thickness, variations in the updip and downdip limit of a 100% locked interplate zone, elastic parameters, and velocity reduction at the base of the subducted slab (Contreras et al., Andean Geology 43(3), 2016). When comparing our modeled predictions with interseismic GPS observations, our results indicated little influence of the subducting plate thickness, but a necessity to reduce the velocity at the corner-base of the subducted slab below the trench region, to 10% of the far-field convergence rate. Complementary numerical models allowed us to link this velocity reduction at the base of subducting slab with a long-term high flexural stress resulting from the mechanical interaction of the slab with the underlying mantle. This study discusses that even if only a small amount of these high deviatoric stresses transfer energy towards the upper portion of the slab, it may participate in triggering large earthquakes such as the Mw8.8 Maule event. The definition of initial and boundary conditions between short-term to long-term models evidence the mechanical inconsistencies that may appear when considering pre-flexed subducting slabs and unloaded underlying asthenosphere, potentially creating mis-balanced large stress discontinuities.

Heterogeneous dissipative composite structures

NASA Astrophysics Data System (ADS)

Ryabov, Victor; Yartsev, Boris; Parshina, Ludmila

2018-05-01

The paper suggests mathematical models of decaying vibrations in layered anisotropic plates and orthotropic rods based on Hamilton variation principle, first-order shear deformation laminated plate theory (FSDT), as well as on the viscous-elastic correspondence principle of the linear viscoelasticity theory. In the description of the physical relationships between the materials of the layers forming stiff polymeric composites, the effect of vibration frequency and ambient temperature is assumed as negligible, whereas for the viscous-elastic polymer layer, temperature-frequency relationship of elastic dissipation and stiffness properties is considered by means of the experimentally determined generalized curves. Mitigation of Hamilton functional makes it possible to describe decaying vibration of anisotropic structures by an algebraic problem of complex eigenvalues. The system of algebraic equation is generated through Ritz method using Legendre polynomials as coordinate functions. First, real solutions are found. To find complex natural frequencies of the system, the obtained real natural frequencies are taken as input values, and then, by means of the 3rd order iteration method, complex natural frequencies are calculated. The paper provides convergence estimates for the numerical procedures. Reliability of the obtained results is confirmed by a good correlation between analytical and experimental values of natural frequencies and loss factors in the lower vibration tones for the two series of unsupported orthotropic rods formed by stiff GRP and CRP layers and a viscoelastic polymer layer. Analysis of the numerical test data has shown the dissipation & stiffness properties of heterogeneous composite plates and rods to considerably depend on relative thickness of the viscoelastic polymer layer, orientation of stiff composite layers, vibration frequency and ambient temperature.

A proposal of monitoring and forecasting system for crustal activity in and around Japan using a large-scale high-fidelity finite element simulation codes

NASA Astrophysics Data System (ADS)

Hori, Takane; Ichimura, Tsuyoshi; Takahashi, Narumi

2017-04-01

Here we propose a system for monitoring and forecasting of crustal activity, such as spatio-temporal variation in slip velocity on the plate interface including earthquakes, seismic wave propagation, and crustal deformation. Although, we can obtain continuous dense surface deformation data on land and partly on the sea floor, the obtained data are not fully utilized for monitoring and forecasting. It is necessary to develop a physics-based data analysis system including (1) a structural model with the 3D geometry of the plate interface and the material property such as elasticity and viscosity, (2) calculation code for crustal deformation and seismic wave propagation using (1), (3) inverse analysis or data assimilation code both for structure and fault slip using (1) & (2). To accomplish this, it is at least necessary to develop highly reliable large-scale simulation code to calculate crustal deformation and seismic wave propagation for 3D heterogeneous structure. Actually, Ichimura et al. (2015, SC15) has developed unstructured FE non-linear seismic wave simulation code, which achieved physics-based urban earthquake simulation enhanced by 1.08 T DOF x 6.6 K time-step. Ichimura et al. (2013, GJI) has developed high fidelity FEM simulation code with mesh generator to calculate crustal deformation in and around Japan with complicated surface topography and subducting plate geometry for 1km mesh. Fujita et al. (2016, SC16) has improved the code for crustal deformation and achieved 2.05 T-DOF with 45m resolution on the plate interface. This high-resolution analysis enables computation of change of stress acting on the plate interface. Further, for inverse analyses, Errol et al. (2012, BSSA) has developed waveform inversion code for modeling 3D crustal structure, and Agata et al. (2015, AGU Fall Meeting) has improved the high-fidelity FEM code to apply an adjoint method for estimating fault slip and asthenosphere viscosity. Hence, we have large-scale simulation and analysis tools for monitoring. Furthermore, we are developing the methods for forecasting the slip velocity variation on the plate interface. Basic concept is given in Hori et al. (2014, Oceanography) introducing ensemble based sequential data assimilation procedure. Although the prototype described there is for elastic half space model, we are applying it for 3D heterogeneous structure with the high-fidelity FE model.

Comparison of Multiscale Method of Cells-Based Models for Predicting Elastic Properties of Filament Wound C/C-SiC

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Fassin, Marek; Bednarcyk, Brett A.; Reese, Stefanie; Simon, Jaan-Willem

2017-01-01

Three different multiscale models, based on the method of cells (generalized and high fidelity) micromechanics models were developed and used to predict the elastic properties of C/C-SiC composites. In particular, the following multiscale modeling strategies were employed: Concurrent multiscale modeling of all phases using the generalized method of cells, synergistic (two-way coupling in space) multiscale modeling with the generalized method of cells, and hierarchical (one-way coupling in space) multiscale modeling with the high fidelity generalized method of cells. The three models are validated against data from a hierarchical multiscale finite element model in the literature for a repeating unit cell of C/C-SiC. Furthermore, the multiscale models are used in conjunction with classical lamination theory to predict the stiffness of C/C-SiC plates manufactured via a wet filament winding and liquid silicon infiltration process recently developed by the German Aerospace Institute.

Slip-deficit rate distribution along the Nankai trough, southwest Japan, with elastic lithosphere and viscoelastic asthenosphere

NASA Astrophysics Data System (ADS)

Noda, A.; Saito, T.; Fukuyama, E.

2017-12-01

In southwest Japan, great thrust earthquakes occurred on the plate interface along the Nankai trough with a recurrence time of about 100 yr. Most studies estimated slip deficits on the seismogenic zone from interseismic GNSS velocity data assuming elastic slip-response functions (e.g. Loveless and Meade, 2016; Yokota et al., 2016). The observed surface velocities, however, include effects of viscoelastic relaxation in the asthenosphere caused by slip history of seismic cycles on the plate interface. Following Noda et al. (2013, GJI), the interseismic surface velocities due to seismic cycle can be represented by the superposition of (1) completely relaxed viscoelastic response to steady slip rate over the whole plate interface, (2) completely relaxed viscoelastic response to steady slip deficit rate in the seismogenic zone, and (3) surface velocity due to viscoelastic stress relaxation after the last interplate earthquake. Subtracting calculated velocities due to steady slip (1) from velocity data observed after the postseismic stress relaxation (3) decays sufficiently, we can formulate an inverse problem of estimating slip deficit rates from the residual velocities using completely relaxed slip-response functions. In an elastic (lithosphere) - viscoelastic (asthenosphere) layered half-space, the completely relaxed responses do not depend on the viscosity of asthenosphere, but depend on the thickness of lithosphere. In this study, we investigate the effects of structure model on the estimation of slip deficit rate distribution. First, we analyze GNSS daily coordinate data (GEONET F3 Solution, GSI), and obtain surface velocity data for overlapped periods of 6 yr (1996-2002, 1999-2005, 2002-2008, 2005-2011). There is no significant temporal change in the velocity data, which suggests that postseismic stress relaxations after the 1944 Tonankai and the 1946 Nankai earthquakes decayed sufficiently. Next, we estimate slip deficit rate distribution from velocity data from 2005 to 2011 together with seafloor geodetic data (Yokota et al., 2016). There is a significant difference between the results using elastic and completely relaxed responses. While the result using elastic responses shows high slip-deficit rate zone in coastal regions, they are located trenchward if using completely relaxed responses.

Adaptive reduction of constitutive model-form error using a posteriori error estimation techniques

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bishop, Joseph E.; Brown, Judith Alice

In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energymore » norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se, but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. As a result, the algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.« less

Adaptive reduction of constitutive model-form error using a posteriori error estimation techniques

DOE PAGES

Bishop, Joseph E.; Brown, Judith Alice

2018-06-15

In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energymore » norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se, but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. As a result, the algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.« less

Wave propagation modeling in composites reinforced by randomly oriented fibers

NASA Astrophysics Data System (ADS)

Kudela, Pawel; Radzienski, Maciej; Ostachowicz, Wieslaw

2018-02-01

A new method for prediction of elastic constants in randomly oriented fiber composites is proposed. It is based on mechanics of composites, the rule of mixtures and total mass balance tailored to the spectral element mesh composed of 3D brick elements. Selected elastic properties predicted by the proposed method are compared with values obtained by another theoretical method. The proposed method is applied for simulation of Lamb waves in glass-epoxy composite plate reinforced by randomly oriented fibers. Full wavefield measurements conducted by the scanning laser Doppler vibrometer are in good agreement with simulations performed by using the time domain spectral element method.

Surface cracks in a plate of finite width under tension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

The problem of a finite plate containing collinear surface cracks is considered and solved by using the line spring model with plane elasticity and Reissner's plate theory. The main focus is on the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors in an effort to provide extensive numerical results which may be useful in applications. Some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks, and two corner cracks for wide range of relative dimensions. Particularly in corner cracks, the agreement with the finite element solution is surprisingly very good. The results are obtained for semi-elliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Surface cracks in a plate of finite width under extension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Pressure distribution under flexible polishing tools. I - Conventional aspheric optics

NASA Astrophysics Data System (ADS)

Mehta, Pravin K.; Hufnagel, Robert E.

1990-10-01

The paper presents a mathematical model, based on Kirchoff's thin flat plate theory, developed to determine polishing pressure distribution for a flexible polishing tool. A two-layered tool in which bending and compressive stiffnesses are equal is developed, which is formulated as a plate on a linearly elastic foundation. An equivalent eigenvalue problem and solution for a free-free plate are created from the plate formulation. For aspheric, anamorphic optical surfaces, the tool misfit is derived; it is defined as the result of movement from the initial perfect fit on the optic to any other position. The Polisher Design (POD) software for circular tools on aspheric optics is introduced. NASTRAN-based finite element analysis results are compared with the POD software, showing high correlation. By employing existing free-free eigenvalues and eigenfunctions, the work may be extended to rectangular polishing tools as well.

Numerical analysis of standard and modified osteosynthesis in long bone fractures treatment.

PubMed

Sisljagić, Vladimir; Jovanović, Savo; Mrcela, Tomislav; Radić, Radivoje; Selthofer, Robert; Mrcela, Milanka

2010-03-01

The fundamental problem in osteoporotic fracture treatment is significant decrease in bone mass and bone tissue density resulting in decreased firmness and elasticity of osteoporotic bone. Application of standard implants and standard surgical techniques in osteoporotic bone fracture treatment makes it almost impossible to achieve stable osteosynthesis sufficient for early mobility, verticalization and load. Taking into account the form and the size of the contact surface as well as distribution of forces between the osteosynthetic materials and the bone tissue numerical analysis showed advantages of modified osteosynthesis with bone cement filling in the screw bed. The applied numerical model consisted of three sub-models: 3D model from solid elements, 3D cross section of the contact between the plate and the bone and the part of 3D cross section of the screw head and body. We have reached the conclusion that modified osteosynthesis with bone cement resulted in weaker strain in the part of the plate above the fracture fissure, more even strain on the screws, plate and bone, more even strain distribution along all the screws' bodies, significantly greater strain in the part of the screw head opposite to the fracture fissure, firm connection of the screw head and neck and the plate hole with the whole plate and more even bone strain around the screw.

Aspects of modelling the tectonics of large volcanoes on the terrestrial planets

NASA Technical Reports Server (NTRS)

Mcgovern, Patrick J.; Solomon, Sean C.

1993-01-01

Analytic solutions for the response of planetary lithospheres to volcanic loads have been used to model faulting and infer elastic plate thicknesses. Predictions of the distribution of faulting around volcanic loads, based on the application of Anderson's criteria for faulting to the results of the models, do not agree well with observations. Such models do not give the stress state and stress history within the edifice. The effects of episodic load growth can also be treated. When these effects are included, models give much better agreement with observations.

Equivalent strike-slip earthquake cycles in half-space and lithosphere-asthenosphere earth models

USGS Publications Warehouse

Savage, J.C.

1990-01-01

By virtue of the images used in the dislocation solution, the deformation at the free surface produced throughout the earthquake cycle by slippage on a long strike-slip fault in an Earth model consisting of an elastic plate (lithosphere) overlying a viscoelastic half-space (asthenosphere) can be duplicated by prescribed slip on a vertical fault embedded in an elastic half-space. Inversion of 1973-1988 geodetic measurements of deformation across the segment of the San Andreas fault in the Transverse Ranges north of Los Angeles for the half-space equivalent slip distribution suggests no significant slip on the fault above 30 km and a uniform slip rate of 36 mm/yr below 30 km. One equivalent lithosphere-asthenosphere model would have a 30-km thick lithosphere and an asthenosphere relaxation time greater than 33 years, but other models are possible. -from Author

Magneto-thermo-elastokinetics of Geometrically Nonlinear Laminated Composite Plates. Part 1: Foundation of the Theory

NASA Technical Reports Server (NTRS)

Hasanyan, Davresh; Librescu, Liviu; Qin, Zhanming; Ambur, Damodar R.

2006-01-01

A fully coupled magneto-thermo-elastokinetic model of laminated composite, finitely electroconductive plates incorporating geometrical nonlinearities and subjected to a combination of magnetic and thermal fields, as well as carrying an electrical current is developed, In this context. the first-order transversely shearable plate theory in conjunction with von-Karman geometrically nonlinear strain concept is adopted. Related to the distribution of electric and magnetic field disturbances within the plate, the assumptions proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e. the ones by Faraday, Ampere, Ohm, Maxwell and Lorentz), the modified Fourier's law of heat conduction and on the elastokinetic field equations, the 3-D coupled problem is reduced to an equivalent 2- D one. The theory developed herein provides a foundation for the investigation, both analytical and numerical, of the interacting effects among the magnetic, thermal and elastic fields in multi-layered thin plates made of anisotropic materials.

Plate convergence and long-term crustal deformation in central Japan

NASA Astrophysics Data System (ADS)

Heki, Kosuke; Miyazaki, Shin'ichi

Surveys by continuous Global Positioning System in and around Japan revealed that the Amurian Plate collides with the North American Plate in central Japan by ∼2 cm/yr. Long-term crustal deformation seems to be influenced mainly by this collision although subduction of oceanic plates governs short-term elastic deformation over the arc. Here we study the long-term deformation field by carefully removing the short-term signals inferred from a-priori plate convergence vectors and coupling strengths predicted by a thermal model. The obtained field shows that the change in velocities occurs along the longitude 135° ∼ 137°, and there exist a relatively rigid block and zones accommodating strains. Characteristic compressional deformation is found northwest of Izu due possibly to the collision of the Izu-Bonin arc with Honshu. Plate convergence rate along the Nankai-Suruga Trough is considerably smaller in eastern parts, due partly to the transition from the Amurian to the North American Plate of the landward side, and partly to the motion of the Izu Microplate relative to the Philippine Sea Plate. This accounts for longer recurrence intervals of interplate earthquakes in the Suruga Trough where the Tokai earthquake is anticipated to occur.

Growth plate stress distribution implications during bone development: a simple framework computational approach.

PubMed

Guevara, J M; Moncayo, M A; Vaca-González, J J; Gutiérrez, M L; Barrera, L A; Garzón-Alvarado, D A

2015-01-01

Mechanical stimuli play a significant role in the process of long bone development as evidenced by clinical observations and in vivo studies. Up to now approaches to understand stimuli characteristics have been limited to the first stages of epiphyseal development. Furthermore, growth plate mechanical behavior has not been widely studied. In order to better understand mechanical influences on bone growth, we used Carter and Wong biomechanical approximation to analyze growth plate mechanical behavior, and explore stress patterns for different morphological stages of the growth plate. To the best of our knowledge this work is the first attempt to study stress distribution on growth plate during different possible stages of bone development, from gestation to adolescence. Stress distribution analysis on the epiphysis and growth plate was performed using axisymmetric (3D) finite element analysis in a simplified generic epiphyseal geometry using a linear elastic model as the first approximation. We took into account different growth plate locations, morphologies and widths, as well as different epiphyseal developmental stages. We found stress distribution during bone development established osteogenic index patterns that seem to influence locally epiphyseal structures growth and coincide with growth plate histological arrangement. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Elastic wave field computation in multilayered nonplanar solid structures: a mesh-free semianalytical approach.

PubMed

Banerjee, Sourav; Kundu, Tribikram

2008-03-01

Multilayered solid structures made of isotropic, transversely isotropic, or general anisotropic materials are frequently used in aerospace, mechanical, and civil structures. Ultrasonic fields developed in such structures by finite size transducers simulating actual experiments in laboratories or in the field have not been rigorously studied. Several attempts to compute the ultrasonic field inside solid media have been made based on approximate paraxial methods like the classical ray tracing and multi-Gaussian beam models. These approximate methods have several limitations. A new semianalytical method is adopted in this article to model elastic wave field in multilayered solid structures with planar or nonplanar interfaces generated by finite size transducers. A general formulation good for both isotropic and anisotropic solids is presented in this article. A variety of conditions have been incorporated in the formulation including irregularities at the interfaces. The method presented here requires frequency domain displacement and stress Green's functions. Due to the presence of different materials in the problem geometry various elastodynamic Green's functions for different materials are used in the formulation. Expressions of displacement and stress Green's functions for isotropic and anisotropic solids as well as for the fluid media are presented. Computed results are verified by checking the stress and displacement continuity conditions across the interface of two different solids of a bimetal plate and investigating if the results for a corrugated plate with very small corrugation match with the flat plate results.

Towards development of enhanced fully-Lagrangian mesh-free computational methods for fluid-structure interaction

NASA Astrophysics Data System (ADS)

Khayyer, Abbas; Gotoh, Hitoshi; Falahaty, Hosein; Shimizu, Yuma

2018-02-01

Simulation of incompressible fluid flow-elastic structure interactions is targeted by using fully-Lagrangian mesh-free computational methods. A projection-based fluid model (moving particle semi-implicit (MPS)) is coupled with either a Newtonian or a Hamiltonian Lagrangian structure model (MPS or HMPS) in a mathematically-physically consistent manner. The fluid model is founded on the solution of Navier-Stokes and continuity equations. The structure models are configured either in the framework of Newtonian mechanics on the basis of conservation of linear and angular momenta, or Hamiltonian mechanics on the basis of variational principle for incompressible elastodynamics. A set of enhanced schemes are incorporated for projection-based fluid model (Enhanced MPS), thus, the developed coupled solvers for fluid structure interaction (FSI) are referred to as Enhanced MPS-MPS and Enhanced MPS-HMPS. Besides, two smoothed particle hydrodynamics (SPH)-based FSI solvers, being developed by the authors, are considered and their potential applicability and comparable performance are briefly discussed in comparison with MPS-based FSI solvers. The SPH-based FSI solvers are established through coupling of projection-based incompressible SPH (ISPH) fluid model and SPH-based Newtonian/Hamiltonian structure models, leading to Enhanced ISPH-SPH and Enhanced ISPH-HSPH. A comparative study is carried out on the performances of the FSI solvers through a set of benchmark tests, including hydrostatic water column on an elastic plate, high speed impact of an elastic aluminum beam, hydroelastic slamming of a marine panel and dam break with elastic gate.

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

NASA Technical Reports Server (NTRS)

Mei, Chuh; Moorthy, Jayashree

1995-01-01

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Diffraction of Harmonic Flexural Waves in a Cracked Elastic Plate Carrying Electrical Current

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.; Hasanyan, Davresh; Librescu, iviu; Qin, Zhanming

2005-01-01

The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal z-axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

Surface instability of an imperfectly bonded thin elastic film under surface van der Waals forces

NASA Astrophysics Data System (ADS)

Wang, Xu; Jing, Rong

2017-02-01

This paper studies surface instability of a thin elastic film imperfectly bonded to a rigid substrate interacting with a rigid contactor through van der Waals forces under plane strain conditions. The film-substrate interface is modeled as a linear spring with vanishing thickness described in terms of the normal and tangential interface parameters. Depending on the ratio of the two imperfect interface parameters, the critical value of the Poisson's ratio for the occurrence of surface wrinkling in the absence of surface energy can be greater than, equal to, or smaller than 0.25, which is the critical Poisson's ratio for a perfect film-substrate interface. The critical surface energy for the inhibition of the surface wrinkling is also obtained. Finally, we propose a very simple and effective method to study the surface instability of a multilayered elastic film with imperfect interfaces interacting with a rigid contactor or with another multilayered elastic film (or a multilayered simply supported plate) with imperfect interfaces.

Fractional Order and Dynamic Simulation of a System Involving an Elastic Wide Plate

NASA Astrophysics Data System (ADS)

David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.

2011-09-01

Numerous researchers have studied about nonlinear dynamics in several areas of science and engineering. However, in most cases, these concepts have been explored mainly from the standpoint of analytical and computational methods involving integer order calculus (IOC). In this paper we have examined the dynamic behavior of an elastic wide plate induced by two electromagnets of a point of view of the fractional order calculus (FOC). The primary focus of this study is on to help gain a better understanding of nonlinear dynamic in fractional order systems.

Effect of Measured Welding Residual Stresses on Crack Growth

NASA Technical Reports Server (NTRS)

Hampton, Roy W.; Nelson, Drew; Doty, Laura W. (Technical Monitor)

1998-01-01

Welding residual stresses in thin plate A516-70 steel and 2219-T87 aluminum butt weldments were measured by the strain-gage hole drilling and X-ray diffraction methods. The residual stress data were used to construct 3D strain fields which were modeled as thermally induced strains. These 3D strain fields were then analyzed with the WARP31) FEM fracture analysis code in order to predict their effect on fatigue and on fracture. For analyses of fatigue crack advance and subsequent verification testing, fatigue crack growth increments were simulated by successive saw-cuts and incremental loading to generate, as a function of crack length, effects on crack growth of the interaction between residual stresses and load induced stresses. The specimen experimental response was characterized and compared to the WARM linear elastic and elastic-plastic fracture mechanics analysis predictions. To perform the fracture analysis, the plate material's crack tearing resistance was determined by tests of thin plate M(T) specimens. Fracture analyses of these specimen were performed using WARP31D to determine the critical Crack Tip Opening Angle [CTOA] of each material. These critical CTOA values were used to predict crack tearing and fracture in the weldments. To verify the fracture predictions, weldment M(T) specimen were tested in monotonic loading to fracture while characterizing the fracture process.

Kinematics of the Southwestern Caribbean from New Geodetic Observations

NASA Astrophysics Data System (ADS)

Ruiz, G.; La Femina, P. C.; Tapia, A.; Camacho, E.; Chichaco, E.; Mora-Paez, H.; Geirsson, H.

2014-12-01

The interaction of the Caribbean, Cocos, Nazca, and South American plates has resulted in a complex plate boundary zone and the formation of second order tectonic blocks (e.g., the North Andean, Choco and Central America Fore Arc blocks). The Panama Region [PR], which is bounded by these plates and blocks, has been interpreted and modeled as a single tectonic block or deformed plate boundary. Previous research has defined the main boundaries: 1) The Caribbean plate subducts beneath the isthmus along the North Panama Deformed Belt, 2) The Nazca plate converges at very high obliquity with the PR and motion is assumed along a left lateral transform fault and the South Panama Deformed Belt, 3) The collision of PR with NW South America (i.e., the N. Andean and Choco blocks) has resulted in the Eastern Panama Deformed Belt, and 4) collision of the Cocos Ridge in the west is accommodated by crustal shortening, Central American Fore Arc translation and deformation across the Central Costa Rican Deformed Belt. In addition, there are several models that suggest internal deformation of this region by cross-isthmus strike-slip faults. Recent GPS observations for the PR indicates movement to the northeast relative to a stable Caribbean plate at rates of 6.9±4.0 - 7.8±4.8 mm a-1 from southern Costa Rica to eastern Panama, respectively (Kobayashi et al., 2014 and references therein). However, the GPS network did not have enough spatial density to estimate elastic strain accumulation across these faults. Recent installation and expansion of geodetic networks in southwestern Caribbean (i.e., Costa Rica, Panama, and Colombia) combined with geological and geophysical observations provide a new input to investigate crustal deformation processes in this complex tectonic setting, specifically related to the PR. We use new and existing GPS data to calculate a new velocity field for the region and to investigate the kinematics of the PR, including elastic strain accumulation on the major plate boundaries. Expanding our GPS observations within these proposed small blocks could allow us to solve for Euler vectors and calculate their rotation, strain accumulation and slip rates on the major fault systems. Our results combined with the local seismicity could help authorities to reduce uncertainties in seismic risk evaluations.

A proposal of monitoring and forecasting system for crustal activity in and around Japan using a large-scale high-fidelity finite element simulation codes

NASA Astrophysics Data System (ADS)

Hori, T.; Ichimura, T.

2015-12-01

Here we propose a system for monitoring and forecasting of crustal activity, especially great interplate earthquake generation and its preparation processes in subduction zone. Basically, we model great earthquake generation as frictional instability on the subjecting plate boundary. So, spatio-temporal variation in slip velocity on the plate interface should be monitored and forecasted. Although, we can obtain continuous dense surface deformation data on land and partly at the sea bottom, the data obtained are not fully utilized for monitoring and forecasting. It is necessary to develop a physics-based data analysis system including (1) a structural model with the 3D geometry of the plate interface and the material property such as elasticity and viscosity, (2) calculation code for crustal deformation and seismic wave propagation using (1), (3) inverse analysis or data assimilation code both for structure and fault slip using (1)&(2). To accomplish this, it is at least necessary to develop highly reliable large-scale simulation code to calculate crustal deformation and seismic wave propagation for 3D heterogeneous structure. Actually, Ichimura et al. (2014, SC14) has developed unstructured FE non-linear seismic wave simulation code, which achieved physics-based urban earthquake simulation enhanced by 10.7 BlnDOF x 30 K time-step. Ichimura et al. (2013, GJI) has developed high fidelity FEM simulation code with mesh generator to calculate crustal deformation in and around Japan with complicated surface topography and subducting plate geometry for 1km mesh. Further, for inverse analyses, Errol et al. (2012, BSSA) has developed waveform inversion code for modeling 3D crustal structure, and Agata et al. (2015, this meeting) has improved the high fidelity FEM code to apply an adjoint method for estimating fault slip and asthenosphere viscosity. Hence, we have large-scale simulation and analysis tools for monitoring. Furthermore, we are developing the methods for forecasting the slip velocity variation on the plate interface. Basic concept is given in Hori et al. (2014, Oceanography) introducing ensemble based sequential data assimilation procedure. Although the prototype described there is for elastic half space model, we will apply it for 3D heterogeneous structure with the high fidelity FE model.

Interaction Between the Himalaya and the Flexed Indian Plate--Spatial Fluctuations in Seismic Hazard in India in the Past Millennium?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bilham, Roger; Szeliga, Walter

2008-07-08

Between the tenth and early 16th centuries three megaquakes allowed most of the northern edge of the Indian plate to slip 20-24 m northward relative to the overlying Himalaya. Although the renewal time for earthquakes with this large amount of slip is less than 1300 years given a geodetic convergence rate of 16-20 mm/yr, recently developed scaling laws for the Himalaya suggest that the past 200 years of great earthquakes may be associated with slip of less than 10 m and renewal times of approximately 500 years. These same theoretical models show that the rupture lengths of the Himalaya's Medievalmore » earthquakes (300-600 km) are too short to permit 24 m of slip given the relationships demonstrated by recent events. There is thus reason to suppose that recent earthquakes may have responded to different elastic driving forces from those that drove the megaquakes of Medieval times.An alternative source of energy to drive Himalayan earthquakes exists in the form of the elastic and gravitational energy stored in flexure of the Indian plate. The flexure is manifest in the form of a 200-450 m high bulge in central India, which is sustained by the forces of collision and by the end-loading of the plate by the Himalaya and southern Tibet. These flexural stresses are responsible for earthquakes in the sub-continent. The abrupt release of stress associated with the northward translation of the northern edge of the Indian plate by 24 m, were the process entirely elastic, would result in a deflation of the crest of the bulge by roughly 0.8 m. Geometrical changes, however, would be moderated by viscous rheologies in the plate and by viscous flow in the mantle in the following centuries.The hypothesized relaxation of flexural geometry following the Himalayan megaquake sequence would have the effect of backing-off stresses throughout central India resulting in quiescence both in the Himalaya and the Indian plate. The historical record shows an absence of great Himalayan earthquakes in the late 16th to early 19th centuries, and colonial records for this period contain few records of earthquakes in central India. Although this may be an artifact caused by a poor recorded history, it is unlikely that Mw>8.2 earthquakes have escaped notice in the Mughal or early colonial histories.Recent mid-plate earthquakes in India may thus represent a redevelopment of flexural stressing of the Indian plate. Their return also signifies the development of stresses in the Himalaya that will eventually be released in great Himalayan earthquakes.« less

A novel model of photothermal diffusion (PTD) for polymer nano-composite semiconducting of thin circular plate

NASA Astrophysics Data System (ADS)

Lotfy, Kh.

2018-05-01

In this article, theoretical discussions for a novel mathematical-physical Photothermal diffusion (PTD) model in the generalized thermoelasticity theory with photothermal processes and chemical action are introduced. The mean idea of this model depends on the interaction between quasi-particles (plasma waves) that depends on the kind of the used materials, the mechanical forces acting on the surface, the generalized thermo and mass diffusion (due to coupling of temperature fields with thermal waves and chemical potential) and the elastic waves. The one dimensional Laplace transforms is used to obtain the exact solution for some physical and chemical quantities for a thin circular plate of a semiconducting polymer nanocomposite such as silicon (Si). New variables are deduced and discussed. The obtained results of the physical quantities are presented analytically and illustrated graphically with some important applications.

Direct synchrotron x-ray measurements of local strain fields in elastically and plastically bent metallic glasses

DOE PAGES

Wu, Yuan; Stoica, Alexandru Dan; Ren, Yang; ...

2015-09-03

In situ high-energy synchrotron X-ray diffraction was conducted on elastically and plastically bent bulk metallic glass (BMG) thin plates, from which distinct local elastic strain fields were mapped spatially. These directly measured residual strain fields can be nicely interpreted by our stress analysis, and also validate a previously proposed indirect residual-stress-measurement method by relating nanoindentation hardness to residual stresses. Local shear strain variations on the cross sections of these thin plates were found in the plastically bent BMG, which however cannot be determined from the indirect indentation method. As a result, this study has important implications in designing and manipulatingmore » internal strain fields in BMGs for the purpose of ductility enhancement.« less

Refined Models for an Analysis of Internal and External Buckling Modes of a Monolayer in a Layered Composite

NASA Astrophysics Data System (ADS)

Paimushin, V. N.

2017-11-01

For an analysis of internal and external buckling modes of a monolayer inside or at the periphery of a layered composite, refined geometrically nonlinear equations are constructed. They are based on modeling the monolayer as a thin plate interacting with binder layers at the points of boundary surfaces. The binder layer is modeled as a transversely soft foundation. It is assumed the foundations, previously compressed in the transverse direction (the first loading stage), have zero displacements of its external boundary surfaces at the second loading stage, but the contact interaction of the plate with foundations occurs without slippage or delamination. The deformation of the plate at a medium flexure is described by geometrically nonlinear relations of the classical plate theory based on the Kirchhoff-Love hypothesis (the first variant) or the refined Timoshenko model with account of the transverse shear and compression (the second variant). The foundation is described by linearized 3D equations of elasticity theory, which are simplified within the framework of the model of a transversely soft layer. Integrating the linearized equations along the transverse coordinate and satisfying the kinematic joining conditions of the plate with foundations, with account of their initial compression in the thickness direction, a system of 2D geometrically nonlinear equations and appropriate boundary conditions are derived. These equations describe the contact interaction between elements of the deformable system. The relations obtained are simplified for the case of a symmetric stacking sequence.

Short-wavelength buckling and shear failures for compression-loaded composite laminates. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Shuart, M. J.

1985-01-01

The short-wavelength buckling (or the microbuckling) and the interlaminar and inplane shear failures of multi-directional composite laminates loaded in uniaxial compression are investigated. A laminate model is presented that idealizes each lamina. The fibers in the lamina are modeled as a plate, and the matrix in the lamina is modeled as an elastic foundation. The out-of-plane w displacement for each plate is expressed as a trigonometric series in the half-wavelength of the mode shape for laminate short-wavelength buckling. Nonlinear strain-displacement relations are used. The model is applied to symmetric laminates having linear material behavior. The laminates are loaded in uniform end shortening and are simply supported. A linear analysis is used to determine the laminate stress, strain, and mode shape when short-wavelength buckling occurs. The equations for the laminate compressive stress at short-wavelength buckling are dominated by matrix contributions.

Shear fracture of jointed steel plates of bolted joints under impact load

NASA Astrophysics Data System (ADS)

Daimaruya, M.; Fujiki, H.; Ambarita, H.; Kobayashi, H.; Shin, H.-S.

2013-07-01

The present study is concerned with the development of a fracture criterion for the impact fracture of jointed steel plates of bolted joints used in a car body, which contributes to crash simulations by CAE. We focus our attention on the shear fracture of the jointed steel plates of lap-bolted joints in the suspension of a car under impact load. Members of lap-bolted joints are modelled as a pair of steel plates connected by a bolt. One of the plates is a specimen subjected to plastic deformation and fracture and the other is a jig subjected to elastic deformation only. Three kinds of steel plate specimens are examined, i.e., a common steel plate with a tensile strength of 270 MPa and high tensile strength steel plates of 440 and 590 MPa used for cars. The impact shear test was performed using the split Hopkinson bar technique for tension impact, together with the static test using a universal testing machine INSTRON 5586. The behaviour of the shear stress and deformation up to rupture taking place in the joint was discussed. The obtained results suggest that a stress-based fracture criterion may be developed for the impact fracture of jointed steel plates of a lap-bolted joint.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

NASA Astrophysics Data System (ADS)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

Buckling delamination of the circular sandwich plate with piezoelectric face and elastic core layers under rotationally symmetric external pressure

NASA Astrophysics Data System (ADS)

Akbarov, Surkay D.; Cafarova, Fazile I.; Yahnioglu, Nazmiye

2017-02-01

The axisymmetric buckling delamination of the piezoelectric circular sandwich plate with piezoelectric face and elastic (metal) core layers around the interface penny-shaped cracks is investigated. The case is considered where short-circuit conditions with respect to the electrical potential on the upper and lower and also lateral surfaces of face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. Solution to the considered nonlinear problem is reduced to solution of the series boundary value problems derived by applying the linearization procedure with respect to small imperfection of the sought values. Numerical results reveal the effect of piezoelectricity as well as geometrical and material parameters on the critical values are determined numerically by employing finite element method (FEM).

Fixation of the stressed state of glass plates by coating them with thin films using a plasma focus installation

NASA Astrophysics Data System (ADS)

Kolokoltsev, V. N.; Degtiarev, V. F.; Borovitskaya, I. V.; Nikulin, V. Ya.; Peregudova, E. N.; Silin, P. V.; Eriskin, A. A.

2018-01-01

Elastic deformation in transparent mediums is usually studied by the photoelasticity method. For opaque mediums the method of film coating and strain gauge method are used. After the external load was removed, the interference pattern corresponding to elastic deformation of the material disappears. It is found that the elastic deformation state of the thin glass plate under the action of concentrated load can be fixed during the deposition of a thin metal film. Deposition of thin copper films was carried out by passing of plasma through the copper tube installed inside the Plasma Focus installation. After removing of the load, interference pattern on the glass plates was observed in the form of Newton’s rings and isogers in non-monochromatic light on the CCD scanners which uses uorescent lamps with cold cathode. It is supposed that the copper film fixes the relief of the surface of the glass plate at the time of deformation and saves it when the load is removed. In the case of a concentrated load, this relief has the shape of a thin lens of large radius. For this reason, the interference of coherent light rays in a thin air gap between the glass of the scanners atbed and the lens surface has the shape of Newton's rings. In this case, when scanning the back side of the plate, isogyres are observed. The presented method can be used in the analysis of the mechanical stress in a various optical elements.

Lithospheric strength and its relationship to the elastic and seismogenic layer thickness

NASA Astrophysics Data System (ADS)

Watts, A. B.; Burov, E. B.

2003-08-01

Plate flexure is a phenomenon that describes how the lithosphere responds to long-term (>105 yr) geological loads. By comparing the flexure in the vicinity of ice, volcano, and sediment loads to predictions based on simple plate models it has been possible to estimate the effective elastic thickness of the lithosphere, Te. In the oceans, Te is the range 2-50 km and is determined mainly by plate and load age. The continents, in contrast, are characterised by Te values of up to 80 km and greater. Rheological considerations based on data from experimental rock mechanics suggest that Te reflects the integrated brittle, elastic and ductile strength of the lithosphere. Te differs, therefore, from the seismogenic layer thickness, Ts, which is indicative of the depth to which anelastic deformation occurs as unstable frictional sliding. Despite differences in their time scales, Te and Ts are similar in the oceans where loading reduces the initial mechanical thickness to values that generally coincide with the thickness of the brittle layer. They differ, however, in continents, which, unlike oceans, are characterised by a multi-layer rheology. As a result, Te≫Ts in cratons, many convergent zones, and some rifts. Most rifts, however, are characterised by a low Te that has been variously attributed to a young thermal age of the rifted lithosphere, thinning and heating at the time of rifting, and yielding due to post-rift sediment loading. Irrespective of their origin, the Wilson cycle makes it possible for low values to be inherited by foreland basins which, in turn, helps explain why similarities between Te and Ts extend beyond rifts into other tectonic regions such as orogenic belts and, occasionally, the cratons themselves.

Instabilities and pattern formation on the pore scale

NASA Astrophysics Data System (ADS)

Juel, Anne

What links a baby's first breath to adhesive debonding, enhanced oil recovery, or even drop-on-demand devices? All these processes involve moving or expanding bubbles displacing fluid in a confined space, bounded by either rigid or elastic walls. In this talk, we show how spatial confinement may either induce or suppress interfacial instabilities and pattern formation in such flows. We demonstrate that a simple change in the bounding geometry can radically alter the behaviour of a fluid-displacing air finger both in rigid and elastic vessels. A rich array of propagation modes, including steady and oscillatory fingers, is uncovered when air displaces oil from axially uniform tubes that have local variations in flow resistance within their cross-sections. Moreover, we show that the experimentally observed states can all be captured by a two-dimensional depth-averaged model for bubble propagation through wide channels. Viscous fingering in Hele-Shaw cells is a classical and widely studied fluid-mechanical instability: when air is injected into the narrow, liquid-filled gap between parallel rigid plates, the axisymmetrically expanding air-liquid interface tends to be unstable to non-axisymmetric disturbances. We show how the introduction of wall elasticity (via the replacement of the upper bounding plate by an elastic membrane) can weaken or even suppress the fingering instability by allowing changes in cell confinement through the flow-induced deflection of the boundary. The presence of a deformable boundary also makes the system prone to additional solid-mechanical instabilities, and these wrinkling instabilities can in turn enhance viscous fingering. The financial support of EPSRC and the Leverhulme Trust is gratefully acknowledged.

The crack problem for a half plane stiffened by elastic cover plates

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

An elastic half plane containing a crack and stiffened by a cover plate is discussed. The asymptotic nature of the stress state in the half plane around an end point of the stiffener to determine the likely orientation of a possible fracture initiation and growth was studied. The problem is formulated for an arbitrary oriented radial crack in a system of singular integral equations. For an internal crack and for an edge crack, the problem is solved and the stress intensity factors at the crack tips and the interface stress are calculated. A cracked half plane with two symmetrically located cover plates is also considered. It is concluded that the case of two stiffeners appears to be more severe than that of a single stiffener.

Efficient swimming of a plunging elastic plate in a viscous fluid

NASA Astrophysics Data System (ADS)

Yeh, Peter; Alexeev, Alexander

2014-03-01

We use three dimensional computer simulations to examine the combined hydrodynamics and structural response of a plunging elastic plate submerged in a viscous fluid with Reynolds number of 250. The plate is actuated at the root with a prescribed vertical sinusoidal displacement and a zero slope (clamped) boundary condition. We explore the steady state swimming velocity and the associated input power as a function of driving frequency, added mass, and aspect ratio. We find a universal bending pattern independent of geometry and added mass that maximizes the distance traveled per unit applied work. This bending pattern is associated with minimizing center of mass oscillations normal to the direction of travel. Subsequently, the flow around the sides of the swimmer, which does not aid in propulsion, is minimized, thereby reducing viscous losses.

The axisymmetric elasticity problem for a laminated plate containing a circular hole

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

The elasticity problem for a laminated thick plate which consists of two bonded dissimilar layers and which contains a circular hole is considered. The problem is formulated for arbitrary axisymmetric tractions on the hole surface by using the Love strain function. Through the expansion of the boundary conditions into Fourier series the problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Of particular interest in the problem are the stresses along the interface as they relate to the question of delamination failure of the composite plate. These stresses are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singular behavior of the stress state is presented and the stress intensity factors are calculated.

Buckling of structures; Proceedings of the Symposium, Harvard University, Cambridge, Mass., June 17-21, 1974

NASA Technical Reports Server (NTRS)

Budiansky, B.

1976-01-01

The papers deal with such topics as the buckling and post-buckling behavior of plates and shells; methods of calculating critical buckling and collapse loads; finite element representations for thin-shell instability analysis; theory and experiment in the creep buckling of plates and shells; creep instability of thick shell structures; analytical and numerical studies of the influence of initial imperfections on the elastic buckling of columns; mode interaction in stiffened panels under compression; imperfection-sensitivity in the interactive buckling of stiffened plates; buckling of stochastically imperfect structures; and the Liapunov stability of elastic dynamic systems. A special chapter is devoted to design problems, including the design of a Mars entry 'aeroshell', and buckling design in vehicle structures. Individual items are announced in this issue.

Computing dispersion curves of elastic/viscoelastic transversely-isotropic bone plates coupled with soft tissue and marrow using semi-analytical finite element (SAFE) method.

PubMed

Nguyen, Vu-Hieu; Tran, Tho N H T; Sacchi, Mauricio D; Naili, Salah; Le, Lawrence H

2017-08-01

We present a semi-analytical finite element (SAFE) scheme for accurately computing the velocity dispersion and attenuation in a trilayered system consisting of a transversely-isotropic (TI) cortical bone plate sandwiched between the soft tissue and marrow layers. The soft tissue and marrow are mimicked by two fluid layers of finite thickness. A Kelvin-Voigt model accounts for the absorption of all three biological domains. The simulated dispersion curves are validated by the results from the commercial software DISPERSE and published literature. Finally, the algorithm is applied to a viscoelastic trilayered TI bone model to interpret the guided modes of an ex-vivo experimental data set from a bone phantom. Copyright © 2017 Elsevier Ltd. All rights reserved.

Non-destructive testing techniques based on nonlinear methods for assessment of debonding in single lap joints

NASA Astrophysics Data System (ADS)

Scarselli, G.; Ciampa, F.; Ginzburg, D.; Meo, M.

2015-04-01

Nonlinear ultrasonic non-destructive evaluation (NDE) methods can be used for the identification of defects within adhesive bonds as they rely on the detection of nonlinear elastic features for the evaluation of the bond strength. In this paper the nonlinear content of the structural response of a single lap joint subjected to ultrasonic harmonic excitation is both numerically and experimentally evaluated to identify and characterize the defects within the bonded region. Different metallic samples with the same geometry were experimentally tested in order to characterize the debonding between two plates by using two surface bonded piezoelectric transducers in pitch-catch mode. The dynamic response of the damaged samples acquired by the single receiver sensor showed the presence of higher harmonics (2nd and 3rd) and subharmonics of the fundamental frequencies. These nonlinear elastic phenomena are clearly due to nonlinear effects induced by the poor adhesion between the two plates. A new constitutive model aimed at representing the nonlinear material response generated by the interaction of the ultrasonic waves with the adhesive joint is also presented. Such a model is implemented in an explicit FE software and uses a nonlinear user defined traction-displacement relationship implemented by means of a cohesive material user model interface. The developed model is verified for the different geometrical and material configurations. Good agreement between the experimental and numerical nonlinear response showed that this model can be used as a simple and useful tool for understanding the quality of the adhesive joint.

Mechanics of composite materials: Recent advances; Proceedings of the Symposium, Virginia Polytechnic Institute and State University, Blacksburg, VA, August 16-19, 1982

NASA Technical Reports Server (NTRS)

Hashin, Z. (Editor); Herakovich, C. T. (Editor)

1983-01-01

The present conference on the mechanics of composites discusses microstructure's influence on particulate and short fiber composites' thermoelastic and transport properties, the elastoplastic deformation of composites, constitutive equations for viscoplastic composites, the plasticity and fatigue of metal matrix composites, laminate damping mechanisms, the micromechanical modeling of Kevlar/epoxy composites' time-dependent failure, the variational characterization of waves in composites, and computational methods for eigenvalue problems in composite design. Also discussed are the elastic response of laminates, elastic coupling nonlinear effects in unsymmetrical laminates, elasticity solutions for laminate problems having stress singularities, the mechanics of bimodular composite structures, the optimization of laminated plates and shells, NDE for laminates, the role of matrix cracking in the continuum constitutive behavior of a damaged composite ply, and the energy release rates of various microcracks in short fiber composites.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Lifeng, E-mail: walfe@nuaa.edu.cn; Hu, Haiyan

The thermal vibration of a rectangular single-layered graphene sheet is investigated by using a rectangular nonlocal elastic plate model with quantum effects taken into account when the law of energy equipartition is unreliable. The relation between the temperature and the Root of Mean Squared (RMS) amplitude of vibration at any point of the rectangular single-layered graphene sheet in simply supported case is derived first from the rectangular nonlocal elastic plate model with the strain gradient of the second order taken into consideration so as to characterize the effect of microstructure of the graphene sheet. Then, the RMS amplitude of thermalmore » vibration of a rectangular single-layered graphene sheet simply supported on an elastic foundation is derived. The study shows that the RMS amplitude of the rectangular single-layered graphene sheet predicted from the quantum theory is lower than that predicted from the law of energy equipartition. The maximal relative difference of RMS amplitude of thermal vibration appears at the sheet corners. The microstructure of the graphene sheet has a little effect on the thermal vibrations of lower modes, but exhibits an obvious effect on the thermal vibrations of higher modes. The quantum effect is more important for the thermal vibration of higher modes in the case of smaller sides and lower temperature. The relative difference of maximal RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet decreases monotonically with an increase of temperature. The absolute difference of maximal RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet increases slowly with the rising of Winkler foundation modulus.« less

Computer simulation of earthquakes

NASA Technical Reports Server (NTRS)

Cohen, S. C.

1976-01-01

Two computer simulation models of earthquakes were studied for the dependence of the pattern of events on the model assumptions and input parameters. Both models represent the seismically active region by mechanical blocks which are connected to one another and to a driving plate. The blocks slide on a friction surface. In the first model elastic forces were employed and time independent friction to simulate main shock events. The size, length, and time and place of event occurrence were influenced strongly by the magnitude and degree of homogeniety in the elastic and friction parameters of the fault region. Periodically reoccurring similar events were frequently observed in simulations with near homogeneous parameters along the fault, whereas, seismic gaps were a common feature of simulations employing large variations in the fault parameters. The second model incorporated viscoelastic forces and time-dependent friction to account for aftershock sequences. The periods between aftershock events increased with time and the aftershock region was confined to that which moved in the main event.

Numerical analysis of composite STEEL-CONCRETE SECTIONS using integral equation of Volterra

NASA Astrophysics Data System (ADS)

Partov, Doncho; Kantchev, Vesselin

2011-09-01

The paper presents analysis of the stress and deflections changes due to creep in statically determinate composite steel-concrete beam. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann — Volterra for the concrete part. On the basis of the theory of the viscoelastic body of Arutyunian-Trost-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time "t", two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernal function in the integral equation is presented. Example with the model proposed is investigated. The creep functions is suggested by the model CEB MC90-99 and the "ACI 209R-92 model. The elastic modulus of concrete E c (t) is assumed to be constant in time `t'. The obtained results from the both models are compared.

Dislocation model for aseismic fault slip in the transverse ranges of Southern California

NASA Technical Reports Server (NTRS)

Cheng, A.; Jackson, D. D.; Matsuura, M.

1985-01-01

Geodetic data at a plate boundary can reveal the pattern of subsurface displacements that accompany plate motion. These displacements are modelled as the sum of rigid block motion and the elastic effects of frictional interaction between blocks. The frictional interactions are represented by uniform dislocation on each of several rectangular fault patches. The block velocities and fault parameters are then estimated from geodetic data. Bayesian inversion procedure employs prior estimates based on geological and seismological data. The method is applied to the Transverse Ranges, using prior geological and seismological data and geodetic data from the USGS trilateration networks. Geodetic data imply a displacement rate of about 20 mm/yr across the San Andreas Fault, while the geologic estimates exceed 30 mm/yr. The prior model and the final estimates both imply about 10 mm/yr crustal shortening normal to the trend of the San Andreas Fault. Aseismic fault motion is a major contributor to plate motion. The geodetic data can help to identify faults that are suffering rapid stress accumulation; in the Transverse Ranges those faults are the San Andreas and the Santa Susana.

Data acquisition of neutron crystallography on tetragonal and triclinic forms of hen-egg-white (HEW) lysozyme with an elastically bent Si monochromator

NASA Astrophysics Data System (ADS)

Tanaka, I.; Minezaki, Y.; Harada, K.; Niimura, N.

An elastically bent silicon (EBSi) as a monochromator has been optimized for neutron diffractometers of biocrystallography. It was found that several stacked thin Si plates were easier to be bent much for the near focusing point and they increased neutron reflectivity by aligning the plates. Currently, an EBSi(1 1 1) monochromator system was equipped at a diffractometer (BIX-I). It took 50 days to collect about 12 000 reflections of hen-egg-white lysozyme. The minimum d-spacing was 2.1 Å.

Design of thin shear blades for crosscut shearing of wood.

Treesearch

Rodger A. Arola; Thomas R. Grimm

1974-01-01

Discusses principles and presents formulations for evaluating the elastic stability of thin plates subjected to edge loadings. Three different prestress methods to increase late stability are presented. A procedure is given to evaluate the elastic stability of thin shear blades under expected shearing loads.

Using Remote Sensing Data to Constrain Models of Fault Interactions and Plate Boundary Deformation

NASA Astrophysics Data System (ADS)

Glasscoe, M. T.; Donnellan, A.; Lyzenga, G. A.; Parker, J. W.; Milliner, C. W. D.

2016-12-01

Determining the distribution of slip and behavior of fault interactions at plate boundaries is a complex problem. Field and remotely sensed data often lack the necessary coverage to fully resolve fault behavior. However, realistic physical models may be used to more accurately characterize the complex behavior of faults constrained with observed data, such as GPS, InSAR, and SfM. These results will improve the utility of using combined models and data to estimate earthquake potential and characterize plate boundary behavior. Plate boundary faults exhibit complex behavior, with partitioned slip and distributed deformation. To investigate what fraction of slip becomes distributed deformation off major faults, we examine a model fault embedded within a damage zone of reduced elastic rigidity that narrows with depth and forward model the slip and resulting surface deformation. The fault segments and slip distributions are modeled using the JPL GeoFEST software. GeoFEST (Geophysical Finite Element Simulation Tool) is a two- and three-dimensional finite element software package for modeling solid stress and strain in geophysical and other continuum domain applications [Lyzenga, et al., 2000; Glasscoe, et al., 2004; Parker, et al., 2008, 2010]. New methods to advance geohazards research using computer simulations and remotely sensed observations for model validation are required to understand fault slip, the complex nature of fault interaction and plate boundary deformation. These models help enhance our understanding of the underlying processes, such as transient deformation and fault creep, and can aid in developing observation strategies for sUAV, airborne, and upcoming satellite missions seeking to determine how faults behave and interact and assess their associated hazard. Models will also help to characterize this behavior, which will enable improvements in hazard estimation. Validating the model results against remotely sensed observations will allow us to better constrain fault zone rheology and physical properties, having implications for the overall understanding of earthquake physics, fault interactions, plate boundary deformation and earthquake hazard, preparedness and risk reduction.

Time Reversal Methods for Structural Health Monitoring of Metallic Structures Using Guided Waves

DTIC Science & Technology

2011-09-01

measure elastic properties of thin isotropic materials and laminated composite plates. Two types of waves propagate a symmetric wave and antisymmetric...compare it to the original signal. In this time reversal procedure wave propagation from point-A to point-B and can be modeled as a convolution ...where * is the convolution operator and transducer transmit and receive transfer function are neglected for simplification. In the frequency

Analysis of Shock Compression of Strong Single Crystals With Logarithmic Thermoelastic-Plastic Theory

DTIC Science & Technology

2014-05-01

Royal Society of London Series A, 465, 307–334. Clayton, J. (2010a). Modeling nonlinear electromechanical behavior of shocked silicon carbide . Journal...and fourth-order longitudinal elastic constants by shock compression techniques–application to sapphire and fused quartz. Journal of the Acoustical...Vogler, T., & Clayton, J. (2008). Heterogeneous deformation and spall of an extruded tungsten alloy: Plate impact experiments and crystal plasticity

Translation by anisotropic peeling or fracturing in elastic media

NASA Astrophysics Data System (ADS)

Zheng, Zhong; Lister, John; Neufeld, Jerome

2017-11-01

The influence of rock anisotropy on the direction of hydraulic fracturing is an important open question. Two canonical systems have been proposed to investigate the fundamental aspects of such fluid-structure interaction problems: (i) Fluid injection and fracturing into an infinite elastic matrix (e.g., solid gelatin) and (ii) Fluid invasion and peeling beneath a deforming elastic sheet (e.g., bending plate). We investigate the second system and impose a non-uniform prewetting film thickness beneath the elastic sheet. We notice that while the bulk of the elastic sheet retains the static blister shape, a non-uniform prewetting film thickness can cause a horizontal translation of the blister. In particular, for a step jump in prewetting film thickness, asymptotic analysis indicates that, under constant fluid injection, the horizontal translation follows a t 7 / 17 time dependence in cartesian coordinates, and the prefactor of power-law translation depends on the ratio of the distinct prewetting film thicknesses on either side. We also provide numerical and experimental evidence demonstrating anisotropic blister evolution. This can be thought of as a model system for fluid-driven fracturing where the non-uniform prewetting film thickness mimics heterogeneity in material toughness.

Landmark-based elastic registration using approximating thin-plate splines.

PubMed

Rohr, K; Stiehl, H S; Sprengel, R; Buzug, T M; Weese, J; Kuhn, M H

2001-06-01

We consider elastic image registration based on a set of corresponding anatomical point landmarks and approximating thin-plate splines. This approach is an extension of the original interpolating thin-plate spline approach and allows to take into account landmark localization errors. The extension is important for clinical applications since landmark extraction is always prone to error. Our approach is based on a minimizing functional and can cope with isotropic as well as anisotropic landmark errors. In particular, in the latter case it is possible to include different types of landmarks, e.g., unique point landmarks as well as arbitrary edge points. Also, the scheme is general with respect to the image dimension and the order of smoothness of the underlying functional. Optimal affine transformations as well as interpolating thin-plate splines are special cases of this scheme. To localize landmarks we use a semi-automatic approach which is based on three-dimensional (3-D) differential operators. Experimental results are presented for two-dimensional as well as 3-D tomographic images of the human brain.

Active control of panel vibrations induced by boundary-layer flow

NASA Technical Reports Server (NTRS)

Chow, Pao-Liu

1991-01-01

Some problems in active control of panel vibration excited by a boundary layer flow over a flat plate are studied. In the first phase of the study, the optimal control problem of vibrating elastic panel induced by a fluid dynamical loading was studied. For a simply supported rectangular plate, the vibration control problem can be analyzed by a modal analysis. The control objective is to minimize the total cost functional, which is the sum of a vibrational energy and the control cost. By means of the modal expansion, the dynamical equation for the plate and the cost functional are reduced to a system of ordinary differential equations and the cost functions for the modes. For the linear elastic plate, the modes become uncoupled. The control of each modal amplitude reduces to the so-called linear regulator problem in control theory. Such problems can then be solved by the method of adjoint state. The optimality system of equations was solved numerically by a shooting method. The results are summarized.

Southern pine veneer laminates at various moduli of elasticity

Treesearch

George E. Woodson

1972-01-01

Modulus of rigidity (GLT) of veneer laminates was shown to be unrelated to dynamic modulus of elasticity (Ed) of single veneers and also, within the range of samples tested, unrelated to specific gravity. Values determined by flexure test (GLR) were consistent with those from standard plate shear...

A convective forecast experiment of global tectonics

NASA Astrophysics Data System (ADS)

Coltice, Nicolas; Giering, Ralf

2016-04-01

Modeling jointly the deep convective motions in the mantle and the deformation of the lithosphere in a self-consistent way is a long-standing quest, for which significant advances have been made in the late 1990's. The complexities used in lithospheric models are making their way into the models of mantle convection (density variations, pseudo-plasticity, elasticity, free surface), hence global models of mantle motions can now display tectonics at their surface, evolving self-consistantly and showing some of the most important properties of plate tectonics on Earth (boundaries, types of boundaries, plate sizes, seafloor spreading properties, continental drift). The goal of this work is to experiment the forecasting power of such convection models with plate-like behavior, being here StagYY (Tackley, 2008). We generate initial conditions for a 3D spherical model in the past (50Ma and younger), using models with imposed plate velocities from 200Ma. By doing this, we introduce errors in the initial conditions that propagate afterwards. From these initial conditions, we run the convection models free, without imposing any sort of motion, letting the self-organization take place. We compare the forecast to the present-day plate velocities and plate boundaries. To investigate the optimal parameterization, and also have a flavor of the sensitivity of the results to rheological parameters, we compute the derivatives of the misfit of the surface velocities relative to the yield stress, the magnitude of the viscosity jump at 660km and the properties of a weak crust. These derivates are computed thanks to the tangent linear model of StagYY, that is built through the automatic differentiation software TAF (Giering and Kaminski, 2003). References Tackley, P. J., Modeling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid, Phys. Earth Planet. Inter. 171, 7-18 (2008). Giering, R., Kaminski, T., Applying TAF to generate efficient derivative code of Fortran 77-95 programs, PAMM 2, 54-57 (2003).

Exact nonstationary responses of rectangular thin plate on Pasternak foundation excited by stochastic moving loads

NASA Astrophysics Data System (ADS)

Chen, Guohai; Meng, Zeng; Yang, Dixiong

2018-01-01

This paper develops an efficient method termed as PE-PIM to address the exact nonstationary responses of pavement structure, which is modeled as a rectangular thin plate resting on bi-parametric Pasternak elastic foundation subjected to stochastic moving loads with constant acceleration. Firstly, analytical power spectral density (PSD) functions of random responses for thin plate are derived by integrating pseudo excitation method (PEM) with Duhamel's integral. Based on PEM, the new equivalent von Mises stress (NEVMS) is proposed, whose PSD function contains all cross-PSD functions between stress components. Then, the PE-PIM that combines the PEM with precise integration method (PIM) is presented to achieve efficiently stochastic responses of the plate by replacing Duhamel's integral with the PIM. Moreover, the semi-analytical Monte Carlo simulation is employed to verify the computational results of the developed PE-PIM. Finally, numerical examples demonstrate the high accuracy and efficiency of PE-PIM for nonstationary random vibration analysis. The effects of velocity and acceleration of moving load, boundary conditions of the plate and foundation stiffness on the deflection and NEVMS responses are scrutinized.

Modeling ramp-hold indentation measurements based on Kelvin-Voigt fractional derivative model

NASA Astrophysics Data System (ADS)

Zhang, Hongmei; zhe Zhang, Qing; Ruan, Litao; Duan, Junbo; Wan, Mingxi; Insana, Michael F.

2018-03-01

Interpretation of experimental data from micro- and nano-scale indentation testing is highly dependent on the constitutive model selected to relate measurements to mechanical properties. The Kelvin-Voigt fractional derivative model (KVFD) offers a compact set of viscoelastic features appropriate for characterizing soft biological materials. This paper provides a set of KVFD solutions for converting indentation testing data acquired for different geometries and scales into viscoelastic properties of soft materials. These solutions, which are mostly in closed-form, apply to ramp-hold relaxation, load-unload and ramp-load creep-testing protocols. We report on applications of these model solutions to macro- and nano-indentation testing of hydrogels, gastric cancer cells and ex vivo breast tissue samples using an atomic force microscope (AFM). We also applied KVFD models to clinical ultrasonic breast data using a compression plate as required for elasticity imaging. Together the results show that KVFD models fit a broad range of experimental data with a correlation coefficient typically R 2  >  0.99. For hydrogel samples, estimation of KVFD model parameters from test data using spherical indentation versus plate compression as well as ramp relaxation versus load-unload compression all agree within one standard deviation. Results from measurements made using macro- and nano-scale indentation agree in trend. For gastric cell and ex vivo breast tissue measurements, KVFD moduli are, respectively, 1/3-1/2 and 1/6 of the elasticity modulus found from the Sneddon model. In vivo breast tissue measurements yield model parameters consistent with literature results. The consistency of results found for a broad range of experimental parameters suggest the KVFD model is a reliable tool for exploring intrinsic features of the cell/tissue microenvironments.

Bending analysis of embedded nanoplates based on the integral formulation of Eringen's nonlocal theory using the finite element method

NASA Astrophysics Data System (ADS)

Ansari, R.; Torabi, J.; Norouzzadeh, A.

2018-04-01

Due to the capability of Eringen's nonlocal elasticity theory to capture the small length scale effect, it is widely used to study the mechanical behaviors of nanostructures. Previous studies have indicated that in some cases, the differential form of this theory cannot correctly predict the behavior of structure, and the integral form should be employed to avoid obtaining inconsistent results. The present study deals with the bending analysis of nanoplates resting on elastic foundation based on the integral formulation of Eringen's nonlocal theory. Since the formulation is presented in a general form, arbitrary kernel functions can be used. The first order shear deformation plate theory is considered to model the nanoplates, and the governing equations for both integral and differential forms are presented. Finally, the finite element method is applied to solve the problem. Selected results are given to investigate the effects of elastic foundation and to compare the predictions of integral nonlocal model with those of its differential nonlocal and local counterparts. It is found that by the use of proposed integral formulation of Eringen's nonlocal model, the paradox observed for the cantilever nanoplate is resolved.

Hydroelectromechanical modelling of a piezoelectric wave energy converter

NASA Astrophysics Data System (ADS)

Renzi, E.

2016-11-01

We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.

Barnacles resist removal by crack trapping

PubMed Central

Hui, Chung-Yuen; Long, Rong; Wahl, Kathryn J.; Everett, Richard K.

2011-01-01

We study the mechanics of pull-off of a barnacle adhering to a thin elastic layer which is bonded to a rigid substrate. We address the case of barnacles having acorn shell geometry and hard, calcarious base plates. Pull-off is initiated by the propagation of an interface edge crack between the base plate and the layer. We compute the energy release rate of this crack as it grows along the interface using a finite element method. We also develop an approximate analytical model to interpret our numerical results and to give a closed-form expression for the energy release rate. Our result shows that the resistance of barnacles to interfacial failure arises from a crack-trapping mechanism. PMID:21208968

Viscoelastic Postseismic Rebound to Strike-Slip Earthquakes in Regions of Oblique Plate Convergence

NASA Technical Reports Server (NTRS)

Cohen, Steven C.

1999-01-01

According to the slip partitioning concept, the trench parallel component of relative plate motion in regions of oblique convergence is accommodated by strike-slip faulting in the overriding continental lithosphere. The pattern of postseismic surface deformation due to viscoelastic flow in the lower crust and asthenosphere following a major earthquake on such a fault is modified from that predicted from the conventual elastic layer over viscoelastic halfspace model by the presence of the subducting slab. The predicted effects, such as a partial suppression of the postseismic velocities by 1 cm/yr or more immediately following a moderate to great earthquake, are potentially detectable using contemporary geodetic techniques.

The surface and through crack problems in layered orthotropic plates

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Wu, Binghua

1991-01-01

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

Numerical modeling of the deformations associated with large subduction earthquakes through the seismic cycle

NASA Astrophysics Data System (ADS)

Fleitout, L.; Trubienko, O.; Garaud, J.; Vigny, C.; Cailletaud, G.; Simons, W. J.; Satirapod, C.; Shestakov, N.

2012-12-01

A 3D finite element code (Zebulon-Zset) is used to model deformations through the seismic cycle in the areas surrounding the last three large subduction earthquakes: Sumatra, Japan and Chile. The mesh featuring a broad spherical shell portion with a viscoelastic asthenosphere is refined close to the subduction zones. The model is constrained by 6 years of postseismic data in Sumatra area and over a year of data for Japan and Chile plus preseismic data in the three areas. The coseismic displacements on the subduction plane are inverted from the coseismic displacements using the finite element program and provide the initial stresses. The predicted horizontal postseismic displacements depend upon the thicknesses of the elastic plate and of the low viscosity asthenosphere. Non-dimensionalized by the coseismic displacements, they present an almost uniform value between 500km and 1500km from the trench for elastic plates 80km thick. The time evolution of the velocities is function of the creep law (Maxwell, Burger or power-law creep). Moreover, the forward models predict a sizable far-field subsidence, also with a spatial distribution which varies with the geometry of the asthenosphere and lithosphere. Slip on the subduction interface does not induce such a subsidence. The observed horizontal velocities, divided by the coseismic displacement, present a similar pattern as function of time and distance from trench for the three areas, indicative of similar lithospheric and asthenospheric thicknesses and asthenospheric viscosity. This pattern cannot be fitted with power-law creep in the asthenosphere but indicates a lithosphere 60 to 90km thick and an asthenosphere of thickness of the order of 100km with a burger rheology represented by a Kelvin-Voigt element with a viscosity of 3.1018Pas and μKelvin=μelastic/3. A second Kelvin-Voigt element with very limited amplitude may explain some characteristics of the short time-scale signal. The postseismic subsidence is conspicuous over Thailand and Malaysia (Satirapod et al., ASR, 2012). A low viscosity wedge, with a viscosity of the order of 3. 1018 Pas is necessary to explain data in the middle-field (volcanic arc area). Post-seismic slip on the fault plane (15% of the cosismic slip) in the months after the earthquakes explains near-field deformations. The creep law and geometry deduced from postseismic data can be used to predict deformations through the seismic cycle. Far away (500 to 1500km) sizable (5mm/yr to 1cm/yr) interseismic horizontal velocities are expected. Although one should not deny the presence of long-term intraplate geologic deformations, the seismic cycle contributes significantly to the intraplate compressive preseismic deformations in the Sunda and Amurian plates. The interseismic peak in vertical velocity, predicted by elastic backslip models over the end of the locked portion of the interface can be, in viscoelastic models, pushed over the continentward border of the LVW. This may explain the pattern of vertical velocities in Northern Honshu previous to Tohoku earthquake. The deviatoric stresses associated with the seismic cycle add up to the long-term tectonic stresses and are predicted to induce a peak in extensional stress in the subducting and overriding plates with a time delay which increases with the distance to the subduction zone.

Efficient rolling texture predictions and texture-sensitive properties of α-uranium foils

DOE PAGES

Steiner, Matthew A.; Klein, Robert W.; Calhoun, Christopher A.; ...

2017-01-01

Here, finite element (FE) analysis was used to simulate the strain history of an α-uranium foil during cold-rolling, with the sheet modeled as an isotropic elastoplastic continuum. The resulting strain history was then used as input for a viscoplastic self-consistent (VPSC) polycrystal plasticity model to simulate crystallographic texture evolution. Mid-plane textures predicted via the combined FE→VPSC approach show alignment of the (010) poles along the rolling direction (RD), and the (001) poles along the normal direction (ND) with a symmetric splitting along RD. The surface texture is similar to that of the mid-plane, but with a shear-induced asymmetry that favorsmore » one of the RD split features of the (001) pole figure. Both the mid-plane and surface textures predicted by the FE→VPSC approach agree with published experimental results for cold-rolled α-uranium plates, as well as predictions made by a more computationally intensive full-field crystal plasticity based finite element model. α-uranium foils produced by cold-rolling must typically undergo a final recrystallization anneal to restore ductility prior to their final application, resulting in significant texture evolution from the cold-rolled plate deformation texture. Using the texture measured from a foil in the final recrystallized state, coefficients of the thermal expansion and elastic stiffness tensors were calculated using a thermo-elastic self-consistent model, and the anisotropic yield loci and flow curves along the RD, TD, and ND were predicted using the VPSC code.« less

Efficient rolling texture predictions and texture-sensitive properties of α-uranium foils

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steiner, Matthew A.; Klein, Robert W.; Calhoun, Christopher A.

Here, finite element (FE) analysis was used to simulate the strain history of an α-uranium foil during cold-rolling, with the sheet modeled as an isotropic elastoplastic continuum. The resulting strain history was then used as input for a viscoplastic self-consistent (VPSC) polycrystal plasticity model to simulate crystallographic texture evolution. Mid-plane textures predicted via the combined FE→VPSC approach show alignment of the (010) poles along the rolling direction (RD), and the (001) poles along the normal direction (ND) with a symmetric splitting along RD. The surface texture is similar to that of the mid-plane, but with a shear-induced asymmetry that favorsmore » one of the RD split features of the (001) pole figure. Both the mid-plane and surface textures predicted by the FE→VPSC approach agree with published experimental results for cold-rolled α-uranium plates, as well as predictions made by a more computationally intensive full-field crystal plasticity based finite element model. α-uranium foils produced by cold-rolling must typically undergo a final recrystallization anneal to restore ductility prior to their final application, resulting in significant texture evolution from the cold-rolled plate deformation texture. Using the texture measured from a foil in the final recrystallized state, coefficients of the thermal expansion and elastic stiffness tensors were calculated using a thermo-elastic self-consistent model, and the anisotropic yield loci and flow curves along the RD, TD, and ND were predicted using the VPSC code.« less

Efficient rolling texture predictions and texture-sensitive thermomechanical properties of α-uranium foils

NASA Astrophysics Data System (ADS)

Steiner, Matthew A.; Klein, Robert W.; Calhoun, Christopher A.; Knezevic, Marko; Garlea, Elena; Agnew, Sean R.

2017-11-01

Finite element (FE) analysis was used to simulate the strain history of an α-uranium foil during cold straight-rolling, with the sheet modeled as an isotropic elastoplastic continuum. The resulting strain history was then used as input for a viscoplastic self-consistent (VPSC) polycrystal plasticity model to simulate crystallographic texture evolution. Mid-plane textures predicted via the combined FE→VPSC approach show alignment of the (010) poles along the rolling direction (RD), and the (001) poles along the normal direction (ND) with a symmetric splitting along RD. The surface texture is similar to that of the mid-plane, but with a shear-induced asymmetry that favors one of the RD split features of the (001) pole figure. Both the mid-plane and surface textures predicted by the FE→VPSC approach agree with published experimental results for cold straight-rolled α-uranium plates, as well as predictions made by a more computationally intensive full-field crystal plasticity based finite element model. α-uranium foils produced by cold-rolling must typically undergo a recrystallization anneal to restore ductility prior to their final application, resulting in significant texture evolution from the cold-rolled plate deformation texture. Using the texture measured from a foil in the final recrystallized state, coefficients of thermal expansion and the elastic stiffness tensors were calculated using a thermo-elastic self-consistent model, and the anisotropic yield loci and flow curves along the RD, TD, and ND were predicted using the VPSC code.

Collapse-driven formation of depressions on comet 67P/Churyumov-Gerasimenko

NASA Astrophysics Data System (ADS)

Leliwa-Kopystynski, J.

2018-03-01

The extremely diverse surface of comet 67P/Churyumov-Gerasimenko contains a large number of depressions or craters of very different scales. Among the most prominent are two large roughly circular depressions, each with radii of several hundred meters. In this work a model for the formation of the depressions is proposed. It is based on the theory of the deformation of a thin circular elastic plate under its own weight. The plate covers a circular cavity with a given radius. The resilience of the plate diminishes over time as a result of its thinning which is itself a consequence of sublimation. When the stress limit is achieved, a gravitational collapse occurs: the plate cracks and the remnants fall into the cavity bottom. A formula that links the radius of the plate corresponding to collapse with the plate thickness has been derived. The formula was discussed for the large intervals of the values of parameters that characterize surface layers of cometary nuclei. It was found that the surface above large cavities collapses sooner than one of a similar thickness that covers a smaller cavity. So, if the collapse mechanism theory works, that larger depressions are therefore older than smaller ones.

Numerical Estimation of the Elastic Properties of Thin-Walled Structures Manufactured from Short-Fiber-Reinforced Thermoplastics

NASA Astrophysics Data System (ADS)

Altenbach, H.; Naumenko, K.; L'vov, G. I.; Pilipenko, S. N.

2003-05-01

A model which allows us to estimate the elastic properties of thin-walled structures manufactured by injection molding is presented. The starting step is the numerical prediction of the microstructure of a short-fiber-reinforced composite developed during the filling stage of the manufacturing process. For this purpose, the Moldflow Plastic Insight® commercial program is used. As a result of simulating the filling process, a second-rank orientation tensor characterizing the microstructure of the material is obtained. The elastic properties of the prepared material locally depend on the orientational distribution of fibers. The constitutive equation is formulated by means of orientational averaging for a given orientation tensor. The tensor of elastic material properties is computed and translated into the format for a stress-strain analysis based on the ANSYSÒ finite-element code. The numerical procedure and the convergence of results are discussed for a thin strip, a rectangular plate, and a shell of revolution. The influence of manufacturing conditions on the stress-strain state of statically loaded thin-walled elements is illustrated.

A new model to simulate the elastic properties of mineralized collagen fibril.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yuan, F.; Stock, S.R.; Haeffner, D.R.

Bone, because of its hierarchical composite structure, exhibits an excellent combination of stiffness and toughness, which is due substantially to the structural order and deformation at the smaller length scales. Here, we focus on the mineralized collagen fibril, consisting of hydroxyapatite plates with nanometric dimensions aligned within a protein matrix, and emphasize the relationship between the structure and elastic properties of a mineralized collagen fibril. We create two- and three-dimensional representative volume elements to represent the structure of the fibril and evaluate the importance of the parameters defining its structure and properties of the constituent mineral and collagen phase. Elasticmore » stiffnesses are calculated by the finite element method and compared with experimental data obtained by synchrotron X-ray diffraction. The computational results match the experimental data well, and provide insight into the role of the phases and morphology on the elastic deformation characteristics. Also, the effects of water, imperfections in the mineral phase and mineral content outside the mineralized collagen fibril upon its elastic properties are discussed.« less

A new model to simulate the elastic properties of mineralized collagen fibril

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yuan, F.; Stock, S.R.; Haeffner, D.R.

Bone, because of its hierarchical composite structure, exhibits an excellent combination of stiffness and toughness, which is due substantially to the structural order and deformation at the smaller length scales. Here, we focus on the mineralized collagen fibril, consisting of hydroxyapatite plates with nanometric dimensions aligned within a protein matrix, and emphasize the relationship between the structure and elastic properties of a mineralized collagen fibril. We create two- and three-dimensional representative volume elements to represent the structure of the fibril and evaluate the importance of the parameters defining its structure and properties of the constituent mineral and collagen phase. Elasticmore » stiffnesses are calculated by the finite element method and compared with experimental data obtained by synchrotron X-ray diffraction. The computational results match the experimental data well, and provide insight into the role of the phases and morphology on the elastic deformation characteristics. Also, the effects of water, imperfections in the mineral phase and mineral content outside the mineralized collagen fibril upon its elastic properties are discussed.« less

Long-term elasticity in the continental lithosphere; modelling the Aden Ridge propagation and the Anatolian extrusion process

NASA Astrophysics Data System (ADS)

Hubert-Ferrari, Aurélia; King, Geoffrey; Manighetti, Isabelle; Armijo, Rolando; Meyer, Bertrand; Tapponnier, Paul

2003-04-01

The evolution of the Gulf of Aden and the Anatolian Fault systems are modelled using the principles of elastic fracture mechanics usually applied to smaller scale cracks or faults. The lithosphere is treated as a plate, and simple boundary conditions are applied that correspond to the known plate boundary geometry and slip vectors. The models provide a simple explanation for many observed geological features. For the Gulf of Aden the model predicts why the ridge propagated from east to west from the Owen Fracture Zone towards the Afar and the overall form of its path. The smaller en echelon offsets can be explained by upward propagation from the initially created mantle dyke while the larger ones may be attributed to the propagating rupture interacting with pre-existing structures. For Anatolia the modelling suggests that the East Anatolian Fault was created before the North Anatolian Fault could form. Once both faults were formed however, activity could switch between them. The time scales over which this should take place are not known, but evidence for switching can be found in the historical seismicity. For Aden and Anatolia pre-existing structures or inhomogeneous stress fields left from earlier orogenic events have modified the processes of propagation and without an understanding of the existence of such features the propagation processes cannot be fully understood. Furthermore a propagating fault can extend into an active region where it would not have initiated. The North Anatolian Fault encountered slow but active extension when it entered the Aegean about 5 Ma and the stress field associated with the extending fault has progressively modified Aegean extension. In the central Aegean activity has been reduced while to the north-west on features such as the Gulfs of Evvia and Corinth activity has been increased. The field observation that major structures propagate and the success of simple elastic models suggest that the continental crust behaves in an elastic-brittle or elastic-plastic fashion even though laboratory tests may be interpreted to suggest viscous behaviour. There are major problems in scaling from the behaviour of small homogeneous samples to the large heterogeneous mantle and large-scale observations should be treated more seriously than extrapolations of the behaviour of laboratory experiments over many orders of magnitude in space and time. The retention of long-term elasticity and localised failure suggests a similar gross rheology for the oceanic and continental lithospheres. Even though it is incorrect to attribute differences in behaviour to the former being rigid (i.e. elastic) and the latter viscous, oceanic and continental lithosphere behave in different ways. Unlike oceanic crust, continental crust is buoyant and cannot be simply created or destroyed. The process of thickening or thinning works against gravity preventing large displacements on extensional or contractional features in the upper mantle. The equivalents of ridge or subduction systems are suppressed before they can accommodate large displacements and activity must shift elsewhere. On the other hand, strike-slip boundaries and extrusion processes are favoured.

Advances and Trends in Plate Buckling Research.

DTIC Science & Technology

1982-12-01

Hydrostatic State of In- Plane Stress. Instituto de Mecanica Aplicada No. 79-21 (Puerto Belgrano, Argentina), June 1979, 10 pp. (to be published). 38. Leissa...and Elastic Stability of Circular Plates With Thickness Varying in a Bilinear Fashion. Instituto de Mecanica Aplicada No. 81-23 (Puerto Belgrano

3-D Simulation of Tectonic Evolution in Mariana with a Coupled Model of Plate Subduction and Back-Arc Spreading

NASA Astrophysics Data System (ADS)

Hashima, A.; Matsu'Ura, M.

2006-12-01

We obtained the expressions for internal deformation fields due to a moment tensor in an elastic-viscoelastic layered holf-space. This unified formulation of internal deformation fields for shear faulting and crack opening enabled us to deal with the problem of tectonic deformation at a composite type of plate boundary zones. The tectonic deformation can be ascribed to mechanical interaction at plate boundaries, which make a closed circuit with the mode of relative plate motion changing from divergence to convergence through transcurrent motion. One of the rational ways to represent mechanical interaction at plate boundaries is specifying the increase rates of normal or tangential displacement discontinuity across plate interfaces. On the basis of such a basic idea we developed a 3-D simulation model for the nonlinear, coupled system of plate subduction and back-arc spreading in Mariana. Through numerical simulations we revealed the evolution process of back-arc spreading. At the first stage, steady plate subduction (shear faulting at a plate interface) gradually forms tensile stress fields in the back-arc region of the overriding plate. When the accumulated tensile stress reaches a critical level, back-arc spreading (crack opening) starts at a structurally weak portion of the overriding plate. The horizontal motion of the frontal part of the overriding plate due to back-arc spreading pushes out the plate boundary toward the oceanic plate. In steady-state plate subduction the shear stress acting on a plate interface must balance with the maximum frictional resistance (shear strength) of the plate interface. Therefore, the increase of shear stress at the plate interface leads to the increase of slip rate at the plate interface. The local increase of slip rate at the plate interface produces the additional tensile stress in the back-arc region. The increased tensile stress must be canceled out by the additional crack opening. Such a feedback mechanism between plate subduction and back-arc spreading is crucial to understand the development of back-ark spreading.

Structural Inference in the Art of Violin Making.

NASA Astrophysics Data System (ADS)

Morse-Fortier, Leonard Joseph

The "secrets" of success of early Italian violins have long been sought. Among their many efforts to reproduce the results of Stradiveri, Guarneri, and Amati, luthiers have attempted to order and match natural resonant frequencies in the free violin plates. This tap-tone plate tuning technique is simply an eigenvalue extraction scheme. In the final stages of carving, the violin maker complements considerable intuitive knowledge of violin plate structure and of modal attributes with tap-tone frequency estimates to better understand plate structure and to inform decisions about plate carving and completeness. Examining the modal attributes of violin plates, this work develops and incorporates an impulse-response scheme for modal inference, measures resonant frequencies and modeshapes for a pair of violin plates, and presents modeshapes through a unique computer visualization scheme developed specifically for this purpose. The work explores, through simple examples questions of how plate modal attributes reflect underlying structure, and questions about the so -called evolution of modeshapes and frequencies through assembly of the violin. Separately, the work develops computer code for a carved, anisotropic, plate/shell finite element. Solutions are found to the static displacement and free-vibration eigenvalue problems for an orthotropic plate, and used to verify element accuracy. Finally, a violin back plate is modelled with full consideration of plate thickness and arching. Model estimates for modal attributes compare very well against experimentally acquired values. Finally, the modal synthesis technique is applied to predicting the modal attributes of the violin top plate with ribs attached from those of the top plate alone, and with an estimate of rib mass and stiffness. This last analysis serves to verify the modal synthesis method, and to quantify its limits of applicability in attempting to solve problems with severe structural modification. Conclusions emphasize the importance of better understanding the underlying structure, improved understanding of its relationship to modal attributes, and better estimates of wood elasticity.

Effects of elastic bed on hydrodynamic forces for a submerged sphere in an ocean of finite depth

NASA Astrophysics Data System (ADS)

Mohapatra, Smrutiranjan

2017-08-01

In this paper, we consider a hydroelastic model to examine the radiation of waves by a submerged sphere for both heave and sway motions in a single-layer fluid flowing over an infinitely extended elastic bottom surface in an ocean of finite depth. The elastic bottom is modeled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The effect of the presence of surface tension at the free-surface is neglected. In such situation, there exist two modes of time-harmonic waves: the one with a lower wavenumber (surface mode) propagates along the free-surface and the other with higher wavenumber (flexural mode) propagates along the elastic bottom surface. Based on the small amplitude wave theory and by using the multipole expansion method, we find the particular solution for the problem of wave radiation by a submerged sphere of finite depth. Furthermore, this method eliminates the need to use large and cumbersome numerical packages for the solution of such problem and leads to an infinite system of linear algebraic equations which are easily solved numerically by any standard technique. The added-mass and damping coefficients for both heave and sway motions are derived and plotted for different submersion depths of the sphere and flexural rigidity of the elastic bottom surface. It is observed that, whenever the sphere nearer to the elastic bed, the added-mass move toward to a constant value of 1, which is approximately twice of the value of added-mass of a moving sphere in a single-layer fluid flowing over a rigid and flat bottom surface.

Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chueshov, Igor, E-mail: chueshov@karazin.ua; Dowell, Earl H., E-mail: dowell@duke.edu; Lasiecka, Irena, E-mail: lasiecka@memphis.edu

2016-06-15

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelasticity, such as flutter and divergence. This leads to a partial differential equation treatment of issues such as well-posedness of finite energy solutions, and long-time (asymptotic) behavior. The latter includes theory of asymptotic stability, convergence to equilibria, and to global attracting sets. We complete the discussion with several well knownmore » observations and conjectures based on experimental/numerical studies.« less

Finite element analysis of three patterns of internal fixation of fractures of the mandibular condyle.

PubMed

Aquilina, Peter; Chamoli, Uphar; Parr, William C H; Clausen, Philip D; Wroe, Stephen

2013-06-01

The most stable pattern of internal fixation for fractures of the mandibular condyle is a matter for ongoing discussion. In this study we investigated the stability of three commonly used patterns of plate fixation, and constructed finite element models of a simulated mandibular condylar fracture. The completed models were heterogeneous in the distribution of bony material properties, contained about 1.2 million elements, and incorporated simulated jaw-adducting musculature. Models were run assuming linear elasticity and isotropic material properties for bone. This model was considerably larger and more complex than previous finite element models that have been used to analyse the biomechanical behaviour of differing plating techniques. The use of two parallel 2.0 titanium miniplates gave a more stable configuration with lower mean element stresses and displacements over the use of a single miniplate. In addition, a parallel orientation of two miniplates resulted in lower stresses and displacements than did the use of two miniplates in an offset pattern. The use of two parallel titanium plates resulted in a superior biomechanical result as defined by mean element stresses and relative movement between the fractured fragments in these finite element models. Copyright © 2012 The British Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.

Quantum revival for elastic waves in thin plate

NASA Astrophysics Data System (ADS)

Dubois, Marc; Lefebvre, Gautier; Sebbah, Patrick

2017-05-01

Quantum revival is described as the time-periodic reconstruction of a wave packet initially localized in space and time. This effect is expected in finite-size systems which exhibit commensurable discrete spectrum such as the infinite quantum well. Here, we report on the experimental observation of full and fractional quantum revival for classical waves in a two dimensional cavity. We consider flexural waves propagating in thin plates, as their quadratic dispersion at low frequencies mimics the dispersion relation of quantum systems governed by Schrödinger equation. Time-dependent excitation and measurement are performed at ultrasonic frequencies and reveal a periodic reconstruction of the initial elastic wave packet.

Completed Beltrami-Michell Formulation for Analyzing Radially Symmetrical Bodies

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Saigal, Sunil; Hopkins, Dale A.; Patnaik, Surya N.

1994-01-01

A force method formulation, the completed Beltrami-Michell formulation (CBMF), has been developed for analyzing boundary value problems in elastic continua. The CBMF is obtained by augmenting the classical Beltrami-Michell formulation with novel boundary compatibility conditions. It can analyze general elastic continua with stress, displacement, or mixed boundary conditions. The CBMF alleviates the limitations of the classical formulation, which can solve stress boundary value problems only. In this report, the CBMF is specialized for plates and shells. All equations of the CBMF, including the boundary compatibility conditions, are derived from the variational formulation of the integrated force method (IFM). These equations are defined only in terms of stresses. Their solution for kinematically stable elastic continua provides stress fields without any reference to displacements. In addition, a stress function formulation for plates and shells is developed by augmenting the classical Airy's formulation with boundary compatibility conditions expressed in terms of the stress function. The versatility of the CBMF and the augmented stress function formulation is demonstrated through analytical solutions of several mixed boundary value problems. The example problems include a composite circular plate and a composite circular cylindrical shell under the simultaneous actions of mechanical and thermal loads.

Measurement of elastic and thermal properties of composite materials using digital speckle pattern interferometry

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Khan, Gufran S.; Shakher, Chandra

2015-08-01

In the present work, application of digital speckle pattern interferometry (DSPI) was applied for the measurement of mechanical/elastic and thermal properties of fibre reinforced plastics (FRP). Digital speckle pattern interferometric technique was used to characterize the material constants (Poisson's ratio and Young's modulus) of the composite material. Poisson ratio based on plate bending and Young's modulus based on plate vibration of material are measured by using DSPI. In addition to this, the coefficient of thermal expansion of composite material is also measured. To study the thermal strain analysis, a single DSPI fringe pattern is used to extract the phase information by using Riesz transform and the monogenic signal. The phase extraction from a single DSPI fringe pattern by using Riesz transform does not require a phase-shifting system or spatial carrier. The elastic and thermal parameters obtained from DSPI are in close agreement with the theoretical predictions available in literature.

The surface crack problem in an orthotropic plate under bending and tension

NASA Technical Reports Server (NTRS)

Wu, Bing-Hua; Erdogan, F.

1987-01-01

The elasticity problem for an infinite orthotropic flat plate containing a series of through and part through cracks and subjected to bending and tension loads is considered. The problem is formulated by using Reissner's plate bending theory and considering three-dimensional material orthotropy. The Line-spring model developed by Rice and Levy is used to formulate the surface crack problem in which a total of nine material constants were used. The effects of material orthotropy on the stress intensity factors was determined, the interaction between two asymmetrically arranged collinear cracks was investigated, and extensive numerical results regarding the stress intensity factors are provided. The problem is reduced to a system of singular integral equations which is solved by using the Gauss-Chebyshev quadrature formulas. The calculated results show that the material orthotropy does have a significant effect on the stress intensity factor.

The surface crack problem in an orthotropic plate under bending and tension

NASA Technical Reports Server (NTRS)

Wu, B. H.; Erdogan, F.

1986-01-01

The elasticity problem for an infinite orthotropic flat plate containing a series of through and part-through cracks and subjected to bending and tension loads is considered. The problem is formulated by using Reissner's plate bending theory and considering three dimensional materials orthotropy. The Line-spring model developed by Rice and Levy is used to formulate the surface crack problem in which a total of nine material constants has been used. The main purpose of this study is to determine the effect of material orthotropy on the stress intensity factors, to investigate the interaction between two asymmetrically arranged collinear cracks, and to provide extensive numerical results regarding the stress intensity factors. The problem is reduced to a system of singular integral equations which is solved by using the Gauss-Chebyshev quadrature formulas. The calculated results show that the material orthotropy does have a significant effect on the stress intensity factor.

Fillet Weld Stress Using Finite Element Methods

NASA Technical Reports Server (NTRS)

Lehnhoff, T. F.; Green, G. W.

1985-01-01

Average elastic Von Mises equivalent stresses were calculated along the throat of a single lap fillet weld. The average elastic stresses were compared to initial yield and to plastic instability conditions to modify conventional design formulas is presented. The factor is a linear function of the thicknesses of the parent plates attached by the fillet weld.

Application of RMS for damage detection by guided elastic waves

NASA Astrophysics Data System (ADS)

Radzieński, M.; Doliński, Ł.; Krawczuk, M.; dot Zak, A.; Ostachowicz, W.

2011-07-01

This paper presents certain results of an experimental study related with a damage detection in structural elements based on deviations in guided elastic wave propagation patterns. In order to excite guided elastic waves within specimens tested piezoelectric transducers have been applied. As excitation signals 5 sine cycles modulated by Hanning window have been used. Propagation of guided elastic waves has been monitored by a scanning Doppler laser vibrometer. The time signals recorded during measurement have been utilised to calculate the values of RMS. It has turned out that the values of RMS differed significantly in damaged areas from the values calculated for the healthy ones. In this way it has become possible to pinpoint precisely the locations of damage over the entire measured surface. All experimental investigations have been carried out for thin aluminium or composite plates. Damage has been simulated by a small additional mass attached on the plate surface or by a narrow notch cut. It has been shown that proposed method allows one to localise damage of various shapes and sizes within structural elements over the whole area under investigation.

Detection and estimation of defects in a circular plate using operational deflection shapes

NASA Astrophysics Data System (ADS)

Pai, Perngjin F.; Oh, Yunje; Kim, Byeong-Seok

2002-06-01

This paper investigates dynamic characteristics (mode shapes and natural frequencies) and defect detection of circular plates using a scanning laser vibrometer. Exact dynamic characteristics of a circular aluminum plate having a clamped inner rim and a free outer rim are obtained using two methods; one uses Bessel functions and the other uses a multiple shooting method. An in-house finite element code GESA is also used to analyze the circular plate using the DKT plate element. Numerical results show that some reports in the literature are incorrect and that high-frequency Operational Deflection Shapes (ODSs) are needed in order to locate small defects. Detection of two defects in the circular aluminum plate is experimentally studied using the distributions of RMS velocities under broadband periodic chirp excitations. RMS velocities of ODSs, symmetry breaking of ODSs, splitting of natural frequencies and ODSs, and a Boundary Effect Detection (BED) method. The BED method is non-destructive and model-independent; it processes experimental ODSs to reveal extra local boundary effects caused by defects to reveal locations of defects. Experimental results show that small defects in circular plates can be pinpointed by these approaches. Moreover, a new concept of using the balance of elastic and kinetic energies within a mode cell for detecting defects in two- dimensional structures of irregular shapes is proposed.

Multidirectional volar fixed-angle plating using cancellous locking screws for distal radius fractures--evaluation of three screw configurations in an extra-articular fracture model.

PubMed

Weninger, Patrick; Dall'Ara, Enrico; Drobetz, Herwig; Nemec, Wolfgang; Figl, Markus; Redl, Heinz; Hertz, Harald; Zysset, Philippe

2011-01-01

Volar fixed-angle plating is a popular treatment for unstable distal radius fractures. Despite the availability of plating systems for treating distal radius fractures, little is known about the mechanical properties of multidirectional fixed-angle plates. The aim of this study was to compare the primary fixation stability of three possible screw configurations in a distal extra-articular fracture model using a multidirectional fixed-angle plate with metaphyseal cancellous screws distally. Eighteen Sawbones radii (Sawbones, Sweden, model# 1027) were used to simulate an extra-articular distal radius fracture according to AO/OTA 23 A3. Plates were fixed to the shaft with one non-locking screw in the oval hole and two locking screws as recommended by the manufacturer. Three groups (n = 6) were defined by screw configuration in the distal metaphyseal fragment: Group 1: distal row of screws only; Group 2: 2 rows of screws, parallel insertion; Group 3: 2 rows of screws, proximal screws inserted with 30° of inclination. Specimens underwent mechanical testing under axial compression within the elastic range and load controlled between 20 N and 200 N at a rate of 40 N/s. Axial stiffness and type of construct failure were recorded. There was no difference regarding axial stiffness between the three groups. In every specimen, failure of the Sawbone-implant-construct occurred as plastic bending of the volar titanium plate when the dorsal wedge was closed. Considering the limitations of the study, the recommendation to use two rows of screws or to place screws in the proximal metaphyseal row with inclination cannot be supported by our mechanical data.

Advanced stress analysis methods applicable to turbine engine structures

NASA Technical Reports Server (NTRS)

Pian, T. H. H.

1985-01-01

Advanced stress analysis methods applicable to turbine engine structures are investigated. Constructions of special elements which containing traction-free circular boundaries are investigated. New versions of mixed variational principle and version of hybrid stress elements are formulated. A method is established for suppression of kinematic deformation modes. semiLoof plate and shell elements are constructed by assumed stress hybrid method. An elastic-plastic analysis is conducted by viscoplasticity theory using the mechanical subelement model.

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

DOE PAGES

Xu, Yongfeng F.; Zhu, Weidong D.; Smith, Scott A.

2017-07-01

Mode shapes (MSs) have been extensively used to identify structural damage. This paper presents a new non-model-based method that uses principal, mean and Gaussian curvature MSs (CMSs) to identify damage in plates; the method is applicable and robust to MSs associated with low and high elastic modes on dense and coarse measurement grids. A multi-scale discrete differential-geometry scheme is proposed to calculate principal, mean and Gaussian CMSs associated with a MS of a plate, which can alleviate adverse effects of measurement noise on calculating the CMSs. Principal, mean and Gaussian CMSs of a damaged plate and those of an undamagedmore » one are used to yield four curvature damage indices (CDIs), including Maximum-CDIs, Minimum-CDIs, Mean-CDIs and Gaussian-CDIs. Damage can be identified near regions with consistently higher values of the CDIs. It is shown that a MS of an undamaged plate can be well approximated using a polynomial with a properly determined order that fits a MS of a damaged one, provided that the undamaged plate has a smooth geometry and is made of material that has no stiffness and mass discontinuities. New fitting and convergence indices are proposed to quantify the level of approximation of a MS from a polynomial fit to that of a damaged plate and to determine the proper order of the polynomial fit, respectively. A MS of an aluminum plate with damage in the form of a machined thickness reduction area was measured to experimentally investigate the effectiveness of the proposed CDIs in damage identification; the damage on the plate was successfully identified.« less

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Yongfeng F.; Zhu, Weidong D.; Smith, Scott A.

Mode shapes (MSs) have been extensively used to identify structural damage. This paper presents a new non-model-based method that uses principal, mean and Gaussian curvature MSs (CMSs) to identify damage in plates; the method is applicable and robust to MSs associated with low and high elastic modes on dense and coarse measurement grids. A multi-scale discrete differential-geometry scheme is proposed to calculate principal, mean and Gaussian CMSs associated with a MS of a plate, which can alleviate adverse effects of measurement noise on calculating the CMSs. Principal, mean and Gaussian CMSs of a damaged plate and those of an undamagedmore » one are used to yield four curvature damage indices (CDIs), including Maximum-CDIs, Minimum-CDIs, Mean-CDIs and Gaussian-CDIs. Damage can be identified near regions with consistently higher values of the CDIs. It is shown that a MS of an undamaged plate can be well approximated using a polynomial with a properly determined order that fits a MS of a damaged one, provided that the undamaged plate has a smooth geometry and is made of material that has no stiffness and mass discontinuities. New fitting and convergence indices are proposed to quantify the level of approximation of a MS from a polynomial fit to that of a damaged plate and to determine the proper order of the polynomial fit, respectively. A MS of an aluminum plate with damage in the form of a machined thickness reduction area was measured to experimentally investigate the effectiveness of the proposed CDIs in damage identification; the damage on the plate was successfully identified.« less

Shear Stress Sensing with Elastic Microfence Structures

NASA Technical Reports Server (NTRS)

Cisotto, Alexxandra; Palmieri, Frank L.; Saini, Aditya; Lin, Yi; Thurman, Christopher S; Kim, Jinwook; Kim, Taeyang; Connell, John W.; Zhu, Yong; Gopalarathnam, Ashok;

Multi-objective optimization of composite structures. A review

NASA Astrophysics Data System (ADS)

Teters, G. A.; Kregers, A. F.

1996-05-01

Studies performed on the optimization of composite structures by coworkers of the Institute of Polymers Mechanics of the Latvian Academy of Sciences in recent years are reviewed. The possibility of controlling the geometry and anisotropy of laminar composite structures will make it possible to design articles that best satisfy the requirements established for them. Conflicting requirements such as maximum bearing capacity, minimum weight and/or cost, prescribed thermal conductivity and thermal expansion, etc. usually exist for optimal design. This results in the multi-objective compromise optimization of structures. Numerical methods have been developed for solution of problems of multi-objective optimization of composite structures; parameters of the structure of the reinforcement and the geometry of the design are assigned as controlling parameters. Programs designed to run on personal computers have been compiled for multi-objective optimization of the properties of composite materials, plates, and shells. Solutions are obtained for both linear and nonlinear models. The programs make it possible to establish the Pareto compromise region and special multicriterial solutions. The problem of the multi-objective optimization of the elastic moduli of a spatially reinforced fiberglass with stochastic stiffness parameters has been solved. The region of permissible solutions and the Pareto region have been found for the elastic moduli. The dimensions of the scatter ellipse have been determined for a multidimensional Gaussian probability distribution where correlation between the composite's properties being optimized are accounted for. Two types of problems involving the optimization of a laminar rectangular composite plate are considered: the plate is considered elastic and anisotropic in the first case, and viscoelastic properties are accounted for in the second. The angle of reinforcement and the relative amount of fibers in the longitudinal direction are controlling parameters. The optimized properties are the critical stresses, thermal conductivity, and thermal expansion. The properties of a plate are determined by the properties of the components in the composite, eight of which are stochastic. The region of multi-objective compromise solutions is presented, and the parameters of the scatter ellipses of the properties are given.

Buckling mode localization in elastic plates due to misplacement in the stiffener location

NASA Technical Reports Server (NTRS)

Elishakoff, I.; Li, Y. W.; Starnes, J. H., Jr.

1998-01-01

This paper deals with the buckling of the stiffened plate under uni-axial compression. The direct integration of the governing differential equation is performed and the exact solution to the problem is obtained. As examples, a square plate with single stiffener, and a stiffened three-span, continuous plate are investigated, with special attention given to the influence of stiffener misplacement on the buckling load and mode shape of the plate. It is found that a small misplacement of the stiffeners from the nominal configuration may change the buckling mode from a global one to a highly localized one.

Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

Energy Bounds for a Compressed Elastic Film on a Substrate

NASA Astrophysics Data System (ADS)

Bourne, David P.; Conti, Sergio; Müller, Stefan

2017-04-01

We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of two parts, describing the two main physical effects. The first part represents the elastic energy of the film, which is approximated using the von Kármán plate theory. The second part represents the fracture or delamination energy, which is approximated using the Griffith model of fracture. A simpler model containing the first term alone was previously studied with similar methods by several authors, assuming that the delaminated region is fixed. We include the fracture term, transforming the elastic minimisation into a free boundary problem, and opening the way for patterns which result from the interplay of elasticity and delamination. After rescaling, the energy depends on only two parameters: the rescaled film thickness, {σ }, and a measure of the bonding strength between the film and substrate, {γ }. We prove upper bounds on the minimum energy of the form {σ }^a {γ }^b and find that there are four different parameter regimes corresponding to different values of a and b and to different folding patterns of the film. In some cases, the upper bounds are attained by self-similar folding patterns as observed in experiments. Moreover, for two of the four parameter regimes we prove matching, optimal lower bounds.

Structure and evolution of the northern Oman margin: gravity and seismic constraints over the Zagros-Makran-Oman collision zone

NASA Astrophysics Data System (ADS)

Ravaut, P.; Bayer, R.; Hassani, R.; Rousset, D.; Yahya'ey, A. Al

1997-09-01

The obduction process in Oman during Late Cretaceous time, and continental-to-oceanic subduction along the Zagros-Makran region during the Tertiary are consequences of the Arabian-Eurasian collision, resulting in construction of complex structures composed of the Oman ophiolite belt, the Zagros continental mountain belt and the Makran subduction zone with its associated accretionary wedge. In this paper, we jointly interpret Bouguer anomaly and available petroleum seismic profiles in terms of crustal structures. We show that the gravity anomaly in northern Oman is characterized by a high-amplitude negative-positive couple. The negative anomaly is coincident with Late Cretaceous (Fiqa) and Tertiary (Pabdeh) foreland basins and with the Zagros-Oman mountain belts, whereas the positive anomaly is correlated to the ophiolite massifs. The Bouguer anomaly map indicates the presence of a post-Late Cretaceous sedimentary basin, the Sohar basin, centred north of the Batinah plain. We interpret the negative/positive couple in terms of loading of the elastic Arabian lithosphere. We estimate the different Cretaceous-to-Recent loads, including topography, ophiolite nappes, sedimentary fill and the accretionary prism of the Makran trench. A new method, using Mindlin's elastic plate theory, is proposed to model the 2D deflection of the heterogeneous elastic Arabian plate, taking into account boundary conditions at the ends of the subducted plate. We show that remnant ophiolites are isolated from Tethyan oceanic lithosphere in the Gulf of Oman by a continental basement ridge, a NW prolongation of the Saih-Hatat window. Loading the northward-limited ophiolite blocks explains the deflection of the Fiqa foredeep basin. West of the Musandam Peninsula, the Tertiary Pabdeh foredeep is probably related to the emplacement of a 8-km-thick tectonic prism located on the Musandam Peninsula and in the Strait of Hormuz. Final 2D density models along profiles through the Oman mountain belt and the Gulf of Oman are discussed in the framework of Late Cretaceous obduction of the Tethys and synchronous subduction and exhumation of the Oman margin.

An equilibrium method for prediction of transverse shear stresses in a thick laminated plate

NASA Technical Reports Server (NTRS)

Chaudhuri, R. Z.

1986-01-01

First two equations of equilibrium are utilized to compute the transverse shear stress variation through thickness of a thick laminated plate after in-plane stresses have been computed using an assumed quadratic displacement triangular element based on transverse inextensibility and layerwise constant shear angle theory (LCST). Centroid of the triangle is the point of exceptional accuracy for transverse shear stresses. Numerical results indicate close agreement with elasticity theory. An interesting comparison between the present theory and that based on assumed stress hybrid finite element approach suggests that the latter does not satisfy the condition of free normal traction at the edge. Comparison with numerical results obtained by using constant shear angle theory suggests that LCST is close to the elasticity solution while the CST is closer to classical (CLT) solution. It is also demonstrated that the reduced integration gives faster convergence when the present theory is applied to a thin plate.

Using the Vertical Component of the Surface Velocity Field to Map the Locked Zone at Cascadia Subduction Zone

NASA Astrophysics Data System (ADS)

Moulas, E.; Brandon, M. T.; Podladchikov, Y.; Bennett, R. A.

2014-12-01

At present, our understanding of the locked zone at Cascadia subduction zone is based on thermal modeling and elastic modeling of horizontal GPS velocities. The thermal model by Hyndman and Wang (1995) provided a first-order assessment of where the subduction thrust might be cold enough for stick-slip behavior. The alternative approach by McCaffrey et al. (2007) is to use a Green's function that relates horizontal surface velocities, as recorded by GPS, to interseismic elastic deformation. The thermal modeling approach is limited by a lack of information about the amount of frictional heating occurring on the thrust (Molnar and England, 1990). The GPS approach is limited in that the horizontal velocity component is fairly insensitive to the structure of the locked zone. The vertical velocity component is much more useful for this purpose. We are fortunate in that vertical velocities can now be measured by GPS to a precision of about 0.2 mm/a. The dislocation model predicts that vertical velocities should range up to about 20 percent of the subduction velocity, which means maximum values of ~7 mm/a. The locked zone is generally entirely offshore at Cascadia, except for the Olympic Peninsula region, where the underlying Juan De Fuca plate has an anomalously low dip. Previous thermal and GPS modeling, as well as tide gauge data and episodic tremors indicate the locked zone there extends about 50 to 75 km onland. This situation provides an opportunity to directly study the locked zone. With that objective in mind, we have constructed a full 3D geodynamic model of the Cascadia subduction zone. At present, the model provides a full representation of the interseismic elastic deformation due to variations of slip on the subduction thrust. The model has been benchmarked against the Savage (2D) and Okada (3D) analytical solutions. This model has an important advantage over traditional dislocation modeling in that we include temperature-sensitive viscosity for the upper and lower plates, and also use realistic constitutive models to represent the locked zone. Another important advantage is that the 3D model provides a full representation of the interseismic deformation, which is important for interpreting GPS data.

Introduction to TAFI - A Matlab® toolbox for analysis of flexural isostasy

NASA Astrophysics Data System (ADS)

Jha, S.; Harry, D. L.; Schutt, D.

2016-12-01

The isostatic response of vertical tectonic loads emplaced on thin elastic plates overlying inviscid substrate and the corresponding gravity anomalies are commonly modeled using well established theories and methodologies of flexural analysis. However, such analysis requires some mathematical and coding expertise on part of users. With that in mind, we designed a new interactive Matlab® toolbox called Toolbox for Analysis of Flexural Isostasy (TAFI). TAFI allows users to create forward models (2-D and 3-D) of flexural deformation of the lithosphere and resulting gravity anomaly. TAFI computes Green's Functions for flexure of the elastic plate subjected to point or line loads, and analytical solution for harmonic loads. Flexure due to non-impulsive, distributed 2-D or 3-D loads are computed by convolving the appropriate Green's function with a user-supplied spatially discretized load function. The gravity anomaly associated with each density interface is calculated by using the Fourier Transform of flexural deflection of these interfaces and estimating the gravity in the wavenumber domain. All models created in TAFI are based on Matlab's intrinsic functions and do not require any specialized toolbox, function or library except those distributed with TAFI. Modeling functions within TAFI can be called from Matlab workspace, from within user written programs or from the TAFI's graphical user interface (GUI). The GUI enables the user to model the flexural deflection of lithosphere interactively, enabling real time comparison of model fit with observed data constraining the flexural deformation and gravity, facilitating rapid search for best fitting flexural model. TAFI is a very useful teaching and research tool and have been tested rigorously in graduate level teaching and basic research environment.

Summary of Research Report

NASA Technical Reports Server (NTRS)

Elishakoff, Isaac

1998-01-01

Ten papers, published in various publications, on buckling, and the effects of imperfections on various structures are presented. These papers are: (1) Buckling mode localization in elastic plates due to misplacement in the stiffner location; (2) On vibrational imperfection sensitivity on Augusti's model structure in the vicinity of a non-linear static state; (3) Imperfection sensitivity due to elastic moduli in the Roorda Koiter frame; (4) Buckling mode localization in a multi-span periodic structure with a disorder in a single span; (5) Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling; (6) Derivation of multi-dimensional ellipsoidal convex model for experimental data; (7) Passive control of buckling deformation via Anderson localization phenomenon; (8)Effect of the thickness and initial im perfection on buckling on composite cylindrical shells: asymptotic analysis and numerical results by BOSOR4 and PANDA2; (9) Worst case estimation of homology design by convex analysis; (10) Buckling of structures with uncertain imperfections - Personal perspective.

Thermal Cycling and Isothermal Deformation Response of Polycrystalline NiTi: Simulations vs. Experiment

NASA Technical Reports Server (NTRS)

Manchiraju, Sivom; Gaydosh, Darrell; Benafan, Othmane; Noebe, Ronald; Vaidyanathan, Raj; Anderson, Peter M.

2011-01-01

A recent microstructure-based FEM model that couples crystal-based plasticity, the B2<-> MB190 phase transformation and anisotropic elasticity at the grain scale is calibrated to recent data for polycrystalline NiTi (49.9 at.% Ni). Inputs include anisotropic elastic properties, texture and differential scanning calorimetry data, as well as a subset of recent isothermal deformation and load-biased thermal cycling data. The model is assessed against additional experimental data. Several experimental trends are captured - in particular, the transformation strain during thermal cycling monotonically increases and reaches a peak with increasing bias stress. This is achieved, in part, by modifying the martensite hardening matrix proposed by Patoor et al. [Patoor E, Eberhardt A, Berveiller M. J Phys IV 1996;6:277]. Some experimental trends are underestimated - in particular, the ratcheting of macrostrain during thermal cycling. This may reflect a model limitation that transformation-plasticity coupling is captured on a coarse (grain) scale but not on a fine (martensitic plate) scale.

Development of a hybrid wave based-transfer matrix model for sound transmission analysis.

PubMed

Dijckmans, A; Vermeir, G

2013-04-01

In this paper, a hybrid wave based-transfer matrix model is presented that allows for the investigation of the sound transmission through finite multilayered structures placed between two reverberant rooms. The multilayered structure may consist of an arbitrary configuration of fluid, elastic, or poro-elastic layers. The field variables (structural displacements and sound pressures) are expanded in terms of structural and acoustic wave functions. The boundary and continuity conditions in the rooms determine the participation factors in the pressure expansions. The displacement of the multilayered structure is determined by the mechanical impedance matrix, which gives a relation between the pressures and transverse displacements at both sides of the structure. The elements of this matrix are calculated with the transfer matrix method. First, the hybrid model is numerically validated. Next a comparison is made with sound transmission loss measurements of a hollow brick wall and a sandwich panel. Finally, numerical simulations show the influence of structural damping, room dimensions and plate dimensions on the sound transmission loss of multilayered structures.

Scattering of Lamb waves by cracks in a composite graphite fiber-reinforced epoxy plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu K.; Shah, Arvind

1990-01-01

Recent investigations of space construction techniques have explored the used of composite materials in the construction of space stations and platforms. These composites offer superior strength to weight ratio and are thermally stable. For example, a composite material being considered is laminates of graphite fibers in an epoxy matrix. The overall effective elastic constants of such a medium can be calculated from fiber and matrix properties by using an effective modulus theory as shown in Datta, el. al. The investigation of propagation and scattering of elastic waves in composite materials is necessary in order to develop an ability to characterize cracks and predict the reliability of composite structures. The objective of this investigation is the characterization of a surface breaking crack by ultrasonic techniques. In particular, the use of Lamb waves for this purpose is studied here. The Lamb waves travel through the plate, encountering a crack, and scatter. Of interest is the modeling of the scattered wave in terms of the Lamb wave modes. The direct problem of propagation and scattering of Lamb waves by a surface breaking crack has been analyzed. This would permit an experimentalist to characterize the crack by comparing the measured response to the analytical model. The plate is assumed to be infinite in the x and y directions with a constant thickness in the z direction. The top and bottom surfaces are traction free. Solving the governing wave equations and using the stress-free boundary conditions results in the dispersion equation. This equation yields the guided modes in the homogeneous plate. The theoretical model is a hybrid method that combines analytical and finite elements techniques to describe the scattered displacements. A finite region containing the defects is discretized by finite elements. Outside the local region, the far field solution is expressed as a Fourier summation of the guided modes obtained from the dispersion equation. Continuity of tractions and displacements at the boundaries of the two regions provides the necessary equations to determine the expansion coefficients and the nodal displacements. In the hybrid method used here these defects can be of arbitrary shapes as well as inclusions of different materials.

PLASTIC-SASS--A COMPUTER PROGRAM FOR STRESSES AND DEFLECTIONS IN A REACTOR SUBASSEMBLY UNDER THERMAL, HYDRAULIC, AND FUEL EXPANSION LOADS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Friedrich, C.M.

1963-05-01

PLASTlC-SASS, an ALTAC-3 computer program that determines stresses and deflections in a flat-plate, rectangular reactor subassembly is described. Elastic, plastic, and creep properties are used to calculate the results of temperature, pressure, and fuel expansion. Plate deflections increase or decrease local channel thicknesses and thus produce a hydraulic load which is a function of fuel plate deflection. (auth)

Three-dimensional estimate of the lithospheric effective elastic thickness of the Line ridge

NASA Astrophysics Data System (ADS)

Hu, Minzhang; Li, Jiancheng; Jin, Taoyong; Xu, Xinyu; Xing, Lelin; Shen, Chongyang; Li, Hui

2015-09-01

Using a new bathymetry grid formed with vertical gravity gradient anomalies and ship soundings (BAT_VGG), a 1° × 1° lithospheric effective elastic thickness (Te) grid of the Line ridge was calculated with the moving window admittance technique. As a comparison, both the GEBCO_08 and SIO V15.1 bathymetry datasets were used to calculate Te as well. The results show that BAT_VGG is suitable for the calculation of lithospheric effective elastic thickness. The lithospheric effective elastic thickness of the Line ridge is shown to be low, in the range of 5.5-13 km, with an average of 8 km and a standard deviation of 1.3 km. Using the plate cooling model as a reference, most of the effective elastic thicknesses are controlled by the 150-300 °C isotherm. Seamounts are primarily present in two zones, with lithospheric ages of 20-35 Ma and 40-60 Ma, at the time of loading. Unlike the Hawaiian-Emperor chain, the lithospheric effective elastic thickness of the Line ridge does not change monotonously. The tectonic setting of the Line ridge is discussed in detail based on our Te results and the seamount ages collected from the literature. The results show that thermal and fracture activities must have played an important role in the origin and evolution of the ridge.

Nonlinear guided wave propagation in prestressed plates.

PubMed

Pau, Annamaria; Lanza di Scalea, Francesco

2015-03-01

The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress.

Effect of pressurization on helical guided wave energy velocity in fluid-filled pipes.

PubMed

Dubuc, Brennan; Ebrahimkhanlou, Arvin; Salamone, Salvatore

2017-03-01

The effect of pressurization stresses on helical guided waves in a thin-walled fluid-filled pipe is studied by modeling leaky Lamb waves in a stressed plate bordered by fluid. Fluid pressurization produces hoop and longitudinal stresses in a thin-walled pipe, which corresponds to biaxial in-plane stress in a plate waveguide model. The effect of stress on guided wave propagation is accounted for through nonlinear elasticity and finite deformation theory. Emphasis is placed on the stress dependence of the energy velocity of the guided wave modes. For this purpose, an expression for the energy velocity of leaky Lamb waves in a stressed plate is derived. Theoretical results are presented for the mode, frequency, and directional dependent variations in energy velocity with respect to stress. An experimental setup is designed for measuring variations in helical wave energy velocity in a thin-walled water-filled steel pipe at different levels of pressure. Good agreement is achieved between the experimental variations in energy velocity for the helical guided waves and the theoretical leaky Lamb wave solutions. Copyright © 2016 Elsevier B.V. All rights reserved.

Finite lateral compression of an elastic plasticfibre-reinforced tube : loading solutions

NASA Astrophysics Data System (ADS)

England, A. H.; Gregory, P. W.

1999-02-01

This paper considers the finite plane-strain deformations of an elastic-plastic tubecompressed between two rigid smooth parallel plates. The tube is composed of an elastic-plasticfibre-reinforced material in which the fibres lie in planes perpendicular to the axis of the tube andreinforce the tube in the circumferential direction. The composite is assumed to be an idealmaterial which is inextensible in the fibre-direction and is incompressible. The unloading of theelastic-plastic tube will be considered in a subsequent paper.

Bulk strain solitons as a tool for determination of the third order elastic moduli of composite materials

NASA Astrophysics Data System (ADS)

Semenova, I. V.; Belashov, A. V.; Garbuzov, F. E.; Samsonov, A. M.; Semenov, A. A.

2017-06-01

We demonstrate an alternative approach to determination of the third order elastic moduli of materials based on registration of nonlinear bulk strain waves in three basic structural waveguides (rod, plate and shell) and further calculation of the Murnaghan moduli from the recorded wave parameters via simple algebra. These elastic moduli are available in literature for a limited number of materials and are measured with considerable errors, that evidences a demand in novel approaches to their determination.

Origin of the Dongsha Event in the South China Sea

NASA Astrophysics Data System (ADS)

Xie, Zhiyuan; Sun, Longtao; Pang, Xiong; Zheng, Jinyun; Sun, Zhen

2017-12-01

Post-rift tectonic activities have been widely observed in the northern continental margin of the South China Sea, especially during the late Miocene. Large numbers of faults became active. Unconformities, uplift of faulted blocks, sequence tilting, erosion along the Dongsha massif and canyon incision were also discriminated at this stage in the Pearl River Mouth basin (PRMB) and the area to the east. This tectonism has been named Dongsha Event. A number of hypotheses have been put forward to explain the mechanism of the Dongsha Event, such as high-velocity lower crustal flow, magmatic underplating, and arc-continent collision. To investigate the tectonic dynamics, sequence contact relationships, fault activities, and magmatism were analyzed along large numbers of seismic profiles that cover the eastern PRMB and Southwest Taiwan Basin. The timing, affected regions, and differences in the intensity of tectonic deformation were assessed, upon which the plate bending model was favored. In order to check the reasonableness of plate bending model, effective elastic thickness and other geodynamic parameters were calculated constrained by uplift area width and regarding the trench as sediment filling. A maximum Te value of 27 km and a minimum value of 4 km were obtained. Integrating with the former stress field calculation, we conclude that the Dongsha Event was mainly affected by subduction and collision of the South China Sea toward the Philippine Sea plate. This event commenced at about 10 Ma and peaked at around 3.6 Ma. Although the high effective elastic thickness required is a problem to be addressed, this research provides by far the most comprehensive evidences to the mechanism of the Dongsha Event.

Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Barati, Mohammad Reza; Dabbagh, Ali

2018-04-01

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton's principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.

Determination of Ice Crust Thickness from Flanking Cracks Along Ridges on Europa

NASA Technical Reports Server (NTRS)

Billings, S. E.; Kattenhorn, S. A.

2002-01-01

We use equations describing the deflection of an elastic plate below a line load to estimate ice crust thickness below ridges on Europa. Using a range of elastic parameters, ice thickness is calculated to fall in the range 0.2 2.6 km. Additional information is contained in the original extended abstract.

Numerical modelling of orthogonal cutting: application to woodworking with a bench plane.

PubMed

Nairn, John A

2016-06-06

A numerical model for orthogonal cutting using the material point method was applied to woodcutting using a bench plane. The cutting process was modelled by accounting for surface energy associated with wood fracture toughness for crack growth parallel to the grain. By using damping to deal with dynamic crack propagation and modelling all contact between wood and the plane, simulations could initiate chip formation and proceed into steady-state chip propagation including chip curling. Once steady-state conditions were achieved, the cutting forces became constant and could be determined as a function of various simulation variables. The modelling details included a cutting tool, the tool's rake and grinding angles, a chip breaker, a base plate and a mouth opening between the base plate and the tool. The wood was modelled as an anisotropic elastic-plastic material. The simulations were verified by comparison to an analytical model and then used to conduct virtual experiments on wood planing. The virtual experiments showed interactions between depth of cut, chip breaker location and mouth opening. Additional simulations investigated the role of tool grinding angle, tool sharpness and friction.

On the Possibility of Interseismic Creep of the Cascadia Megathrust

NASA Astrophysics Data System (ADS)

Wang, Y.; Wang, K.; He, J.

2012-12-01

Without any instrumental records of large megathrust earthquakes, our knowledge of the seismic potential of the Cascadia subduction zone depends critically on our understanding of the present state of interseismic fault locking. The traditional view of a fully and uniformly locked Cascadia megathrust, consistent with the extremely low modern interplate seismicity, is now challenged for two reasons. First, recent quantitative analyses of high-quality microfossil data indicate that fault slip in the great Cascadia earthquake of 1700 was heterogeneous, with high-slip areas separated by low-slip areas. This leads to the question whether the low-slip areas should exhibit interseismic creeping after the earthquake and even at present. Second, the most recent inversion of GPS measurements to infer simultaneously megathrust locking, permanent upper plate deformation, and block motion features large creeping (i.e., partial locking) segments along the margin. For example, in northern Cascadia offshore of Vancouver Island, the creep rate is reported to be about 40% of the plate convergence rate of ~50 mm/yr used in this inversion. Here we re-examine the locking state of the northern Cascadia megathrust by exploring the following issues. (1) The geodetically observed contemporary margin-normal shortening has a relatively low velocity gradient but extends quite far inland. In an elastic model, the near-field low strain rate can be explained by partial locking, and the broad pattern is explained by permanent shortening, e.g., across the Canadian Coast Mountains. We investigate whether a viscoelastic model can explain the geodetic strains with a fully locked megathrust without permanent upper plate shortening. (2) The new global plate motion model MORVEL predicts a lower convergence rate of only ~40 mm/yr at northern Cascadia. We investigate its implications to the interpretation of the geodetic observations. (3) Globally, afterslip following a great earthquake is generally observed to have a short duration. We investigate whether the contemporary Cascadia deformation field could still be under the influence of the 1700 event, especially that of the post-seismic behaviour of its low-slip areas. (4) We investigate to what extent land-based GPS observations can resolve partial locking vs. full locking of the offshore seismogenic zone. We develop a 3-D viscoelastic model with a fully locked plate interface but with the locking width varying along strike and test whether this model can explain GPS observations as well as does the partially locked elastic model. We also develop an alternative model with multiple slow slip events of spatiotemporally varying source regions, in order to investigate whether their integrated effect could be identified as partial locking by land-based GPS. Our work at Cascadia may also help understand the interseismic creep reported for other subduction zones.

Laminated anisotropic reinforced plastic plates and shells

NASA Technical Reports Server (NTRS)

Korolev, V. I.

1981-01-01

Basic technical theories and engineering calculation equations for anisotropic plates and shells made of rigid reinforced plastics, mainly laminated fiberglass, are presented and discussed. Solutions are given for many problems of design of structural plates and shells, including curved sections and tanks, as well as two chapters on selection of the optimum materials, are given. Accounting for interlayer shearing and transverse separation, which are new engineering properties, are discussed. Application of the results obtained to thin three ply plates and shells wth a light elastic filler is presented and discussed.

Present-day kinematics of the East African Rift

NASA Astrophysics Data System (ADS)

Saria, E.; Calais, E.; Stamps, D. S.; Delvaux, D.; Hartnady, C. J. H.

2014-04-01

The East African Rift (EAR) is a type locale for investigating the processes that drive continental rifting and breakup. The current kinematics of this 5000 km long divergent plate boundary between the Nubia and Somalia plates is starting to be unraveled thanks to a recent augmentation of space geodetic data in Africa. Here we use a new data set combining episodic GPS measurements with continuous measurements on the Nubian, Somalian, and Antarctic plates, together with earthquake slip vector directions and geologic indicators along the Southwest Indian Ridge to update the present-day kinematics of the EAR. We use geological and seismological data to determine the main rift faults and solve for rigid block rotations while accounting for elastic strain accumulation on locked active faults. We find that the data are best fit with a model that includes three microplates embedded within the EAR, between Nubia and Somalia (Victoria, Rovuma, and Lwandle), consistent with previous findings but with slower extension rates. We find that earthquake slip vectors provide information that is consistent with the GPS velocities and helps to significantly reduce uncertainties of plate angular velocity estimates. We also find that 3.16 Myr MORVEL average spreading rates along the Southwest Indian Ridge are systematically faster than prediction from GPS data alone. This likely indicates that outward displacement along the SWIR is larger than the default value used in the MORVEL plate motion model.

Charts relating the compressive buckling stress of longitudinally supported plates to the effective deflectional and rotational stiffness of the supports

NASA Technical Reports Server (NTRS)

Anderson, Roger A; Semonian, Joseph W

1954-01-01

A stability analysis is made of a long flat rectangular plate subjected to a uniform longitudinal compressive stress and supported along its longitudinal edges and along one or more longitudinal lines by elastic line supports. The elastic supports possess deflectional and rotational stiffness. Such configuration is an idealization of the compression cover skin and internal structure of a wing and tail surfaces. The results of the analysis are presented in the form of charts in which the buckling-stress coefficient is plotted against the buckle length of the plate for a wide range of support stiffnesses. The charts make possible the determination of the compressive buckling stress of plates supported by members whose stiffness may or may not be defined by elementary beam bending and twisting theory but yet whose effective restraint is amenable to evaluation. The deflectional and rotational stiffness provided by longitudinal stiffeners and full-depth webs is discussed and numerical examples are given to illustrate the application of the charts to the design of wing structures.

Exact result in strong wave turbulence of thin elastic plates

NASA Astrophysics Data System (ADS)

Düring, Gustavo; Krstulovic, Giorgio

2018-02-01

An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5 -Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛ ℓ , where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

Vibration and flutter of mistuned bladed-disk assemblies

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.; Kielb, R. E.

1984-01-01

An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbofans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.

Vibration and flutter of mistuned bladed-disk assemblies

NASA Technical Reports Server (NTRS)

Rao, K.; Kaza, V.; Kielb, R. E.

1984-01-01

An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbufans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.

Automated Finite Element Analysis of Elastically-Tailored Plates

NASA Technical Reports Server (NTRS)

Jegley, Dawn C. (Technical Monitor); Tatting, Brian F.; Guerdal, Zafer

2003-01-01

A procedure for analyzing and designing elastically tailored composite laminates using the STAGS finite element solver has been presented. The methodology used to produce the elastic tailoring, namely computer-controlled steering of unidirectionally reinforced composite material tows, has been reduced to a handful of design parameters along with a selection of construction methods. The generality of the tow-steered ply definition provides the user a wide variety of options for laminate design, which can be automatically incorporated with any finite element model that is composed of STAGS shell elements. Furthermore, the variable stiffness parameterization is formulated so that manufacturability can be assessed during the design process, plus new ideas using tow steering concepts can be easily integrated within the general framework of the elastic tailoring definitions. Details for the necessary implementation of the tow-steering definitions within the STAGS hierarchy is provided, and the format of the ply definitions is discussed in detail to provide easy access to the elastic tailoring choices. Integration of the automated STAGS solver with laminate design software has been demonstrated, so that the large design space generated by the tow-steering options can be traversed effectively. Several design problems are presented which confirm the usefulness of the design tool as well as further establish the potential of tow-steered plies for laminate design.

An anisotropic elastoplastic constitutive formulation generalised for orthotropic materials

NASA Astrophysics Data System (ADS)

Mohd Nor, M. K.; Ma'at, N.; Ho, C. S.

2018-03-01

This paper presents a finite strain constitutive model to predict a complex elastoplastic deformation behaviour that involves very high pressures and shockwaves in orthotropic materials using an anisotropic Hill's yield criterion by means of the evolving structural tensors. The yield surface of this hyperelastic-plastic constitutive model is aligned uniquely within the principal stress space due to the combination of Mandel stress tensor and a new generalised orthotropic pressure. The formulation is developed in the isoclinic configuration and allows for a unique treatment for elastic and plastic orthotropy. An isotropic hardening is adopted to define the evolution of plastic orthotropy. The important feature of the proposed hyperelastic-plastic constitutive model is the introduction of anisotropic effect in the Mie-Gruneisen equation of state (EOS). The formulation is further combined with Grady spall failure model to predict spall failure in the materials. The proposed constitutive model is implemented as a new material model in the Lawrence Livermore National Laboratory (LLNL)-DYNA3D code of UTHM's version, named Material Type 92 (Mat92). The combination of the proposed stress tensor decomposition and the Mie-Gruneisen EOS requires some modifications in the code to reflect the formulation of the generalised orthotropic pressure. The validation approach is also presented in this paper for guidance purpose. The \\varvec{ψ} tensor used to define the alignment of the adopted yield surface is first validated. This is continued with an internal validation related to elastic isotropic, elastic orthotropic and elastic-plastic orthotropic of the proposed formulation before a comparison against range of plate impact test data at 234, 450 and {895 ms}^{-1} impact velocities is performed. A good agreement is obtained in each test.

Design and Manufacture of Elastically Tailored Tow Placed Plates

NASA Technical Reports Server (NTRS)

Tatting, Brain F.; Guerdal, Zafer; Jegley, Dawn (Technical Monitor)

2002-01-01

Elastic stiffness tailoring of laminated composite panels by allowing the fibers to curve within the plane of the laminate is a relatively novel design concept that has been demonstrated to be both beneficial and practical. In particular, for structures with highly non-uniform stress states, such as the case of a flat panel with a central hole subjected to in-plane loading, the concept is likely to provide substantial improvements in load carrying capability. The objective of the present study is to determine the effectiveness of stiffness tailoring through the use of curvilinear fibers to reduce stress concentrations around the hole and improve the load carrying capability of panels with holes. In this study software was created that translates standard finite element models with traditional laminate definitions into ones that possess stacking sequences with curvilinear fiber paths that are directly manufacturable using an advanced tow placement machine. Preliminary designs for the manufacturing and testing phase were determined through rudimentary design studies for flat plates without holes under axial compression. These candidate designs were then analyzed using finite element models that accurately reflect the test conditions and geometries in order to select final designs for testing. A total of six large panels, measuring three feet by six feet, each of which are used to produce four specimens with or without holes, were fabricated and delivered to NASA for machining and testing.

Suppression of vortex-induced vibrations in a flexible cylinder with elastic splitter plates

NASA Astrophysics Data System (ADS)

Huera-Huarte, Francisco

2013-11-01

Suppression of vortex-induced vibrations (VIV) is a topic that has received a lot of attention due to its practical implications in engineering design. Experiments have been conducted in a recirculating free surface water channel, with a working section of dimensions 1 × 1.1 × 2.5 m. A cylinder model made of a spring and a plastic cover was used for the experiments. It was placed horizontally and fully submerged in the water channel's free stream, hanging from two submersible load cells arranged to measure the total drag force on the cylinder. The model had several white points painted on its surface, so its VIV motion was obtained by imaging it with two cameras synchronised with a strobe light. Image processing allowed to obtain the displacements along the length of the cylinder with sub-pixel accuracy. Digital Particle Image Velocimetry (DPIV) was also used to quantify the wake downstream the cylinder. A full set of experiments was made for reference purposes with a plain cylinder without suppressors, and for the same conditions, several passive suppression devices such as elastic splitter plates of different sizes and shapes, were installed on the cylinder. Passive VIV suppression with drag reduction was achieved with some of the configurations tested. Funding provided by the Spanish Ministry of Science through grant DPI2012-37904 is acknowledged.

The plume head-continental lithosphere interaction using a tectonically realistic formulation for the lithosphere

NASA Astrophysics Data System (ADS)

Burov, E.; Guillou-Frottier, L.

2005-05-01

Current debates on the existence of mantle plumes largely originate from interpretations of supposed signatures of plume-induced surface topography that are compared with predictions of geodynamic models of plume-lithosphere interactions. These models often inaccurately predict surface evolution: in general, they assume a fixed upper surface and consider the lithosphere as a single viscous layer. In nature, the surface evolution is affected by the elastic-brittle-ductile deformation, by a free upper surface and by the layered structure of the lithosphere. We make a step towards reconciling mantle- and tectonic-scale studies by introducing a tectonically realistic continental plate model in large-scale plume-lithosphere interaction. This model includes (i) a natural free surface boundary condition, (ii) an explicit elastic-viscous(ductile)-plastic(brittle) rheology and (iii) a stratified structure of continental lithosphere. The numerical experiments demonstrate a number of important differences from predictions of conventional models. In particular, this relates to plate bending, mechanical decoupling of crustal and mantle layers and tension-compression instabilities, which produce transient topographic signatures such as uplift and subsidence at large (>500 km) and small scale (300-400, 200-300 and 50-100 km). The mantle plumes do not necessarily produce detectable large-scale topographic highs but often generate only alternating small-scale surface features that could otherwise be attributed to regional tectonics. A single large-wavelength deformation, predicted by conventional models, develops only for a very cold and thick lithosphere. Distinct topographic wavelengths or temporarily spaced events observed in the East African rift system, as well as over French Massif Central, can be explained by a single plume impinging at the base of the continental lithosphere, without evoking complex asthenospheric upwelling.

Variational asymptotic modeling of composite dimensionally reducible structures

NASA Astrophysics Data System (ADS)

Yu, Wenbin

A general framework to construct accurate reduced models for composite dimensionally reducible structures (beams, plates and shells) was formulated based on two theoretical foundations: decomposition of the rotation tensor and the variational asymptotic method. Two engineering software systems, Variational Asymptotic Beam Sectional Analysis (VABS, new version) and Variational Asymptotic Plate and Shell Analysis (VAPAS), were developed. Several restrictions found in previous work on beam modeling were removed in the present effort. A general formulation of Timoshenko-like cross-sectional analysis was developed, through which the shear center coordinates and a consistent Vlasov model can be obtained. Recovery relations are given to recover the asymptotic approximations for the three-dimensional field variables. A new version of VABS has been developed, which is a much improved program in comparison to the old one. Numerous examples are given for validation. A Reissner-like model being as asymptotically correct as possible was obtained for composite plates and shells. After formulating the three-dimensional elasticity problem in intrinsic form, the variational asymptotic method was used to systematically reduce the dimensionality of the problem by taking advantage of the smallness of the thickness. The through-the-thickness analysis is solved by a one-dimensional finite element method to provide the stiffnesses as input for the two-dimensional nonlinear plate or shell analysis as well as recovery relations to approximately express the three-dimensional results. The known fact that there exists more than one theory that is asymptotically correct to a given order is adopted to cast the refined energy into a Reissner-like form. A two-dimensional nonlinear shell theory consistent with the present modeling process was developed. The engineering computer code VAPAS was developed and inserted into DYMORE to provide an efficient and accurate analysis of composite plates and shells. Numerical results are compared with the exact solutions, and the excellent agreement proves that one can use VAPAS to analyze composite plates and shells efficiently and accurately. In conclusion, rigorous modeling approaches were developed for composite beams, plates and shells within a general framework. No such consistent and general treatment is found in the literature. The associated computer programs VABS and VAPAS are envisioned to have many applications in industry.

Vibration of functionally graded plate resting on viscoelastic elastic foundation subjected to moving loads

NASA Astrophysics Data System (ADS)

Duy Hien, Ta; Lam, Nguyen Ngoc

2018-04-01

The dynamics of plates subjected to a moving load must be considered by engineering mechanics and design structures. This paper deals with the dynamic responses of functionally graded (FG) rectangular plates resting on a viscoelastic foundation under moving loads. It is assumed that material properties of the plate vary continuously in the thickness direction according to the power-law. The governing equations are derived by using Hamilton’s principle, which considers the effect of the higher-order shear deformation in the plate. Transient responses of simply supported FG rectangular plates are employed by using state-space methods. Several examples are given for displacement and stresses in the plates with various structural parameters, and the effects of these parameters are discussed.

Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam

NASA Astrophysics Data System (ADS)

Awrejcewicz, J.; Krysko, V. A.; Yakovleva, T. V.; Pavlov, S. P.; Krysko, V. A.

2018-05-01

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

Moho depth and equivalent elastic thickness of the lithosphere over the Vema Channel: A new evidence of an aborted ridge

NASA Astrophysics Data System (ADS)

Constantino, Renata Regina; Costa, Iago Sousa Lima; Hackspacher, Peter Christian; de Souza, Iata Anderson

2018-03-01

We investigate the Vema Channel in terms of spatial variations of the elastic thickness (Te) in the frame of the thin plate flexure model using the convolutive method. The modeling of the Moho in terms of the thin plate flexure model is done by a least squares approximation of the Moho obtained from gravity inversion. The flexure is calculated by the convolution of the crustal load with the point-load flexure response curves. The RMS difference between the gravity and flexure Moho surfaces is minimized by varying the Te by inverse modeling. The result is a solution of the flexed crust that is in best agreement with the long-wavelength component of the gravity field. The flexure Moho depths vary between 12 and 18 km and agree well with those obtained from gravity inversion. The spatial variations of Te range from 2 to 30 km and have a good correlation with the geological interpretation for an aborted ridge near Vema Channel, called in this paper as the Vema Aborted Ridge (VAR). The occurring of seamounts appears to be correlated to a weak and deformed region. Attempts of crustal breakup are marked by high Te values (30 km) while lower values (3-12 km) are found for the suggested aborted ridge. The VAR is on Isochron of 93 Ma and shows symmetrical older along both sides of its axis. Asymmetric magnetic anomalies are found over the ridge and may be related to upper-extended continental crust broken by the Vema.

Effect of a weak layer at the base of an oceanic plate on subduction dynamics

NASA Astrophysics Data System (ADS)

Carluccio, Roberta; Kaus, Boris

2017-04-01

The plate tectonics model relies on the concept of a relatively rigid lithospheric lid moving over a weaker asthenosphere. In this frame, the lithosphere asthenosphere boundary (LAB) is a first-order discontinuity that accommodates differential motions between tectonic plates and the underlying mantle. Recent seismic studies have revealed the existence of a low velocity and high electrical conductivity layer at the base of subducting tectonic plates. This thin layer has been interpreted as being weak and slightly buoyant and was suggested to affect the dynamics of subducting plates. However, geodynamically, the role of a weak layer at the base of the lithosphere remains poorly studied, especially at subduction zones. Therefore, we here use numerical models to investigate the first-order effects of a weak buoyant layer at the LAB on subduction dynamics. We employ both 2-D and 3-D models in which the slab and mantle are either linear viscous or have a more realistic temperature-dependent visco-elastic-plastic rheology. Results show that a weak layer affects the dynamics of the plates, foremost by increasing the subduction speed. The impact of this effect depends on the thickness of the layer and the viscosity contrast between the mantle and the weak layer. For moderate viscosity contrasts (<100) and a layer thickness of 30 km, it increases the plate velocity but not the overall shape of the slab. However, for larger viscosity contrasts (>1000), it can also change the morphology of the subduction itself, perhaps because this changes the overall effective viscosity contrast between the slab the and the mantle. For thinner layers, the overall effect is reduced. Yet, if seismological observations are correct that suggests that this layer is 10 km thick and partially molten, such that the viscosity is 1000 times lower than that of the mantle, our models suggest that this effect should be measurable. Some of our models also show a pile-up of weak material in the bending zone of the subducting plate, consistent with recent seismological observations.

Forearc kinematics in obliquely convergent margins: Examples from Nicaragua and the northern Lesser Antilles

NASA Astrophysics Data System (ADS)

Turner, Henry L., III

In this study, I use surface velocities derived from GPS geodesy, elastic half-space dislocation models, and modeled Coulomb stress changes to investigate deformation in the over-riding plate at obliquely convergent margins at the leading and trailing edges of the Caribbean plate. The two principal study areas are western Nicaragua, where the Cocos plate subducts beneath the Caribbean plate, and the northern Lesser Antilles, where the North American plate subducts beneath the Caribbean plate. In Nicaragua, plate convergence is rapid at 84 mm yr1 with a small angle of obliquity of 10° along a slightly concave portion of the Middle America Trench. GPS velocities for the period from 2000 to 2004 from sites located in the Nicaraguan forearc confirmed forearc sliver motion on the order of ˜14 mm yr1 in close agreement with the value predicted by DeMets (2001). These results are presented here in Chapter 3 and were reported in Geophysical Research Letters (Turner et al., 2007). GPS observations made on sites located in the interior and on the eastern coast of Nicaragua during the same time period were combined with new data from eastern Honduras to help better constrain estimates of rigid Caribbean plate motion (DeMets et al., 2007). Slip approaching the plate convergence rate along the Nicaraguan and El Salvadoran sections of the Middle America Trench was quantitatively demonstrated by finite element modeling of this section of the plate interface using GPS velocities from our Nicaraguan network together with velocities from El Salvador and Honduras as model constraints (Correa-Mora, 2009). The MW 6.9 earthquake that ruptured the seismogenic zone offshore Nicaragua on October 9, 2004 resulted in coseismic displacements and post-seismic motion at GPS sites in the central part of the Nicaraguan forearc that currently prevent extension of interseismic time-series in this region. An elastic half-space dislocation model was used to estimate coseismic displacements at these sites and to qualitatively examine the observed post-seismic motion. Coseismic and post-seismic motion in this portion of the forearc indicate that long-term motion of the forearc across the earthquake cycle may proceed in a zig-zag pattern, which may contribute to east-west extension as observed in the Managua graben. Sites to the northwest and southeast were not substantially effected by the earthquake, and longer duration time-series (˜7 yrs) from these areas support the earlier estimates of forearc sliver motion. Results from our analysis of Nicaraguan GPS time-series from 2004--2008 and our earthquake modeling efforts are discussed in Chapter 4 and will form the basis of an article to be submitted for publication. In the northern Lesser Antilles, plate convergence is slow at ˜2 cm yr1, and obliquity varies substantially along the convex Lesser Antilles Subduction Zone. In chapter 5, I present GPS velocities derived from a decade of observations on sites in the northern Lesser Antilles and Virgin Islands. The velocities support forearc sliver motion on the order of ˜2--3 mm yr1 consistent with the lower value estimated by Lopez et al. (2006), indicating convergence in the northern region is only partially partitioned. GPS velocities in the northern Lesser Antilles show considerable variation between islands, suggesting possible independent block motion and internal deformation within the forearc region, however, velocity uncertainties for some sites remain high and may reflect the low signal-to-noise ratio of our residual velocities for the region. The lack of a substantial arc-normal component of shortening is similar to that seen in Nicaragua and may indicate a small amount of locking along the subduction interface with forearc sliver motion being driven from a more fully locked region south of Guadeloupe where the Barracuda and Tiburon aseismic ridges impinge on the subduction zone. (Abstract shortened by UMI.)

Geodynamic inversion to constrain the rheology of the lithosphere: What is the effect of elasticity?

NASA Astrophysics Data System (ADS)

Baumann, Tobias; Kaus, Boris; Thielmann, Marcel

2016-04-01

The concept of elastic thickness (T_e) is one of the main methods to describe the integrated strength of oceanic lithosphere (e.g. Watts, 2001). Observations of the Te are in general agreement with yield strength envelopes estimated from laboratory experiments (Burov, 2007, Goetze & Evans 1979). Yet, applying the same concept to the continental lithosphere has proven to be more difficult (Burov & Diament, 1995), which resulted in an ongoing discussion on the rheological structure of the lithosphere (e.g. Burov & Watts, 2006, Jackson, 2002; Maggi et al., 2000). Recently, we proposed a new approach, which constrains rheological properties of the lithosphere directly from geophysical observations such as GPS-velocity, topography and gravity (Baumann & Kaus, 2015). This approach has the advantage that available data sets (such as Moho depth) can be directly taken into account without making the a-priori assumption that the lithosphere is thin elastic plate floating on the mantle. Our results show that a Bayesian inversion method combined with numerical thermo-mechanical models can be used as independent tool to constrain non-linear viscous and plastic parameters of the lithosphere. As the rheology of the lithosphere is strongly temperature dependent, it is even possible to add a temperature parameterisation to the inversion method and constrain the thermal structure of the lithosphere in this manner. Results for the India-Asia collision zone show that existing geophysical data require India to have a quite high effective viscosity. Yet, the rheological structure of Tibet less well constrained and a number of scenarios give a nearly equally good fit to the data. Yet, one of the assumptions that we make while doing this geodynamic inversion is that the rheology is viscoplastic, and that elastic effects do not significantly alter the large-scale dynamics of the lithosphere. Here, we test the validity of this assumption by performing synthetic forward models and retrieving the rheological parameters of these models with viscoplastic geodynamic inversions. We focus on a typical intra-oceanic subduction system as well as a typical scenario of subduction of an oceanic plate underneath a continental arc. Baumann, T. S. & Kaus, B. J. P., 2015. Geodynamic inversion to constrain thenon-linear rheology of the lithosphere, Geophys. J. Int., 202(2), 1289-1316. Burov, E. B. & Diament, M., 1995. The effective elastic thickness (Te) of continental lithosphere: What does it really mean?, J. Geophys. Res., 100, 3905-3927. Burov, E. B. & Watts, A. B., 2006. The long-term strength of continental lithosphere : jelly sandwich or crème brûlée?, GSA today, 16(1), 4-10. Burov, E. B., 2007. Crust and Lithosphere Dynamics: Plate Rheology and Mechanics, in Treatise Geophys., vol. 6, chap. 3, pp. 99-151, ed. Watts, A. B., Elsevier. Goetze, C. & Evans, B., 1979. Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics, Geophys. J. Int., 59(3), 463-478. Jackson, J., 2002. Strength of the continental lithosphere: Time to abandon the jelly sandwich?, GSA today, 12(9), 4-9. Maggi, A., Jackson, J. A., McKenzie, D., & Priestley, K., 2000a. Earthquake focal depths, effective elastic thickness, and the strength of the continental lithosphere, Geology, 28, 495-498. Watts, A. B., 2001. Isostasy and Flexure of the Lithosphere, Cambridge University Press.

Edge-Driven Block Rotations Interpreted From New GPS Results: Papua New Guinea

NASA Astrophysics Data System (ADS)

Wallace, L.

2001-12-01

An ongoing discussion in plate tectonics involves whether microplate motions are driven by plate edge forces or by flow at the base of the lithosphere. We present results from a GPS network of 40 sites spanning much of the mainland of Papua New Guinea (PNG). Most of the sites are concentrated in the region of the active Finisterre arc-continent collision and have been observed on multiple campaigns from 1993-2001. Significant portions of the Ramu-Markham fault are locked, which has implications for seismic hazard assessment in the Markham Valley region. Additionally, we find that out-of-sequence thrusting is important in emplacement of the Finisterre arc terrane onto the PNG mainland. Site velocities derived from these GPS data have helped to delineate the major tectonic blocks in the region. We model site velocities by simultaneously dealing with rigid block rotation and elastic strain. We find that the mainland of PNG consists of four distinct tectonic plates: the Australian, South Bismarck and Woodlark plates (in agreement with previous studies), and a previously unrecognized New Guinea Highlands plate. The relative rotation poles for at least two of these plate pairs plot on their respective boundaries, indicating that microplate motion in PNG may be dominantly edge-driven, as predicted for this region by Schouten and Benes (1993).

Estimates of effective elastic thickness of oceanic lithosphere using model including surface and subsurface loads and effective elastic thickness of subduction zones

NASA Astrophysics Data System (ADS)

Yang, A.; Yongtao, F.

2016-12-01

The effective elastic thickness (Te) is an important parameter that characterizes the long term strength of the lithosphere, which has great significance on understanding the mechanical properties and evolution of the lithosphere. In contrast with many controversies regarding elastic thickness of continent lithosphere, the Te of oceanic lithosphere is thought to be in a simple way that is dependent on the age of the plate. However, rescent studies show that there is no simple relationship between Te and age at time of loading for both seamounts and subduction zones. As subsurface loading is very importand and has large influence in the estimate of Te for continent lithosphere, and many oceanic features such as subduction zones also have considerable subsurface loading. We introduce the method to estimate the effective elastic thickness of oceanic lithosphere using model including surface and subsurface loads by using free-air gravity anomaly and bathymetric data, together with a moving window admittance technique (MWAT). We use the multitaper spectral estimation method to calculate the power spectral density. Through tests with synthetic subduction zone like bathymetry and gravity data show that the Te can be recovered in an accurance similar to that in the continent and there is also a trade-off between spatial resolution and variance for different window sizes. We estimate Te of many subduction zones (Peru-Chile trench, Middle America trench, Caribbean trench, Kuril-Japan trench, Mariana trench, Tonga trench, Java trench, Ryukyu-Philippine trench) with an age range of 0-160 Myr to reassess the relationship between elastic thickness and the age of the lithosphere at the time of loading. The results do not show a simple relationship between Te and age.

Damping mathematical modelling and dynamic responses for FRP laminated composite plates with polymer matrix

NASA Astrophysics Data System (ADS)

Liu, Qimao

2018-02-01

This paper proposes an assumption that the fibre is elastic material and polymer matrix is viscoelastic material so that the energy dissipation depends only on the polymer matrix in dynamic response process. The damping force vectors in frequency and time domains, of FRP (Fibre-Reinforced Polymer matrix) laminated composite plates, are derived based on this assumption. The governing equations of FRP laminated composite plates are formulated in both frequency and time domains. The direct inversion method and direct time integration method for nonviscously damped systems are employed to solve the governing equations and achieve the dynamic responses in frequency and time domains, respectively. The computational procedure is given in detail. Finally, dynamic responses (frequency responses with nonzero and zero initial conditions, free vibration, forced vibrations with nonzero and zero initial conditions) of a FRP laminated composite plate are computed using the proposed methodology. The proposed methodology in this paper is easy to be inserted into the commercial finite element analysis software. The proposed assumption, based on the theory of material mechanics, needs to be further proved by experiment technique in the future.

Wave energy trapping and localization in a plate with a delamination

NASA Astrophysics Data System (ADS)

Glushkov, Evgeny; Glushkova, Natalia; Golub, Mikhail V.; Moll, Jochen; Fritzen, Claus-Peter

2012-12-01

The research aims at an experimental approval of the trapping mode effect theoretically predicted for an elastic plate-like structure with a horizontal crack. The effect is featured by a sharp capture of incident wave energy at certain resonance frequencies with its localization between the crack and plate surfaces in the form of energy vortices yielding long-enduring standing waves. The trapping modes are eigensolutions of the related diffraction problem associated with nearly real complex points of its discrete frequency spectrum. To detect such resonance motion, a laser vibrometer based system has been employed for the acquisition and appropriate visualization of piezoelectrically actuated out-of-plane surface motion of a two-layer aluminum plate with an artificial strip-like delamination. The measurements at resonance and off-resonance frequencies have revealed a time-harmonic oscillation of good quality above the delamination in the resonance case. It lasts for a long time after the scattered waves have left that area. The measured frequency of the trapped standing-wave oscillation is in a good agreement with that predicted using the integral equation based mathematical model.

Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory. II - Buckling and free vibration

NASA Technical Reports Server (NTRS)

Khdeir, A. A.; Librescu, L.

1988-01-01

A previously developed higher-order plate theory and a technique based on the state space concept are used to investigate free vibration and buckling problems of rectangular cross-ply laminated plates. Unified results are presented for the case of arbitrary boundary conditions on two opposite edges. Good agreement is obtained with previous data for simply supported edge conditions. It is pointed out that classical laminated plate theory tends to overpredict both eigenfrequencies and buckling loads, leading to an increase of the degree of orthotropicity of individual layers and of the thickness ratio of the plate.

A physical model for the acousto-ultrasonic method. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Kiernan, Michael T.; Duke, John C., Jr.

1990-01-01

A basic physical explanation, a model, and comments on NDE application of the acousto-ultrasonic (AU) method for composite materials are presented. The basis of this work is a set of experiments where a sending and a receiving piezoelectric transducer were both oriented normal to the surface, at different points, on aluminum plates, various composite plates, and a tapered aluminum plate. The purpose and basic idea is introduced. Also, general comments on the AU method are offered. A literature review is offered for areas pertinent, such as composite materials, wave propagation, ultrasonics, and the AU. Special emphasis is given to theory which is used later on and past experimental results that are important to the physical understanding of the AU method. The experimental set-up, procedure, and the ensuing analysis are described. The experimental results are presented in both a quantitative and qualitative manner. A physical understanding of experimental results based on elasticity solution is furnished. Modeling and applications of the AU method is discussed for composite material and general conclusions are stated. The physical model of the AU method for composite materials is offered, something which has been much needed and sorely lacking. This physical understanding is possible due to the extensive set of experimental measurements, also reported.

Impact of GRM: New evidence from the Soviet Union

NASA Technical Reports Server (NTRS)

Mcnutt, M.

1985-01-01

Gravity information released by the Soviet Union allows the quantitative assessment of how the geopotential research mission (GRM) mission might effect the ability to use global gravity data for continental tectonic interpretation. The information is of an isostatic response spectra for eight individual tectonic units in the USSR. The regions examined include the Caroathians, Caucasus, Urals, Pamirs, Tien-Shan, Altal, Chersky Ridge, and East Siberian Platform. The 1 deg x 1 deg gravity data are used to calculate the admittances are used in two different sorts of tectonic studies of mountain belts in the USSR: (1) interpretation of isostatic responses in terms of plate models of compensation for mountainous terrain. Using geologic information concerning time of the orogeny, lithospheric plates involved, and polarity of subduction in collision zones, they convert the best-fitting flexural rigidity to an elastic plate thickness for the lithospheric plate inferred to underlie the mountains; the isostatic admittance functions is an attempt to directly model gravity and topography data for a few select regions in the Soviet Union. By knowing the value of the expected correlation between topography and gravity from the admittances, the Artemjev's map in mountainous areas can be calibrated, and the maps are converted back to Bouguer gravity. This procedure is applied to the Caucasus and southern Urals.

Demonstration of nonlinear effects in acoustic landmine experiments using a clamped-plate soil oscillator

NASA Astrophysics Data System (ADS)

Korman, Murray S.; Bond, Emilia

2005-09-01

Current nonlinear experiments involving the detection of plastic landmines using acoustic-to-seismic coupling have been developed from Sabatier's (linear) and Donskoy's (nonlinear) earlier methods. A laboratory apparatus called the soil-plate oscillator has been developed at the National Center for Physical Acoustics, and later at the U.S. Naval Academy, to model acoustic mine detection. The apparatus consists of a thick-walled cylinder filled with sifted homogeneous soil resting on a thin elastic plate that is clamped to the bottom of the column. It represents a good simplified physical model for VS 1.6 and VS 2.2 inert anti-tank plastic buried landmines. Using a loudspeaker (located over the soil) that is driven by a swept sinusoid, tuning curve experiments are performed. The vibration amplitude versus frequency is measured on a swept spectrum analyzer using an accelerometer located on the soil-air interface or under the plate. The backbone curve shows a linear decrease in peak frequency versus increasing amplitude. A two-tone test experiment is performed using two loudspeakers generating acoustic frequencies (closely spaced on either side of resonance, typically ~100 Hz). A rich vibration spectrum of combination frequency tones (along with the primaries) is observed which is characteristic of actual nonlinear detection schemes.

Crustal block motion model and interplate coupling along Ecuador-Colombia trench based on GNSS observation network

NASA Astrophysics Data System (ADS)

Ito, T.; Mora-Páez, H.; Peláez-Gaviria, J. R.; Kimura, H.; Sagiya, T.

2017-12-01

IntroductionEcuador-Colombia trench is located at the boundary between South-America plate, Nazca Plate and Caribrian plate. This region is very complexes such as subducting Caribrian plate and Nazca plate, and collision between Panama and northern part of the Andes mountains. The previous large earthquakes occurred along the subducting boundary of Nazca plate, such as 1906 (M8.8) and 1979 (M8.2). And also, earthquakes occurred inland, too. So, it is important to evaluate earthquake potentials for preparing huge damage due to large earthquake in near future. GNSS observation In the last decade, the GNSS observation was established in Columbia. The GNSS observation is called by GEORED, which is operated by servicing Geologico Colomiano. The purpose of GEORED is research of crustal deformation. The number of GNSS site of GEORED is consist of 60 continuous GNSS observation site at 2017 (Mora et al., 2017). The sampling interval of almost GNSS site is 30 seconds. These GNSS data were processed by PPP processing using GIPSY-OASYS II software. GEORED can obtain the detailed crustal deformation map in whole Colombia. In addition, we use 100 GNSS data at Ecuador-Peru region (Nocquet et al. 2014). Method We developed a crustal block movements model based on crustal deformation derived from GNSS observation. Our model considers to the block motion with pole location and angular velocity and the interplate coupling between each block boundaries, including subduction between the South-American plate and the Nazca plate. And also, our approach of estimation of crustal block motion and coefficient of interplate coupling are based on MCMC method. The estimated each parameter is obtained probably density function (PDF). Result We tested 11 crustal block models based on geological data, such as active fault trace at surface. The optimal number of crustal blocks is 11 for based on geological and geodetic data using AIC. We use optimal block motion model. And also, we estimate interplate coupling along the plate interface and rigid block motion. We can evaluate to contribution of elastic deformation and rigid motion. In result, weak plate coupling was found northern part of 3 degree in latitude. Almost crustal deformation are explained by rigid block motion.

Biomechanical evaluation of a new MatrixMandible plating system on cadaver mandibles.

PubMed

Gateno, Jaime; Cookston, Christopher; Hsu, Sam Sheng-Pin; Stal, Drew N; Durrani, Salim K; Gold, Jonathan; Ismaily, Sabir; Alexander, Jerry W; Noble, Philip C; Xia, James J

2013-11-01

Current mandibular plating systems contain a wide range of plates and screws needed for the treatment of mandibular reconstruction and mandibular fractures. The authors' hypothesis was that a single diameter screw could be used in all applications in a plating system. Therefore, the purpose of this study was to test if the 2.0-mm locking screws could replace the 2.4-mm screws to stabilize a 2.5-mm-thick reconstruction plate in the treatment of mandibular discontinuity. Thirty-six fresh human cadaveric mandibles were used: 18 were plated using 2.0-mm locking screws (experimental) and the other 18 were plated using 2.4-mm locking screws (control). Each group was further divided into 3 subgroups based on the site of loading application: the ipsilateral (right) second premolar region, the central incisal region, and the contralateral (left) first molar region. The same ipsilateral (right) mandibular angular discontinuity was created by the same surgeon. The mandible was mounted on a material testing machine. The micromotions between the 2 segments, permanent and elastic displacements, were recorded after incremental ramping loads. The magnitude of screw back-out and the separation between plate and bone were recorded using a laser scanner (resolution, 0.12 mm) before and after the loading applications. The data were processed. Descriptive analyses and a general linear model for repeated measures analysis of variance were performed. There was no statistically significant difference in permanent displacement (mean, 1.16 and 0.82 mm, respectively) between the 2.0-mm and 2.4-mm screw groups. There also was no statistically significant difference in elastic displacement between the 2 groups (mean, 1.48 and 1.21 mm, respectively). Finally, there were no statistically significant differences in screw back-out or separation between plate and bone between the 2 groups. All means for screw back-out and separation between screw and bone for each group were judged within the error of the laser scanning system (<0.12 mm). One may anticipate that the mechanical functions of the 2.0-mm locking screws are not different from those of the 2.4-mm screws when a 2.5-mm-thick reconstruction plate is used to reconstruct mandibular angular discontinuity. However, further biomechanical studies (ie, fatigue of screws) are warranted before a randomized clinical trial can be conducted to definitively prove that the 2.4-mm screws can be replaced by 2.0-mm screws. Copyright © 2013 American Association of Oral and Maxillofacial Surgeons. Published by Elsevier Inc. All rights reserved.

Numerical study of the shape parameter dependence of the local radial point interpolation method in linear elasticity.

PubMed

Moussaoui, Ahmed; Bouziane, Touria

2016-01-01

The method LRPIM is a Meshless method with properties of simple implementation of the essential boundary conditions and less costly than the moving least squares (MLS) methods. This method is proposed to overcome the singularity associated to polynomial basis by using radial basis functions. In this paper, we will present a study of a 2D problem of an elastic homogenous rectangular plate by using the method LRPIM. Our numerical investigations will concern the influence of different shape parameters on the domain of convergence,accuracy and using the radial basis function of the thin plate spline. It also will presents a comparison between numerical results for different materials and the convergence domain by precising maximum and minimum values as a function of distribution nodes number. The analytical solution of the deflection confirms the numerical results. The essential points in the method are: •The LRPIM is derived from the local weak form of the equilibrium equations for solving a thin elastic plate.•The convergence of the LRPIM method depends on number of parameters derived from local weak form and sub-domains.•The effect of distributions nodes number by varying nature of material and the radial basis function (TPS).

An ultrasonic method for determination of elastic moduli, density, attenuation and thickness of a polymer coating on a stiff plate.

PubMed

Lavrentyev, A I; Rokhlin, S I

2001-04-01

An ultrasonic method proposed by us for determination of the complete set of acoustical and geometrical properties of a thin isotropic layer between semispaces (J. Acoust. Soc. Am. 102 (1997) 3467) is extended to determination of the properties of a coating on a thin plate. The method allows simultaneous determination of the coating thickness, density, elastic moduli and attenuation (longitudinal and shear) from normal and oblique incidence reflection (transmission) frequency spectra. Reflection (transmission) from the coated plate is represented as a function of six nondimensional parameters of the coating which are determined from two experimentally measured spectra: one at normal and one at oblique incidence. The introduction of the set of nondimensional parameters allows one to transform the reconstruction process from one search in a six-dimensional space to two searches in three-dimensional spaces (one search for normal incidence and one for oblique). Thickness, density, and longitudinal and shear elastic moduli of the coating are calculated from the nondimensional parameters determined. The sensitivity of the method to individual properties and its stability against experimental noise are studied and the inversion algorithm is accordingly optimized. An example of the method and experimental measurement for comparison is given for a polypropylene coating on a steel foil.

Reconciling Pre- and Co-Seismic Deformation at Megathrusts: Tohoku Informing Cascadia

NASA Astrophysics Data System (ADS)

Furlong, K. P.; Govers, R. M.

2013-12-01

One of the outstanding goals of earthquake science is to effectively anticipate the earthquake characteristics of a future event - magnitude, rupture area, slip history - through the judicious application of models that use observations of inter-earthquake deformation and the history of earthquakes along that plate boundary segment. The series of great earthquakes over the past decade since the 2004 Mw 9.2 Sumatra earthquake have demonstrated both the sobering reality that our current models of subduction zone earthquake genesis are insufficient but more positively have provided a wealth of data and observations that can be used to develop improved framework models of the lithospheric behavior through the earthquake cycle in subduction zones. Some of the issues that recent observations raise are straightforward, while others imply aspects of the subduction process that have not been previously considered important. Based on observations of a range of great earthquakes since 2004, and with a particular focus on the 2011 Mw 9.0 Tohoku event we can identify a suite of key issues that include: (1) Patterns of inter-seismic deformation (strain accumulation) are not simply the converse of the co-seismic elastic strain release. (2) Deformation of the slab during the earthquake cycle is a common occurrence and its role in buffering upper-plate deformation is a key consideration in the potential tsunamigenic character of a subduction system. (3) Rates of pre-earthquake deformation (e.g. observed upper-plate GPS displacements) and inferred slip deficit accumulation on the megathrust are inconsistent with co-seismic displacements/fault slip and recurrence intervals. (4) Patterns of megathrust locked patches, degrees of coupling and other parameterizations that are used to define earthquake potential have only a loose agreement with the actual patterns of slip and moment release seen in the ensuing great earthquake. Simple elastic models do provide a general agreement between processes along the megathrust and observations regionally - i.e. with such models (e.g. Okada-type solutions) we find reasonable agreement among geodetic and seismologic models. In assessing sensitivities in our preliminary modeling, we find that depending on the strength and rheologic considerations in the model, similar patterns of displacement in the upper plate in the typical observing zones (on-shore, ~ 100+ km from trench) can have significantly different displacement effects in the vicinity of the earthquake rupture and trench - the areas most critical to tsunamigenesis and assessing earthquake magnitude. Also although it is perhaps reassuring to see that there is general agreement between the seismologically determined finite fault models (FFM) and the observed surface deformation; this information after-the-fact does not tell us why the slip deficit accumulated as it did. Here we report on improved (numerical) models of the strain accumulation and release cycle in megathrust zones that better incorporate variations in rheology, the effects of plate boundary character (pre- and co-seismic), and the relationships between pre-earthquakes observed deformation and co-seismic rupture characteristics.

Vibration characteristics of two-stage planetary transmission system with thin-walled ring gear on elastic supports

NASA Astrophysics Data System (ADS)

Li, JianYing; Hu, QingChun; Zong, ChangFu; Zhu, TianJun; Zhang, ZeXing

2018-03-01

A dual-clutch and dual-speed planetary gears mechanism of a hybrid car coupled-system is taken as research subject, in which the ring gear of planet set II is a thin-walled structure and the clutch friction plates of planet set II are used as its elastic supports. Based on the lumped parameter-rigid elastic coupled dynamic model of two-stage planetary transmission system with thin-walled ring gear on elastic supports, the motion differential equations are established and the dynamic responses are solved by the Runge-Kutta method considering each stage internal and external time-varying mesh stiffness. The vibration displacements of each stage ring gear have been affected differently in time-domain, the translational vibration displacement of the ring gear of planet set I are obviously more than the torsional vibration displacement, but it is opposite for the ring gear of planet set II; The translational and torsional vibration responses of each stage ring gear arrive the peak in low-frequency. The analysis results of this paper can enrich the theoretical research of multistage planetary transmission and provide guidance for dynamic design.

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface. Part 2: Solution and results

NASA Technical Reports Server (NTRS)

Lu, M. C.; Erdogan, F.

1980-01-01

The numerical method is given for solving the plane problem for two bonded infinite dissimilar elastic strips which contain cracks of various configurations. The problem is intended to approximate a composite beam or a plate having cracks perpendicular to and on the interface of the two layers.

Practical solution of plastic deformation problems in elastic-plastic range

NASA Technical Reports Server (NTRS)

Mendelson, A; Manson, S

1957-01-01

A practical method for solving plastic deformation problems in the elastic-plastic range is presented. The method is one of successive approximations and is illustrated by four examples which include a flat plate with temperature distribution across the width, a thin shell with axial temperature distribution, a solid cylinder with radial temperature distribution, and a rotating disk with radial temperature distribution.

Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial.

PubMed

Zhu, R; Liu, X N; Hu, G K; Sun, C T; Huang, G L

2014-11-24

Negative refraction of elastic waves has been studied and experimentally demonstrated in three- and two-dimensional phononic crystals, but Bragg scattering is impractical for low-frequency wave control because of the need to scale the structures to manageable sizes. Here we present an elastic metamaterial with chiral microstructure made of a single-phase solid material that aims to achieve subwavelength negative refraction of elastic waves. Both negative effective mass density and modulus are observed owing to simultaneous translational and rotational resonances. We experimentally demonstrate negative refraction of the longitudinal elastic wave at the deep-subwavelength scale in the metamaterial fabricated in a stainless steel plate. The experimental measurements are in good agreement with numerical simulations. Moreover, wave mode conversion related with negative refraction is revealed and discussed. The proposed elastic metamaterial may thus be used as a flat lens for elastic wave focusing.

Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.

PubMed

Nguyen, Vu-Hieu; Naili, Salah

2012-08-01

This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. Copyright © 2012 John Wiley & Sons, Ltd.

Numerical Study of Effects of Fluid-Structure Interaction on Dynamic Responses of Composite Plates

DTIC Science & Technology

2009-09-01

FORCE LOAD AND CLAMPED BOUNDARY.................73 APPENDIX F: ADDITIONAL FIGURES FOR COMPOSITE DE NSITY EFFECTS WITH CONCE NTRATED FORCE LOAD AND...Structure Strain and Kine tic Energy Comparison for Elastic Modulus Variations with Concentrated Force and Clamped Boundary .........................31...48 Figure 49. Experiment Strain Gage La yout on Underside of Composite Plate

Nonlinear thermal dynamic analysis of graphit/aluminum composite plates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tenneti, R.; Chandrashekhara, K.

1994-09-01

Because of the increased application of composite materials in high-temperature environments, the thermoelastic analysis of laminated composite structures is important. Many researchers have applied the classical lamination theory to analyze laminated plates under thermomechanical loading, which neglects shear deformation effects. The transverse shear deformation effects are not negligible as the ratios of inplane elastic modulus to transverse shear modulus are relatively large for fiber-reinforced composite laminates. The application of first-order shear deformation theory for the thermoelastic analysis of laminated plates has been reported by only a few investigators. Reddy and Hsu have considered the thermal bending of laminated plates. Themore » analytical and finite element solutions for the thermal bucking of laminated plates have been reported by Tauchert and Chandrashekara, respectively. However, the first-order shear deformation theory, based on the assumption of constant distribution of transverse shear through the thickness, requires a shear correction factor to account for the parabolic shear strain distribution. Higher order theories have been proposed which eliminate the need for a shear correction factor. In the present work, nonlinear dynamic analysis of laminated plates subjected to rapid heating is investigated using a higher order shear deformation theory. A C(sup 0) finite element model with seven degrees of freedom per node is implmented and numerical results are presented for laminated graphite/aluminum plates.« less

Developing ultrasensitive pressure sensor based on graphene nanoribbon: Molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Kwon, Oh Kuen; Lee, Jun Ha; Kim, Ki-Sub; Kang, Jeong Won

2013-01-01

We propose schematics for an ultra-sensitive pressure sensor based on graphene-nanoribbon (GNR) and investigate its electromechanical properties using classical molecular dynamics simulations and piezo-electricity theory. Since the top plate applied to the actual pressure is large whereas the contact area on the GNR is very small, both the sensitivity and the sensing range can be adjusted by controlling the aspect ratio between the top plate and the contact point areas. Our calculation shows that the electrical conductivity of GNRs can be tuned by the applied pressure and the electric conductance of the deflected GNR linearly increases with increasing applied pressure for the linear elastic region in low pressure below the cut-off point. In the curves for both the deflection and potential energy, the linear elastic regime in low pressure was explicitly separated with the non-linear elastic regime in high pressure. The proposed GNR-based nanoelectromechanical devices have great potential for application as electromechanical memory, relay or switching devices.

Acoustic emission source localization based on distance domain signal representation

NASA Astrophysics Data System (ADS)

Gawronski, M.; Grabowski, K.; Russek, P.; Staszewski, W. J.; Uhl, T.; Packo, P.

2016-04-01

Acoustic emission is a vital non-destructive testing technique and is widely used in industry for damage detection, localisation and characterization. The latter two aspects are particularly challenging, as AE data are typically noisy. What is more, elastic waves generated by an AE event, propagate through a structural path and are significantly distorted. This effect is particularly prominent for thin elastic plates. In these media the dispersion phenomenon results in severe localisation and characterization issues. Traditional Time Difference of Arrival methods for localisation techniques typically fail when signals are highly dispersive. Hence, algorithms capable of dispersion compensation are sought. This paper presents a method based on the Time - Distance Domain Transform for an accurate AE event localisation. The source localisation is found through a minimization problem. The proposed technique focuses on transforming the time signal to the distance domain response, which would be recorded at the source. Only, basic elastic material properties and plate thickness are used in the approach, avoiding arbitrary parameters tuning.

Isostatic Gravity Anomalies, Flexure and the Origin of Seaward Dipping Reflectors at Volcanic Rifted Margins

NASA Astrophysics Data System (ADS)

Morgan, R. L.; Watts, A. B.

2016-12-01

Seaward Dipping Reflectors (SDRs) are ubiquitous features of volcanic rifted continental margins where they comprise characteristic wedge-shaped packages of mainly extrusive lava flows. However, their origin has been disputed with some workers suggesting they form by progressive subsidence of extended crust while others propose they are accommodated within the crust by one or more continent-dipping normal faults. We present here a simple model in which SDRs are formed by successive dykes, which intrude and load the crust causing a surface flexure which is subsequently infilled and then loaded by volcanic material, including lava flows. The model explains the arcuate shape, limited offlap geometries and down-dip thickening of SDRs as observed in seismic reflection profiles. By comparing observed and calculated dips we have been able to constrain the elastic plate model type and the effective elastic thickness of rifted lithosphere, Te. Results suggest a broken rather than continuous plate model and Te in the range 3-15 km. The thickness of the resulting SDR package increases with decreasing Te and decreasing compensation density. Decreasing the Tefor successive loads as rifting progresses produces offlap of sub-packages. We have verified our results using process-oriented gravity modelling, in which the gravity effect of surface volcanic infill loads is calculated and combined with the gravity effect of buried dyke loads. Results show good general agreement between observed Airy isostatic anomalies and calculated gravity anomalies. This suggests that the steep gradient that is often observed in the Airy isostatic gravity anomaly at rifted margins is a useful proxy for the landward edge of the dykes that intrude the crust prior to seafloor spreading, rather than a change in basement elevation at the boundary between oceanic and continental crust, as proposed by previous workers.

Advanced stress analysis methods applicable to turbine engine structures

NASA Technical Reports Server (NTRS)

Pian, Theodore H. H.

1991-01-01

The following tasks on the study of advanced stress analysis methods applicable to turbine engine structures are described: (1) constructions of special elements which contain traction-free circular boundaries; (2) formulation of new version of mixed variational principles and new version of hybrid stress elements; (3) establishment of methods for suppression of kinematic deformation modes; (4) construction of semiLoof plate and shell elements by assumed stress hybrid method; and (5) elastic-plastic analysis by viscoplasticity theory using the mechanical subelement model.

Theoretical study of corrugated plates: Shearing of a trapezoidally corrugated plate with trough lines permitted to curve

NASA Technical Reports Server (NTRS)

Lin, C.; Libove, C.

1971-01-01

A theoretical analysis is presented of the elastic shearing of a trapezoidally corrugated plate with discrete attachments at the ends of the corrugations. Numerical results on effective shear stiffness, stresses, and displacements are presented for selected geometries and end-attachment conditions. It is shown that the frame-like deformation of the cross-sections, which results from the absence of continuous end attachments, can lead to large transverse bending stresses and large reductions in shearing stiffness.

The Nonlinear Dynamic Response of an Elastic-Plastic Thin Plate under Impulsive Loading,

DTIC Science & Technology

1987-06-11

Among those numerical methods, the finite element method is the most effective one. The method presented in this paper is an " influence function " numerical...computational time is much less than the finite element method. Its precision is higher also. II. Basic Assumption and the Influence Function of a Simple...calculation. Fig. 1 3 2. The Influence function of a Simple Supported Plate The motion differential equation of a thin plate can be written as DV’w+ _.eluq() (1

Phenomena after meteoroid penetration of a bumper plate

NASA Technical Reports Server (NTRS)

Todd, F. C.

1971-01-01

The analysis of hypervelocity impact of particles on a detector in space, with flow and shock penetration through fluid, plastic, and elastic zones was studied. The original paper and computer program on this topic is presented. Improvements in the program for the study of the formation of a cone of debris are discussed. The truncated apex of the cone is at the hole formed by the penetration of an initially spherical rock through a thin plate. A solution for the penetration of the thin plate was sought.

The mechanical and morphological properties of bone beneath internal fixation plates of differing rigidity.

PubMed

Claes, L

1989-01-01

The internal fixation of diaphyseal fractures by bone plates is a well recognized treatment. The normal physiological stress of bone is reduced by plates that cause a negative balance of bone-remodeling processes. Many investigators have shown that the degree of stress protection is dependent on the rigidity of the plates. It was the aim of this study to quantify mechanical and morphological changes at different locations in a plated diaphyseal bone as a function of differing plate rigidity. Two types of plates with the same size but different materials were used. The stainless steel plates had a modulus of elasticity and bending stiffness 3.2 times higher than the carbon fiber reinforced carbon plates. Both types of plates were applied to the intact right and left femora of six foxhounds for 6 months. The stiffer stainless steel plates led to a significantly higher bone loss and correspondingly greater loss of mechanical properties. These effects were greatest directly beneath the plate and less with increasing distance from the plate.

Small amplitude, transverse vibrations of circular plates with an eccentric rectangular perforation elastically restrained against rotation and translation on both edges

NASA Astrophysics Data System (ADS)

Laura, P. A. A.; Avalos, D. R.

2008-05-01

The Rayleigh-Ritz variational method is applied to the determination of the first four frequency coefficients for small amplitude, transverse vibrations of circular plates with an eccentric, rectangular perforation that is elastically restrained against rotation and translation on both edges. Coordinate functions are used which identically satisfy the boundary conditions at the outer circular edge, while the restraining boundary conditions at the inner edge of the cutout are dealt with directly through the energetic terms in the functional expressions. The procedure seems to show very good numerical stability and convergence properties. As an added bonus, the method allows for increased flexibility in dealing with boundary conditions at the edge of the cutout.

The trampoline aftereffect: the motor and sensory modulations associated with jumping on an elastic surface.

PubMed

Márquez, Gonzalo; Aguado, Xavier; Alegre, Luis M; Lago, Angel; Acero, Rafael M; Fernández-del-Olmo, Miguel

2010-08-01

After repeated jumps over an elastic surface (e.g. a trampoline), subjects usually report a strange sensation when they jump again overground (e.g. they feel unable to jump because their body feels heavy). However, the motor and sensory effects of exposure to an elastic surface are unknown. In the present study, we examined the motor and perceptual effects of repeated jumps over two different surfaces (stiff and elastic), measuring how this affected maximal countermovement vertical jump (CMJ). Fourteen subjects participated in two counterbalanced sessions, 1 week apart. Each experimental session consisted of a series of maximal CMJs over a force plate before and after 1 min of light jumping on an elastic or stiff surface. We measured actual motor performance (height jump and leg stiffness during CMJ) and how that related to perceptual experience (jump height estimation and subjective sensation). After repeated jumps on an elastic surface, the first CMJ showed a significant increase in leg stiffness (P < or = 0.01), decrease in jump height (P < or = 0.01) increase in perceptual misestimation (P < or = 0.05) and abnormal subjective sensation (P < or = 0.001). These changes were not observed after repeated jumps on a rigid surface. In a complementary experiment, continuous surface transitions show that the effects persist across cycles, and the effects over the leg stiffness and subjective experience are minimized (P < or = 0.05). We propose that these aftereffects could be the consequence of an erroneous internal model resulting from the high vertical forces produced by the elastic surface.

Transformation elastodynamics and cloaking for flexural waves

NASA Astrophysics Data System (ADS)

Colquitt, D. J.; Brun, M.; Gei, M.; Movchan, A. B.; Movchan, N. V.; Jones, I. S.

2014-12-01

The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general form of the partial differential equation is not invariant with respect to the cloaking transformation. The significant result of this paper is the analysis of the transformed equation and its interpretation in the framework of the linear theory of pre-stressed plates. The paper provides a formal framework for transformation elastodynamics as applied to elastic plates. Furthermore, an algorithm is proposed for designing a broadband square cloak for flexural waves, which employs a regularised push-out transformation. Illustrative numerical examples show high accuracy and efficiency of the proposed cloaking algorithm. In particular, a physical configuration involving a perturbation of an interference pattern generated by two coherent sources is presented. It is demonstrated that the perturbation produced by a cloaked defect is negligibly small even for such a delicate interference pattern.

Elasto-plastic deformation and plate weakening due to normal faulting in the subducting plate along the Mariana Trench

NASA Astrophysics Data System (ADS)

Zhou, Z.; Lin, J.

2017-12-01

We investigated variations in the elasto-plastic deformation of the subducting plate along the Mariana Trench through an analysis of flexural bending, normal fault characteristics, and geodynamic modeling. It was observed that most of the normal faults were initiated along the outer-rise region and grew toward the trench axis with strikes that are mostly subparallel to the local trend of the trench axis. The average trench relief is more than 5 km in the southern region while only about 2 km in the northern and central regions. Fault throws were measured to be significantly greater in the southern region (maximum 320 m) than the northern and central regions (maximum 200 m). The subducting plate was modeled as an elasto-plastic slab subjected to tectonic loading along the trench axis. The "apparent" slab-pull dip angle of the subducting plate, calculated from the ratio of the inverted vertical loading versus horizontal tensional force, was significantly larger in the southern region (51-64°) than in the northern (22-35°) and central (20-34°) regions, which is consistent with the seismologically determined dip angle within the shallow part of the subducting slab. This result suggests that the differences in the plate flexure and normal faulting characteristics along the Mariana Trench might be influenced, at least in part, by significant variations in the dip angle within the shallow part of the subducting plate. Normal faults were modeled to penetrate to a maximum depth of 15, 14, and 25 km in the upper mantle for the northern, central, and southern regions, respectively, which is consistent with the depths of available relocated normal faulting earthquakes in the central region. We calculated that the average reduction of the effective elastic plate thickness Te due to normal faulting is 31% in the southern region, which is almost twice that in both the northern and central regions ( 16%). Furthermore, model results revealed that the stress reduction associated with individual normal faults could also decrease Te locally.

The Role of a Weak Layer at the Base of an Oceanic Plate on Subduction Dynamics

NASA Astrophysics Data System (ADS)

Carluccio, R.; Moresi, L. N.; Kaus, B. J. P.

2017-12-01

Plate tectonics relies on the concept of an effectively rigid lithospheric lid moving over a weaker asthenosphere. In this model, the lithosphere asthenosphere boundary (LAB) is a first-order discontinuity that accommodates differential motion between tectonic plates and the underlying mantle. Recent seismic studies have revealed the existence of a low velocity and high electrical conductivity layer at the base of subducting tectonic plates. This thin layer has been interpreted as being weak and slightly buoyant and it has the potential to influence the dynamics of subducting plates. However, geodynamically, the role of a weak layer at the base of the lithosphere remains poorly studied, especially at subduction zones. Here, we use numerical models to investigate the first-order effects of a weak buoyant layer at the LAB on subduction dynamics. We employ both 2-D and 3-D models in which the slab and the mantle are either linear viscous or have a more realistic temperature-dependent, visco-elastic-plastic rheology and we vary the properties of the layer at the base of the oceanic lithosphere. Our results show that the presence of a weak layer affects the dynamics of plates, primarily by increasing the subduction speed and also influences the morphology of subducting slab. For moderate viscosity contrasts (<100) and a layer thickness of ˜30 km, it increases the plate velocity but not the overall shape of the slab. However, for larger viscosity contrasts (>1000), it can also change the morphology of the subduction itself and for thinner and more buoyant layers, the overall effect is reduced. The overall impact of this effects may depend on the effective contrast between the properties of the slab and the weak layer + mantle systems, and so, by the layer characteristics modelled such as its viscosity, density, thickness and rheology. In this study, we show and summarise this impact consistently with the recent seismological constraints and observations, for example, a pile-up of weak material in the bending zone of the subducting plate.

Experimental evidence of locally resonant sonic band gap in two-dimensional phononic stubbed plates

NASA Astrophysics Data System (ADS)

Oudich, Mourad; Senesi, Matteo; Assouar, M. Badreddine; Ruzenne, Massimo; Sun, Jia-Hong; Vincent, Brice; Hou, Zhilin; Wu, Tsung-Tsong

2011-10-01

We provide experimental evidence of the existence of a locally resonant sonic band gap in a two-dimensional stubbed plate. Structures consisting of a periodic arrangement of silicone rubber stubs deposited on a thin aluminium plate were fabricated and characterized. Brillouin spectroscopy analysis is carried out to determine the elastic constants of the used rubber. The constants are then implemented in an efficient finite-element model that predicts the band structure and transmission to identify the theoretical band gap. We measure a complete sonic band gap for the out-of-plane Lamb wave modes propagating in various samples fabricated with different stub heights. Frequency domain measurements of full wave field and transmission are performed through a scanning laser Doppler vibrometer. A complete band gap from 1.9 to 2.6 kHz is showed using a sample with 6-mm stub diameter, 5-mm thickness, and 1-cm structure periodicity. Very good agreement between numerical and experimental results is obtained.

Mass-stiffness substructuring of an elastic metasurface for full transmission beam steering

NASA Astrophysics Data System (ADS)

Lee, Hyuk; Lee, Jun Kyu; Seung, Hong Min; Kim, Yoon Young

2018-03-01

The metasurface concept has a significant potential due to its novel wavefront-shaping functionalities that can be critically useful for ultrasonic and solid wave-based applications. To achieve the desired functionalities, elastic metasurfaces should cover full 2π phase shift and also acquire full transmission within subwavelength scale. However, they have not been explored much with respect to the elastic regime, because the intrinsic proportionality of mass-stiffness within the continuum elastic media causes an inevitable trade-off between abrupt phase shift and sufficient transmission. Our goal is to engineer an elastic metasurface that can realize an inverse relation between (amplified) effective mass and (weakened) stiffness in order to satisfy full 2π phase shift as well as full transmission. To achieve this goal, we propose a continuum elastic metasurface unit cell that is decomposed into two substructures, namely a mass-tuning substructure with a local dipolar resonator and a stiffness-tuning substructure composed of non-resonant multiply-perforated slits. We demonstrate analytically, numerically, and experimentally that this unique substructured unit cell can satisfy the required phase shift with high transmission. The substructuring enables independent tuning of the elastic properties over a wide range of values. We use a mass-spring model of the proposed continuum unit cell to investigate the working mechanism of the proposed metasurface. With the designed metasurface consisting of substructured unit cells embedded in an aluminum plate, we demonstrate that our metasurface can successfully realize anomalous steering and focusing of in-plane longitudinal ultrasonic beams. The proposed substructuring concept is expected to provide a new principle for the design of general elastic metasurfaces that can be used to efficiently engineer arbitrary wave profiles.

Study of Graphite/Epoxy Composites for Material Flaw Criticality.

DTIC Science & Technology

1980-11-01

criticality of disbonds with two-dimensional planforms located in laminated graphite/epoxy composites has been examined. Linear elastic fracture...mechanics approach, semi-empirical growth laws and methods of stress analysis based on a modified laminated plate theory have been studied for assessing...growth rates of disbonds in a transverse shear environ- ment. Elastic stability analysis has been utilized for laminates with disbonds subjected to in

Continuous deflation and plate spreading at the Askja volcanic system, Iceland: Constrains on deformation processes from finite element models using temperature-dependent non-linear rheology

NASA Astrophysics Data System (ADS)

Tariqul Islam, Md.; Sturkell, Erik; Sigmundsson, Freysteinn; Drouin, Vincent Jean Paul B.; Ófeigsson, Benedikt G.

2014-05-01

Iceland is located on the mid Atlantic ridge, where the spreading rate is nearly 2 cm/yr. The high rate of magmatism in Iceland is caused by the interaction between the Iceland hotspot and the divergent mid-Atlantic plate boundary. Iceland hosts about 35 volcanoes or volcanic systems that are active. Most of these are aliened along the plate boundary. The best studied magma chamber of central volcanoes (e.g., Askja, Krafla, Grimsvötn, Katla) have verified (suggested) a shallow magma chamber (< 5 km), which has been model successfully with a Mogi source, using elastic and/or elastic-viscoelastic half-space. Maxwell and Newtonian viscosity is mainly considered for viscoelastic half-space. Therefore, rheology may be oversimplified. Our attempt is to study deformation of the Askja volcano together with plate spreading in Iceland using temperature-dependent non-linear rheology. It offers continuous variation of rheology, laterally and vertically from rift axis and surface. To implement it, we consider thermo-mechanic coupling models where rheology follows dislocation flow in dry condition based on a temperature distribution. Continuous deflation of the Askja volcanic system is associated with solidification of magma in the magma chamber and post eruption relaxation. A long time series of levelling data show its subsidence trend to exponentially. In our preliminary models, a magma chamber at 2.8 km depth with 0.5 km radius is introduced at the ridge axis as a Mogi source. Simultaneously far field of rift axis stretching by 18.4 mm/yr (measured during 2007 to 20013) is applied to reproduce plate spreading. Predicted surface deformation caused of combined effect of tectonic-volcanic activities is evaluated with GPS during 2003-2009 and RADARSAT InSAR data during 2000 to 2010. During 2003-2009, data from the GPS site OLAF (close to the centre of subsidence) shows average rate of subsidence 19±1 mm/yr relative to the ITRF2005 reference frame. The MASK (Mid ASKJA) site is another GPS station at the top of predicted centre of magma chamber correlates well with OLAF site at 500 m distance from MASK. Average subsidence rates derived from GPS measurements show comparable rate derived from InSAR data. Velocities derived from InSAR show that the yearly maximum subsidence rates in the Askja caldera decrease linearly. The optimized pressure decrease in the magma chamber from the model follows an exponential decay, with P (MPa) = 2.0177 EXP(-0.0176x), where x is the numbers of years (1,2,3 .. 10). However total ramp pressure drop during this period (10 years) is 4 MPa and additional 4.68 MPa pressure drop may be caused of rheological relaxation.

Magnetic-saturation zone model for two semipermeable cracks in magneto-electro-elastic medium

NASA Astrophysics Data System (ADS)

Jangid, Kamlesh

2018-03-01

Extension of the PS model (Gao et al. [1]) in piezoelectric materials and the SEMPS model (Fan and Zhao [2]) in MEE materials, is proposed for two semi-permeable cracks in a MEE medium. It is assumed that the magnetic yielding occurs at the continuation of the cracks due to the prescribed loads. We have model these crack continuations as the zones with cohesive saturation limit magnetic induction. Stroh's formalism and complex variable techniques are used to formulate the problem. Closed form analytical expressions are derived for various fracture parameters. A numerical case study is presented for BaTiO3 - CoFe2O4 ceramic cracked plate.

[Research Progress and Development Prospect of Biomedical Plate].

PubMed

Li, Xiao; Liu, Jing; Wu, Qiang; Wang, Yanjie; Xiao, Tao; Liu, Lihong; Yu, Shu

2016-12-01

Different generations of biomedical materials are analyzed in this paper.The current clinical uses of plates made of metals,polymers or composite materials are evaluated,and nano hydroxyapatite/polylactic acid composites and carbon/carbon composite plates are introduced as emphasis.It is pointed out that the carbon/carbon composites are of great feasibility and advantage as a new generation of biomedical materials,especially in the field of bone plate.Compared to other biomaterials,carbon/carbon composites have a good biocompatibility and mechanical compatibility because they have similar elastic modulus,porosity and density to that of human bones.With the development of the technology in knitting and material preparation,carbon/carbon composite plates have a good application prospect.

Non-collinear interaction of guided elastic waves in an isotropic plate

NASA Astrophysics Data System (ADS)

Ishii, Yosuke; Biwa, Shiro; Adachi, Tadaharu

2018-04-01

The nonlinear wave propagation in a homogeneous and isotropic elastic plate is analyzed theoretically to investigate the non-collinear interaction of plate wave modes. In the presence of two primary plate waves (Rayleigh-Lamb or shear horizontal modes) propagating in arbitrary directions, an explicit expression for the modal amplitude of nonlinearly generated wave fields with the sum or difference frequency of the primary modes is derived by using the perturbation analysis. The modal amplitude is shown to grow in proportion with the propagation distance when the resonance condition is satisfied, i.e., when the wavevector of secondary wave coincides with the sum or difference of those of primary modes. Furthermore, the non-collinear interaction of two symmetric or two antisymmetric modes is shown to produce the secondary wave fields consisting only of the symmetric modes, while a pair of symmetric and antisymmetric primary modes is shown to produce only the antisymmetric modes. The influence of the intersection angle, the primary frequencies, and the mode combinations on the modal amplitude of secondary wave is examined for a low-frequency range where the lowest-order symmetric and antisymmetric Rayleigh-Lamb waves and the lowest-order symmetric shear horizontal wave are the only propagating modes.

Slip Distribution of the 2011 Tohoku-oki Earthquake obtained by Geodetic and Tsunami Data and with a 3-D Finite Element Model

NASA Astrophysics Data System (ADS)

Romano, F.; Trasatti, E.; Lorito, S.; Ito, Y.; Piatanesi, A.; Lanucara, P.; Hirata, K.; D'Agostino, N.; Cocco, M.

2012-12-01

The rupture process of the Great 2011 Tohoku-oki earthquake has been particularly well studied by using an unprecedented collection of geophysical data. There is a general agreement among the different source models obtained by modeling seismological, geodetic and tsunami data. A slip patch of nearly 40÷50 meters has been imaged and located around and up-dip from the hypocenter by most of published models, while some differences exist in the slip pattern retrieved at shallow depths near the trench, likely due to the different resolving power of distinct data sets and to the adopted fault geometry. It is well known that the modeling of great subduction earthquakes requires the use of 3-D structural models in order to properly account for the effects of topography, bathymetry and the geometrical variations of the plate interface as well as for the effects of elastic contrasts between the subducting plate and the continental lithosphere. In this study we build a 3-D Finite Element (FE) model of the Tohoku-oki area in order to infer the slip distribution of the 2011 earthquake by performing a joint inversion of geodetic (GPS and seafloor observations) and tsunami (ocean bottom pressure sensors, DART and GPS buoys) data. The FE model is used to compute the geodetic and tsunami Green's functions. In order to understand how geometrical and elastic heterogeneities control the inferred slip distribution of the Tohoku-oki earthquake, we compare the slip patterns obtained using both homogeneous and heterogeneous structural models. The goal of this study is to better constrain the slip distribution and the maximum slip amplitudes. In particular, we aim to focus on the rupture process in the shallower part of the fault plane and near the trench, which is crucial to model the tsunami data and to assess the tsunamigenic potential of earthquakes in this region.

Subduction Initiation under Unfavorable Conditions and New Fault Formation

NASA Astrophysics Data System (ADS)

Mao, X.; Gurnis, M.; May, D.

2017-12-01

How subduction initiates with unfavorable dipping lithospheric heterogeneities is an important and rarely studied topic. We build a geodynamic model starting with a vertical weak zone for the Puysegur incipient subduction zone (PISZ). A true free surface is tracked in pTatin3D, based on the Arbitrary Lagrangian Eulerian (ALE) finite element method, and is used to follow the dynamic mantle-surface interaction and topographic evolution. A simplified surface process, based on linear topography diffusion, is implemented. Density and free water content for different phase assemblages are gained by referring to precalculated 4D (temperature, pressure, rock type and total water content) phase maps using Perplex. Darcy's law is used to migrate free water, and a linear water weakening is applied to the mantle material. A new visco-elastic formulation called Elastic Viscous Stress Splitting (EVSS) method is also included. Our predictions fit the morphology of the Puysegur Trench and Ridge and the deformation history on the overriding plate. We show a new thrust fault forms and evolves into a smooth subduction interface, and the preexisting weak zone becomes a vertical fault inboard of the thrust fault during subduction initiation, which explains the two-fault system at PISZ. Our model suggests that the PISZ may not yet be self-sustaining. We propose that the Snares Trough is caused by plate coupling differences between shallower and deeper parts, the tectonic sliver between two faults experiences strong rotation, and low density materials accumulate beneath the Snares trough. Extended models show that with favorable dipping heterogeneities, no new fault forms, and subduction initiates with smaller resisting forces.

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

NASA Astrophysics Data System (ADS)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

ZIP3D: An elastic and elastic-plastic finite-element analysis program for cracked bodies

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Newman, J. C., Jr.

1990-01-01

ZIP3D is an elastic and an elastic-plastic finite element program to analyze cracks in three dimensional solids. The program may also be used to analyze uncracked bodies or multi-body problems involving contacting surfaces. For crack problems, the program has several unique features including the calculation of mixed-mode strain energy release rates using the three dimensional virtual crack closure technique, the calculation of the J integral using the equivalent domain integral method, the capability to extend the crack front under monotonic or cyclic loading, and the capability to close or open the crack surfaces during cyclic loading. The theories behind the various aspects of the program are explained briefly. Line-by-line data preparation is presented. Input data and results for an elastic analysis of a surface crack in a plate and for an elastic-plastic analysis of a single-edge-crack-tension specimen are also presented.

Rubber Impact on 3D Textile Composites

NASA Astrophysics Data System (ADS)

Heimbs, Sebastian; Van Den Broucke, Björn; Duplessis Kergomard, Yann; Dau, Frederic; Malherbe, Benoit

2012-06-01

A low velocity impact study of aircraft tire rubber on 3D textile-reinforced composite plates was performed experimentally and numerically. In contrast to regular unidirectional composite laminates, no delaminations occur in such a 3D textile composite. Yarn decohesions, matrix cracks and yarn ruptures have been identified as the major damage mechanisms under impact load. An increase in the number of 3D warp yarns is proposed to improve the impact damage resistance. The characteristic of a rubber impact is the high amount of elastic energy stored in the impactor during impact, which was more than 90% of the initial kinetic energy. This large geometrical deformation of the rubber during impact leads to a less localised loading of the target structure and poses great challenges for the numerical modelling. A hyperelastic Mooney-Rivlin constitutive law was used in Abaqus/Explicit based on a step-by-step validation with static rubber compression tests and low velocity impact tests on aluminium plates. Simulation models of the textile weave were developed on the meso- and macro-scale. The final correlation between impact simulation results on 3D textile-reinforced composite plates and impact test data was promising, highlighting the potential of such numerical simulation tools.

Concurrent prediction of ground reaction forces and moments and tibiofemoral contact forces during walking using musculoskeletal modelling.

PubMed

Peng, Yinghu; Zhang, Zhifeng; Gao, Yongchang; Chen, Zhenxian; Xin, Hua; Zhang, Qida; Fan, Xunjian; Jin, Zhongmin

2018-02-01

Ground reaction forces and moments (GRFs and GRMs) measured from force plates in a gait laboratory are usually used as the input conditions to predict the knee joint forces and moments via musculoskeletal (MSK) multibody dynamics (MBD) model. However, the measurements of the GRFs and GRMs data rely on force plates and sometimes are limited by the difficulty in some patient's gait patterns (e.g. treadmill gait). In addition, the force plate calibration error may influence the prediction accuracy of the MSK model. In this study, a prediction method of the GRFs and GRMs based on elastic contact element was integrated into a subject-specific MSK MBD modelling framework of total knee arthroplasty (TKA), and the GRFs and GRMs and knee contact forces (KCFs) during walking were predicted simultaneously with reasonable accuracy. The ground reaction forces and moments were predicted with an average root mean square errors (RMSEs) of 0.021 body weight (BW), 0.014 BW and 0.089 BW in the antero-posterior, medio-lateral and vertical directions and 0.005 BW•body height (BH), 0.011 BW•BH, 0.004 BW•BH in the sagittal, frontal and transverse planes, respectively. Meanwhile, the medial, lateral and total tibiofemoral (TF) contact forces were predicted by the developed MSK model with RMSEs of 0.025-0.032 BW, 0.018-0.022 BW, and 0.089-0.132 BW, respectively. The accuracy of the predicted medial TF contact force was improved by 12% using the present method. The proposed method can extend the application of the MSK model of TKA and is valuable for understanding the in vivo knee biomechanics and tribological conditions without the force plate data. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Uplift of the Transantarctic Mountains and the bedrock beneath the East Antarctic ice sheet

USGS Publications Warehouse

ten Brink, Uri S.; Hackney, R.I.; Bannister, S.; Stern, T.A.; Makovsky, Y.

1997-01-01

In recent years the Transantarctic Mountains (TAM), the largest noncontractional mountain belt in the world, have become the focus of modelers who explained their uplift by a variety of isostatic and thermal mechanisms. A problem with these models is a lack of available data to compare with model predictions. We report here the results of a 312-km-long geophysical traverse conducted in 1993/1994 in the hinterland of the TAM. Using detailed subglacial topography and gravity measurements, we confirm the origin of the TAM as a flexural uplift of the edge of East Antarctica. Using an elastic model with a free edge, we can jointly fit the topography and the gravity with a plate having an elastic thickness of 85 ?? 15 km and a preuplift elevation of 700 ?? 50 m for East Antarctica. Using a variety of evidence, we argue that the uplift is coincident with a relatively minor tectonic event of transtensional motion between East and West Antarctica during the Eocene rather than the Late Cretaceous rifting event that created the Ross Embayment. We suggest that this transtensional motion caused the continuous plate to break, which created an escarpment that significantly increased the rates of erosion and exhumation. Results from the geophysical traverse also extend our knowledge of the bedrock geology from the exposures within the TAM to the ice covered interior. Our interpretation suggests that the Ferrar flood basalts extend at least 100 km westward under the ice. The Beacon Supergroup of Paleozoic and Mesozoic sediments thins gradually under the ice and its reconstructed thickness is reminiscent of profiles of foreland basins. Finally, there is no indication in the gravity field for an incomplete rebound due to significant melting of the East Antarctic ice sheet since the last glacial period.

Strong interseismic coupling, fault afterslip, and viscoelastic flow before and after the Oct. 9, 1995 Colima-Jalisco earthquake: continuous GPS measurements from Colima, Mexico

USGS Publications Warehouse

Azua, B.M.; DeMets, C.; Masterlark, Timothy

2002-01-01

Continuous GPS measurements from Colima, Mexico during 4/93-6/01, bracketing the Oct. 9, 1995 M = 8.0 Colima-Jalisco earthquake, provide new constraints on Rivera plate subduction mechanics. Modeling of margin-normal strain accumulation before the earthquake suggests the Rivera-North America subduction interface was fully locked. Transient postseismic motion from 10/ 95-6/97 is well fit by a model that includes logarithmically-decaying fault afterslip, elastic strain from shallow fault relocking, and possibly a minor viscoelastic response, but is fit poorly by models that assume a dominant Maxwell viscoelastic response of the lower crust and upper mantle, independent of the assumed viscosities. Landward, margin-normal motion since mid-1997 is parallel to but ??? 75% slower than the pre-seismic velocity. Afterslip alone fails to account for this slowdown. The viscoelastic response predicted by a FEM correctly resolves the remaining velocity difference within the uncertainties. Both processes thus offset elastic strain accumulating from the relocked subduction interface.

Dynamic response of a poroelastic half-space to accelerating or decelerating trains

NASA Astrophysics Data System (ADS)

Cao, Zhigang; Boström, Anders

2013-05-01

The dynamic response of a fully saturated poroelastic half-space due to accelerating or decelerating trains is investigated by a semi-analytical method. The ground is modeled as a saturated poroelastic half-space and Biot's theory is applied to characterize the soil medium, taking the coupling effects between the soil skeleton and the pore fluid into account. A detailed track system is considered incorporating rails, sleepers and embankment, which are modeled as Euler-Bernoulli beams, an anisotropic Kirchhoff plate, and an elastic layer, respectively. The acceleration or deceleration of the train is simulated by properly choosing the time history of the train speed using Fourier transforms combined with Fresnel integrals in the transformed domain. The time domain results are obtained by the fast Fourier transform (FFT). It is found that the deceleration of moving trains can cause a significant increase to the ground vibrations as well as the excess pore water pressure responses at the train speed 200 km/h. Furthermore, the single-phase elastic soil model would underestimate the vertical displacement responses caused by both the accelerating and decelerating trains at the speed 200 km/h.

Lateral variations in foreland flexure of a rifted continental margin: The Aquitaine Basin (SW France)

NASA Astrophysics Data System (ADS)

Angrand, P.; Ford, M.; Watts, A. B.

2017-12-01

We study the effects of the inherited Aptian to Cenomanian rift on crustal rheology and evolution of the Late Cretaceous to Neogene flexural Aquitaine foreland basin, northern Pyrenees. We use surface and subsurface geological data to define the crustal geometry and the post-rift thermal subsidence, and Bouguer gravity anomalies and flexural modeling to study the lateral variation of the elastic thickness, flexure of the European plate and controlling loads. The Aquitaine foreland can be divided along-strike into three sectors. The eastern foreland is un-rifted and is associated with a simple flexural subsidence. The central sector is affected by crustal stretching and the observed foreland base is modeled by combining topographic and buried loads, with post-rift thermal subsidence. In the western sector the foreland basin geometry is mainly controlled by post-rift thermal subsidence. These three sectors are separated by major lineaments, which affect both crustal and foreland geometry. These lineaments seem to be part of a larger structural pattern that includes the Toulouse and Pamplona Faults. The European foreland shows lateral variations in flexural behavior: the relative role of surface and sub-surface (i.e., buried) loading varies along-strike and the elastic thickness values decrease from the north-east to the south-west where the plate is the most stretched. We suggest that foreland basins are influenced by the thermal state of the underlying lithosphere if it was initiated soon after rifting and that thermal cooling can contribute significantly to subsidence.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, J.K.; Yoo, M.H.

The aspect of elastic strain for a deformation twin with a pure shear strain is studied through Eshelby's inclusion theory. Beta-Sn, TiO[sub 2], and TiAl of tetragonal structures are considered. As the aspect ratio of a twin approaches zero, its elastic strain energy vanishes since the stress components coupled with the twin shear strain vanish, suggesting that the twin habit plane cannot be determined solely from the shear energy viewpoint, for any twin mode would provide a vanishingly small strain energy for a thin twin. The application of Johnson and Cahn's shape bifurcation theory predicts that the transition from amore » circular to an elliptic shape would occur when the linear dimension of a lenticular twin is only in the order of 10 nm, indicating that most twins with a substantial aspect ratio should be influenced by growth kinetics. Under an applied stress. The extreme condition of the free energy change usually occurs when the resolved shear stress becomes extreme in the direction of the twin shear strain, thus following the relationship of Schmid's law. The analysis of the matrix stress field immediately outside a twin plate shows a biomodal stress distribution around the lateral tip of the lenticular plate. The locations of stress concentrations depend on both the twin aspect ratio and the elastic anisotropy. The locations of stress concentrations depend on both the twin aspect ratio and the elastic anisotropy. As the twin aspect ratio approaches zero, however, the two exterior stress concentrations merge together at the lateral tip of the lenticular plate, yielding a maximum stress value in the order of [mu]g, where [mu] and g are shear modulus and twin shear strain, respectively.« less

Optimization of Elastically Tailored Tow-Placed Plates with Holes

NASA Technical Reports Server (NTRS)

Jegley, Dawn C.; Tatting, Brian F.; Guerdal, Zafer

2003-01-01

Elastic stiffness tailoring of laminated composite panels by allowing the fibers to curve within the plane of the laminate is a design concept that has been demonstrated to be both beneficial and practical. The objective of the present paper is to demonstrate the effectiveness of stiffness tailoring through the use of curvilinear fibers to reduce stress concentrations around the hole and improve the load carrying capability of panels. Preliminary panel designs that are to be manufactured and tested were determined through design studies for flat plates without holes under axial compression using an optimization program. These candidate designs were then analyzed with finite element models that accurately reflect the test conditions and geometries in order to decide upon the final designs for manufacture and testing. An advanced tow-placement machine is used to manufacture the test panels with varying fiber orientation angles. A total of six large panels measuring three feet by six feet, each of which is used to produce four specimens with or without holes, are fabricated. The panels were machined into specimens with holes and tested at NASA Langley Research Center. Buckling response and failure of panels without holes and with two different hole dimensions are presented. Buckling and failure loads of tow-steered specimens are significantly greater than the buckling and failure loads of traditional straight-fiber specimens.

Lateral variations in upper-mantle seismic anisotropy in the Pacific from inversion of a surface-wave dispersion dataset

NASA Astrophysics Data System (ADS)

Eddy, C. L.; Ekstrom, G.; Nettles, M.; Gaherty, J. B.

2017-12-01

We present a three-dimensional model of the anisotropic velocity structure of the Pacific lithosphere and asthenosphere. The presence of seismic anisotropy in the oceanic upper mantle provides information about the geometry of flow in the mantle, the nature of the lithosphere-asthenosphere boundary, and the possible presence of partial melt in the asthenosphere. Our dataset consists of fundamental-mode dispersion for Rayleigh and Love waves measured between 25-250 s with paths crossing the Pacific Ocean. We invert the phase anomaly measurements directly for three-dimensional anisotropic velocity structure. Our models are radially anisotropic and include the full set of elastic parameters that describe azimuthal variations in velocity (e.g. Gc, Gs). We investigate the age dependence of seismic velocity and radial anisotropy and find that there are significant deviations from the velocities predicted by a simple oceanic plate cooling model. We observe strong radial anisotropy with vsh > vsv in the asthenosphere of the central Pacific. We investigate the radial anisotropy in the shallow lithosphere, where previous models have reported conflicting results. There is a contrast in both upper-mantle isotropic velocities and radial anisotropy between the Pacific and Nazca plates, across the East Pacific Rise. We also investigate lateral variations in azimuthal anisotropy throughout the Pacific upper mantle and find that there are large areas over which the anisotropy fast axis does not align with absolute plate motion, suggesting the presence of small-scale convection or pressure-driven flow beneath the base of the oceanic plate.

Measurement of the residual stress distribution in a thick pre-stretched aluminum plate

NASA Astrophysics Data System (ADS)

Yuan, S. X.; Li, X. Q.; M, S.; Zhang, Y. C.; Gong, Y. D.

2008-12-01

Thick pre-stretched aluminum alloy plates are widely used in aircraft, while machining distortion caused by initial residual stress release in thick plates is a common and serious problem. To reduce the distortion, the residual stress distribution in thick plate must be measured. According to the characteristics of the thick pre-stretched aluminum alloy plate, based the elastic mechanical theory, this article deduces the modified layer-removal strain method adapting two different strain situations, which are caused by tensile and compressive stress. To validate this method, the residual stresses distribution along the thick direction of plate 2D70T351 is measured by this method, it is shown that the new method deduced in this paper is simple and accurate, and is very useful in engineering.

A {1,2}-Order Plate Theory Accounting for Three-Dimensional Thermoelastic Deformations in Thick Composite and Sandwich Laminates

NASA Technical Reports Server (NTRS)

Tessler, A.; Annett, M. S.; Gendron, G.

2001-01-01

A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.

Analogies between Kirchhoff plates and functionally graded Saint-Venant beams under torsion

NASA Astrophysics Data System (ADS)

Barretta, Raffaele; Luciano, Raimondo

2015-05-01

Exact solutions of elastic Kirchhoff plates are available only for special geometries, loadings and kinematic boundary constraints. An effective solution procedure, based on an analogy between functionally graded orthotropic Saint-Venant beams under torsion and inhomogeneous isotropic Kirchhoff plates, with no kinematic boundary constraints, is proposed. The result extends the one contributed in Barretta (Acta Mech 224(12):2955-2964, 2013) for the special case of homogeneous Saint-Venant beams under torsion. Closed-form solutions for displacement, bending-twisting moment and curvature fields of an elliptic plate, corresponding to a functionally graded orthotropic beam, are evaluated. A new benchmark for computational mechanics is thus provided.

Finite-element nonlinear transient response computer programs PLATE 1 and CIVM-PLATE 1 for the analysis of panels subjected to impulse or impact loads

NASA Technical Reports Server (NTRS)

Spilker, R. L.; Witmer, E. A.; French, S. E.; Rodal, J. J. A.

1980-01-01

Two computer programs are described for predicting the transient large deflection elastic viscoplastic responses of thin single layer, initially flat unstiffened or integrally stiffened, Kirchhoff-Lov ductile metal panels. The PLATE 1 program pertains to structural responses produced by prescribed externally applied transient loading or prescribed initial velocity distributions. The collision imparted velocity method PLATE 1 program concerns structural responses produced by impact of an idealized nondeformable fragment. Finite elements are used to represent the structure in both programs. Strain hardening and strain rate effects of initially isotropic material are considered.

Interaction of Lamb Waves with Fatigue Cracks in Aluminum

DTIC Science & Technology

2011-09-01

Interaction of Lamb Waves with Fatigue Cracks in Aluminum E. D. SWENSON, C. T. OWENS and C. ALLEN ABSTRACT Elastic waves can travel across...the interaction of Lamb waves with both open and closed low-cycle fatigue cracks in aluminum plates using a three-dimensional laser Doppler vibrometer...and antisymmetric Lamb wave modes differ upon encountering fatigue cracks. INTRODUCTION The use of guided elastic waves (Lamb waves) has shown

Lithospheric bending at subduction zones based on depth soundings and satellite gravity

NASA Technical Reports Server (NTRS)

Levitt, Daniel A.; Sandwell, David T.

1995-01-01

A global study of trench flexure was performed by simultaneously modeling 117 bathymetric profiles (original depth soundings) and satellite-derived gravity profiles. A thin, elastic plate flexure model was fit to each bathymetry/gravity profile by minimization of the L(sub 1) norm. The six model parameters were regional depth, regional gravity, trench axis location, flexural wavelength, flexural amplitude, and lithospheric density. A regional tilt parameter was not required after correcting for age-related trend using a new high-resolution age map. Estimates of the density parameter confirm that most outer rises are uncompensated. We find that flexural wavelength is not an accurate estimate of plate thickness because of the high curvatures observed at a majority of trenches. As in previous studies, we find that the gravity data favor a longer-wavelength flexure than the bathymetry data. A joint topography-gravity modeling scheme and fit criteria are used to limit acceptable parameter values to models for which topography and gravity yield consistent results. Even after the elastic thicknesses are converted to mechanical thicknesses using the yield strength envelope model, residual scatter obscures the systematic increase of mechanical thickness with age; perhaps this reflects the combination of uncertainties inherent in estimating flexural wavelength, such as extreme inelastic bending and accumulated thermoelastic stress. The bending moment needed to support the trench and outer rise topography increases by a factor of 10 as lithospheric age increases from 20 to 150 Ma; this reflects the increase in saturation bending moment that the lithosphere can maintain. Using a stiff, dry-olivine rheology, we find that the lithosphere of the GDH1 thermal model (Stein and Stein, 1992) is too hot and thin to maintain the observed bending moments. Moreover, the regional depth seaward of the oldest trenches (approximately 150 Ma) exceeds the GDH1 model depths by about 400 m.

Conical Refraction of Elastic Waves by Anisotropic Metamaterials and Application for Parallel Translation of Elastic Waves.

PubMed

Ahn, Young Kwan; Lee, Hyung Jin; Kim, Yoon Young

2017-08-30

Conical refraction, which is quite well-known in electromagnetic waves, has not been explored well in elastic waves due to the lack of proper natural elastic media. Here, we propose and design a unique anisotropic elastic metamaterial slab that realizes conical refraction for horizontally incident longitudinal or transverse waves; the single-mode wave is split into two oblique coupled longitudinal-shear waves. As an interesting application, we carried out an experiment of parallel translation of an incident elastic wave system through the anisotropic metamaterial slab. The parallel translation can be useful for ultrasonic non-destructive testing of a system hidden by obstacles. While the parallel translation resembles light refraction through a parallel plate without angle deviation between entry and exit beams, this wave behavior cannot be achieved without the engineered metamaterial because an elastic wave incident upon a dissimilar medium is always split at different refraction angles into two different modes, longitudinal and shear.

Various methods of determining the natural frequencies and damping of composite cantilever plates. 2. Approximate solution by Galerkin's method for the trinomial model of damping

NASA Astrophysics Data System (ADS)

Ekel'chik, V. S.; Ryabov, V. M.

1997-01-01

The application of Kantorovich's method to a trinomial model of deformation taking into account transverse bending of a plate leads to a connected system of three ordinary differential equations of fourth order with respect to three unknown functions of the longitudinal coordinate and to the coresponding boundary conditions for them at the fixed end and on the free edge. For the approximate calculation of the frequencies and forms of natural vibrations Galerkin's method is used, and as coordinate functions we chose orthogonal Jacobi polynomials with weight function. The dimensionless frequencies depend on the magnitude of the four dimensionless complexes, three of which characterize the anisotropy of the elastic properties of the composite. For the fibrous composites used at present we determined the possible range of change of the dimensionless complexes d16 and d26 attained by oblique placement. The article examines the influence of the angle of reinforcement on some first dimensionless frequencies of a plate made of unidirectional carbon reinforced plastic. It also analyzes the asymptotics of the frequencies when the length of the plate is increased, and it shows that for strongly anisotropic material with the structure [ϕ]T the frequencies of the flexural as well as of the torsional vibrations may be substantially lower when flexural-torsional interaction is taken into account.

A unified nonlocal strain gradient plate model for nonlinear axial instability of functionally graded porous micro/nano-plates reinforced with graphene platelets

NASA Astrophysics Data System (ADS)

Sahmani, Saeid; Aghdam, Mohammad Mohammadi; Rabczuk, Timon

2018-04-01

By gradually changing of the porosity across a specific direction, functionally graded porous materials (FGPMs) are produced which can impart desirable mechanical properties. To enhance these properties, it is common to reinforce FGPMs with nanofillers. The main aim of the current study is to investigate the size-dependent nonlinear axial postbuckling characteristics of FGPM micro/nano-plates reinforced with graphene platelets. For this purpose, the theory of nonlocal strain gradient elasticity incorporating the both stiffness reduction and stiffness enhancement mechanisms of size effects is applied to the refined exponential shear deformation plate theory. Three different patterns of porosity dispersion across the plate thickness in conjunction with the uniform one are assumed for FGPM as an open-cell metal foam is utilized associated with the coefficients of the relative density and porosity. With the aid of the virtual work’s principle, the non-classical governing differential equations are constructed. Thereafter, an improved perturbation technique is employed to capture the size dependencies in the nonlinear load-deflection and load-shortening responses of the reinforced FGPM micro/nano-plates with and without initial geometric imperfection. It is indicated that by increasing the value of porosity coefficient, the size-dependent critical buckling loads of reinforced FGPM micro/nano-plates with all types of porosity dispersion pattern reduce, but the associated shortening may increase or decrease which depends on the type of dispersion pattern.

Simulation of Impact on a Ductile Polymer Plate

NASA Technical Reports Server (NTRS)

Cremona, Rebecca L.; Hinkley, Jeffrey A.

2005-01-01

Explicit finite element calculations were used to visualize the deformation and temperature rise in an elastic-plastic plate impacted by a rigid projectile. Results were compared to results of experiments involving ballistic penetration of a "self-healing" thermoplastic. The calculated temperature rise agreed well with the experimental observation, but the total energy absorbed in the penetration event was underestimated in the calculation, which neglected friction.

Knudsen temperature jump and the Navier-Stokes hydrodynamics of granular gases driven by thermal walls.

PubMed

Khain, Evgeniy; Meerson, Baruch; Sasorov, Pavel V

2008-10-01

Thermal wall is a convenient idealization of a rapidly vibrating plate used for vibrofluidization of granular materials. The objective of this work is to incorporate the Knudsen temperature jump at thermal wall in the Navier-Stokes hydrodynamic modeling of dilute granular gases of monodisperse particles that collide nearly elastically. The Knudsen temperature jump manifests itself as an additional term, proportional to the temperature gradient, in the boundary condition for the temperature. Up to a numerical prefactor O(1) , this term is known from kinetic theory of elastic gases. We determine the previously unknown numerical prefactor by measuring, in a series of molecular dynamics (MD) simulations, steady-state temperature profiles of a gas of elastically colliding hard disks, confined between two thermal walls kept at different temperatures, and comparing the results with the predictions of a hydrodynamic calculation employing the modified boundary condition. The modified boundary condition is then applied, without any adjustable parameters, to a hydrodynamic calculation of the temperature profile of a gas of inelastic hard disks driven by a thermal wall. We find the hydrodynamic prediction to be in very good agreement with MD simulations of the same system. The results of this work pave the way to a more accurate hydrodynamic modeling of driven granular gases.

Reduced order modeling of fluid/structure interaction.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barone, Matthew Franklin; Kalashnikova, Irina; Segalman, Daniel Joseph

2009-11-01

This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled 'Reduced Order Modeling of Fluid/Structure Interaction.' This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preservesmore » numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convection-diffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.« less

Comparison of short-term effects between face mask and skeletal anchorage therapy with intermaxillary elastics in patients with maxillary retrognathia.

PubMed

Ağlarcı, Cahide; Esenlik, Elçin; Fındık, Yavuz

2016-06-01

The aim of this study was to compare the short-term dental and skeletal effects of a face mask (FM) with those of skeletal anchorage (SA) therapy with intermaxillary elastics in prepubertal patients with skeletal Class III malocclusion. Fifty patients with skeletal Class III malocclusion and maxillary deficiency were divided into two groups. In the FM group, an FM was applied by a bite plate with a force of 400g for each side. In the SA group, mini-plates were placed between mandibular lateral incisors and canines, and mini-implants were inserted between maxillary second premolars and first molars. A bite plate was inserted into the upper arch, and Class III elastics were applied with a force of 200g between each mini-plate and mini-implant. Mean treatment durations were 0.52±0.09 years for FM and 0.76±0.09 years for SA. After the treatment, statistically significant increases in SNA°, ANB°, A-y, 1-NA, SnGoGn°, Co-A, Co-Gn, and A-Nperp, and reductions in SNB° and FH┴N-Pg were observed in both groups, and these changes were similar in both groups. In the FM group, 1-NB decreased significantly, and in the SA group, it increased significantly (P < 0.05). The undesired dentoalveolar effects of the FM treatment were eliminated with SA treatment, except with regard to lower incisor inclination. Favourable skeletal outcomes can be achieved by SA therapies, which could be an alternative to the extraoral appliances frequently applied to treat skeletal Class III patients with maxillary deficiency. © The Author 2015. Published by Oxford University Press on behalf of the European Orthodontic Society. All rights reserved. For permissions, please email: journals.permissions@oup.com.

The roles of auxeticity and volume fraction on γ‧ precipitate microstructures in nickel-base alloys

NASA Astrophysics Data System (ADS)

Ardell, Alan J.

2017-01-01

New correlations are found between the elastic constants and late-stage precipitate microstructures in Ni-Al, Ni-Ga, Ni-Ge and Ni-Si alloys. The auxetic behaviour of Poisson's ratio, ν, measured parallel to [0 0 1] or ? in response to [1 1 0] loading, favours the amalgamation of Ni3Al and Ni3Ga precipitates into non-equilibrium shapes along cube directions when δν = (νγ‧ - νγ)/νγ‧ > 0, the superscripts referring to the γ‧ (Ni3X) and γ (Ni-X) phases, respectively. When δν < 0 amalgamation of Ni3Ge and Ni3Si precipitates does not occur and the particles retain cuboidal shapes. When δν > 0 amalgamation of Ni3Al and Ni3Ga occurs readily, primarily producing laths of both phases. The γ‧ volume fraction, f, is also shown to play a role in the late-stage microstructures of Ni-Al alloys, with an increasing tendency to form Ni3Al laths, rather than plates, as f increases. The shapes of elastically soft γ precipitates in inverse Ni-Al and Ni-Ge alloys are different; Ni-Al precipitates are lath shaped, but Ni-Ge precipitates are plate shaped. The Ni-Ge plate shape, in a non-auxetic Ni3Ge matrix (Ni3Ge being the sole non-auxetic Ni3X phase of the four studied), is the only example of persistent plates in any of the Ni-base alloys investigated to date. The combination of an elastically soft precipitate (Ni-Ge) in a non-auxetic matrix suggests a connection between auxeticity and shape.

Application of homomorphic signal processing to stress wave factor analysis

NASA Technical Reports Server (NTRS)

Karagulle, H.; Williams, J. H., Jr.; Lee, S. S.

1985-01-01

The stress wave factor (SWF) signal, which is the output of an ultrasonic testing system where the transmitting and receiving transducers are coupled to the same face of the test structure, is analyzed in the frequency domain. The SWF signal generated in an isotropic elastic plate is modelled as the superposition of successive reflections. The reflection which is generated by the stress waves which travel p times as a longitudinal (P) wave and s times as a shear (S) wave through the plate while reflecting back and forth between the bottom and top faces of the plate is designated as the reflection with p, s. Short-time portions of the SWF signal are considered for obtaining spectral information on individual reflections. If the significant reflections are not overlapped, the short-time Fourier analysis is used. A summary of the elevant points of homomorphic signal processing, which is also called cepstrum analysis, is given. Homomorphic signal processing is applied to short-time SWF signals to obtain estimates of the log spectra of individual reflections for cases in which the reflections are overlapped. Two typical SWF signals generated in aluminum plates (overlapping and non-overlapping reflections) are analyzed.

Plate and Plume Flux: Constraints for paleomagnetic reference frames and interpretation of deep mantle seismic heterogeneity. (Invited)

NASA Astrophysics Data System (ADS)

Bunge, H.; Schuberth, B. S.; Shephard, G. E.; Müller, D.

2010-12-01

Plate and plume flow are dominant modes of mantle convection, as pointed out by Geoff Davies early on. Driven, respectively, from a cold upper and a hot lower thermal boundary layer these modes are now sufficiently well imaged by seismic tomographers to exploit the thermal boundary layer concept as an effective tool in exploring two long standing geodynamic problems. One relates to the choice of an absolute reference frame in plate tectonic reconstructions. Several absolute reference frames have been proposed over the last decade, including those based on hotspot tracks displaying age progression and assuming either fixity or motion, as well as palaeomagnetically-based reference frames, a subduction reference frame and hybrid versions. Each reference frame implies a particular history of the location of subduction zones through time and thus the evolution of mantle heterogeneity via mixing of subducted slab material in the mantle. Here we compare five alternative absolute plate motion models in terms of their consequences for deep mantle structure. Taking global paleo-plate boundaries and plate velocities back to 140 Ma derived from the new plate tectonic reconstruction software GPlates and assimilating them into vigorous 3-D spherical mantle circulation models, we infer geodynamic mantle heterogeneity and compare it to seismic tomography for each absolute rotation model. We also focus on the challenging problem of interpreting deep mantle seismic heterogeneity in terms of thermal and compositional variations. Using published thermodynamically self-consistent mantle mineralogy models in the pyrolite composition, we find strong plume flux from the CMB, with a high temperature contrast (on the order of 1000 K) across the lower thermal boundary layer is entirely sufficient to explain elastic heterogeneity in the deep mantle for a number of quantitative measures. A high excess temperatures of +1000--1500 K for plumes in the lowermost mantle is particularly important in understanding the strong seismic velocity reduction mapped by tomography in low-velocity bodies of the deep mantle, as this produces significant negative anomalies of shear wave velocity of up to -4%. We note, however, that our results do not account for the curious observation of seismic anti-correlation, which appears difficult to explain in any case. Our results provide important constraints for the integration of plate tectonics and mantle dynamics and their use in forward and inverse geodynamic mantle models.

The Elasto-Plastic Stability of Plates

NASA Technical Reports Server (NTRS)

Ilyushin, A. A.

1947-01-01

This article explains results developed from the following research: 'The Stability of Plates and Shells beyond the Elastic Limit.' A significant improvement is found in the derivation of the relations between the stress factors and the strains resulting from the instability of plates and shells. In a strict analysis, the problem reduces to the solution of two simultaneous nonlinear partial differential equations of the fourth order in the deflection and stress function, and in the approximate analysis to a single linear equation of the Bryan type. Solutions are given for the special cases of a rectangular plate buckling into a cylindrical form, and of an arbitrarily shaped plate under uniform compression. These solutions indicate that the accuracy obtained by the approximate method is satisfactory.

Elastic contact mechanics: percolation of the contact area and fluid squeeze-out.

PubMed

Persson, B N J; Prodanov, N; Krick, B A; Rodriguez, N; Mulakaluri, N; Sawyer, W G; Mangiagalli, P

2012-01-01

The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.

Investigating physical field effects on the size-dependent dynamic behavior of inhomogeneous nanoscale plates

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Reza Barati, Mohammad

2017-02-01

This article investigates the thermo-mechanical vibration frequencies of magneto-electro-thermo-elastic functionally graded (METE-FG) nanoplates in the framework of refined four-unknown shear deformation plate theory. The present nanoplate is subjected to various kinds of thermal loads with uniform, linear and nonlinear distributions. The nonlinear distribution is considered as heat conduction and sinusoidal temperature rise. The present refined theory captures the influences of shear deformations without the need for shear correction factors. Thermo-magneto-electro-elastic coefficients of the FG nanoplate vary gradually along the thickness according to the power-law form. The scale coefficient is taken into consideration implementing the nonlocal elasticity of Eringen. The governing equations are derived through Hamilton's principle and are solved analytically. The frequency response is compared with those of previously published data. The obtained results are presented for the thermo-mechanical vibrations of the FG nanobeams to investigate the effects of material graduation, nonlocal parameter, mode number, slenderness ratio and thermal loading in detail. The present study is associated to aerospace, mechanical and nuclear engineering structures which are under thermal loads.

The Khachaturyan theory of elastic inclusions: Recollections and results

NASA Astrophysics Data System (ADS)

Morris, J. W.

2010-01-01

In keeping with the assignment, this paper has two parts. The first is a personal recollection of my interactions with Professor Armen Khachaturyan since he first visited Berkeley in the 1970s. The second part is a review of the Khachaturyan formulation of the theory of elastic inclusions, with emphasis on results found since his classic monograph on the Theory of Structural Transformations in Solids [Wiley, New York, 1983]. The focus here is on the shapes and habits of coherent inclusions. The basic theory is presented, briefly, to exhibit Khachaturyan's results for the strain and energy within a coherent inclusion and show that the elastic energy is minimal for a thin-plate morphology with a definite habit. The preferred habit of the thin-plate inclusion is then discussed and computed for inclusions with dyadic strain (including the dislocation loop) and coherent inclusions with orthorhombic or simpler symmetry. This is followed by a discussion of the evolution of precipitate shape during coarsening, including the theory of the spontaneous splitting of coarsening precipitates and the development of octahedral or tetrahedral shapes.

Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Bigelow, C. A.; Shivakumar, K. N.

1993-01-01

Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonic and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor alpha(sub g) was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of alpha(sub g) were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness.

Polynomial Expressions for Estimating Elastic Constants From the Resonance of Circular Plates

NASA Technical Reports Server (NTRS)

Salem, Jonathan A.; Singh, Abhishek

2005-01-01

Two approaches were taken to make convenient spread sheet calculations of elastic constants from resonance data and the tables in ASTM C1259 and E1876: polynomials were fit to the tables; and an automated spread sheet interpolation routine was generated. To compare the approaches, the resonant frequencies of circular plates made of glass, hardened maraging steel, alpha silicon carbide, silicon nitride, tungsten carbide, tape cast NiO-YSZ, and zinc selenide were measured. The elastic constants, as calculated via the polynomials and linear interpolation of the tabular data in ASTM C1259 and E1876, were found comparable for engineering purposes, with the differences typically being less than 0.5 percent. Calculation of additional v values at t/R between 0 and 0.2 would allow better curve fits. This is not necessary for common engineering purposes, however, it might benefit the testing of emerging thin structures such as fuel cell electrolytes, gas conversion membranes, and coatings when Poisson s ratio is less than 0.15 and high precision is needed.

Predicting the Influence of Nano-Scale Material Structure on the In-Plane Buckling of Orthotropic Plates

NASA Technical Reports Server (NTRS)

Gates, Thomas S.; Odegard, Gregory M.; Nemeth, Michael P.; Frankland, Sarah-Jane V.

2004-01-01

A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the non-functionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.

Finite-size effect on the dynamic and sensing performances of graphene resonators: the role of edge stress.

PubMed

Kim, Chang-Wan; Dai, Mai Duc; Eom, Kilho

2016-01-01

We have studied the finite-size effect on the dynamic behavior of graphene resonators and their applications in atomic mass detection using a continuum elastic model such as modified plate theory. In particular, we developed a model based on von Karman plate theory with including the edge stress, which arises from the imbalance between the coordination numbers of bulk atoms and edge atoms of graphene. It is shown that as the size of a graphene resonator decreases, the edge stress depending on the edge structure of a graphene resonator plays a critical role on both its dynamic and sensing performances. We found that the resonance behavior of graphene can be tuned not only through edge stress but also through nonlinear vibration, and that the detection sensitivity of a graphene resonator can be controlled by using the edge stress. Our study sheds light on the important role of the finite-size effect in the effective design of graphene resonators for their mass sensing applications.

Thermal Behaviour of Beams with Slant End-Plate Connection Subjected to Nonsymmetric Gravity Load

PubMed Central

Osman, Mohd Hanim; Talebi, Elnaz

2014-01-01

Research on the steel structures with confining of axial expansion in fixed beams has been quite intensive in the past decade. It is well established that the thermal behaviour has a key influence on steel structural behaviours. This paper describes mechanical behaviour of beams with bolted slant end-plate connection with nonsymmetric gravity load, subjected to temperature increase. Furthermore, the performance of slant connections of beams in steel moment frame structures in the elastic field is investigated. The proposed model proved that this flexible connection system could successfully decrease the extra thermal induced axial force by both of the friction force dissipation among two faces of slant connection and a small upward movement on the slant plane. The applicability of primary assumption is illustrated. The results from the proposed model are examined within various slant angles, thermal and friction factors. It can be concluded that higher thermal conditions are tolerable when slanting connection is used. PMID:24587720

Thermal behaviour of beams with slant end-plate connection subjected to nonsymmetric gravity load.

PubMed

Zahmatkesh, Farshad; Osman, Mohd Hanim; Talebi, Elnaz

2014-01-01

Research on the steel structures with confining of axial expansion in fixed beams has been quite intensive in the past decade. It is well established that the thermal behaviour has a key influence on steel structural behaviours. This paper describes mechanical behaviour of beams with bolted slant end-plate connection with nonsymmetric gravity load, subjected to temperature increase. Furthermore, the performance of slant connections of beams in steel moment frame structures in the elastic field is investigated. The proposed model proved that this flexible connection system could successfully decrease the extra thermal induced axial force by both of the friction force dissipation among two faces of slant connection and a small upward movement on the slant plane. The applicability of primary assumption is illustrated. The results from the proposed model are examined within various slant angles, thermal and friction factors. It can be concluded that higher thermal conditions are tolerable when slanting connection is used.

The 1923 Kanto earthquake reevaluated using a newly augmented geodetic data set

USGS Publications Warehouse

Nyst, M.; Nishimura, T.; Pollitz, F.F.; Thatcher, W.

2006-01-01

This study revisits the mechanism of the 1923 Ms = 7.9 Kanto earthquake in Japan. We derive a new source model and use it to assess quantitative and qualitative aspects of the accommodation of plate motion in the Kanto region. We use a new geodetic data set that consists of displacements from leveling and angle changes from triangulation measurements obtained in surveys between 1883 and 1927. Two unique aspects of our analysis are the inclusion of a large number of second-order triangulation measurements and the application of a correction to remove interseismic deformation. The geometry of the fault planes is adopted from a recent seismic reflection study of the Kanto region. We evaluate the minimum complexity necessary in the model to fit the data optimally. Our final uniform-slip elastic dislocation model consists of two adjacent ???20?? dipping low-angle planes accommodating reverse dextral slip of 6.0 in on the larger, eastern plane and 9.5 m on the smaller, western plane with azimuths of 163?? and 121??, respectively. The earthquake was located in the Sagami trough, where the Philippine Sea plate subducts under Honshu. Compared to the highly oblique angle of plate convergence, the coseismic slip on the large fault plane has a more orthogonal orientation to the strike of the plate boundary, suggesting that slip partitioning plays a role in accommodation of plate motion. What other structure is involved in the partitioning is unclear. Uplift records of marine coastal terraces in Sagami Bay document 7500 years of earthquake activity and predict average recurrence intervals of 400 years for events with vertical displacement profiles similar to those of the 1923 earthquake. This means that the average slip deficit per recurrence interval is ???50% of the relative plate convergence. These findings of plate motion partitioning and slip deficit lead us to suggest that instead of a simple recurrence model with characteristic earthquakes, additional mechanisms are necessary to describe the accommodation of deformation in the Kanto region. So far, obvious candidates for these alternative mechanisms have not been discovered. Copyright 2006 by the American Geophysical Union.

Effect of length to thickness ratio on free vibration analysis of thick fiber reinforced plastic skew cross-ply laminate with circular cutout

NASA Astrophysics Data System (ADS)

Srividya, K.; Reddy, Ch. Kishore; Sumanth, Ch. Mohan; Krishnaiah, P. Gopala; Kishan, V. Mallikharjuna

2018-04-01

The present investigation deals with the free vibration analysis of a thick four-layered symmetric cross-ply skew laminated composite plate with a circular cutout. Three dimensional finite element models (FEM) which use the elasticity theory for the determination of stiffness matrices are modeled in ANSYS software to evaluate first five natural frequencies of the laminate. The variations of the first five natural frequencies with respect to length to thickness ratio (S) for different diameter to length ratios (d/l) are presented. It is observed that, the natural frequencies decreases with increase of thickness ratio(S).

Cochlear mechanics: Analysis for a pure tone

NASA Astrophysics Data System (ADS)

Holmes, M. H.; Cole, J. D.

1983-11-01

The dynamical response of a three-dimensional hydroelastic model of the cochlea is studied for a pure tone forcing. The basilar membrane is modeled as an inhomogenous, orthotropic elastic plate and the fluid is assumed to be Newtonian. The resulting mathematical problem is reduced using viscous boundary layer theory and slender body approximations. This leads to a nonlinear eigenvalue problem in the transverse cross-section. The solutions for the case of a rectangular and semi-circular cross-section are computed and comparison is made with experiment. The role of the place principle in determining the difference limen is presented and it is shown how the theory agrees with the experimental measurements.

Stress on the seismogenic and deep creep plate interface during the earthquake cycle in subduction zones

NASA Astrophysics Data System (ADS)

Ruff, Larry J.

2001-04-01

The deep creep plate interface extends from the down-dip edge of the seismogenic zone down to the base of the overlying lithosphere in subduction zones. Seismogenic/deep creep zone interaction during the earthquake cycle produces spatial and temporal variations in strains within the surrounding elastic material. Strain observations in the Nankai subduction zone show distinct deformation styles in the co-seismic, post-seismic, and inter-seismic phases associated with the 1946 great earthquake. The most widely used kinematic model to match geodetic observations has been a 2-D Savage-type model where a plate interface is placed in an elastic half-space and co-seismic slip occurs in the upper seismogenic portion of the interface, while inter-seismic deformation is modeled by a locked seismogenic zone and a constant slip velocity across the deep creep interface. Here, I use the simplest possible 2-D mechanical model with just two blocks to study the stress interaction between the seismogenic and deep creep zones. The seismogenic zone behaves as a stick-slip interface where co-seismic slip or stress drop constrain the model. A linear constitutive law for the deep creep zone connects the shear stress (σ) to the slip velocity across the plate interface (s') with the material property of interface viscosity (ζ ) as: σ = ζ s'. The analytic solution for the steady-state two-block model produces simple formulas that connect some spatially-averaged geodetic observations to model quantities. Aside from the basic subduction zone geometry, the key observed parameter is τ, the characteristic time of the rapid post-seismic slip in the deep creep interface. Observations of τ range from about 5 years (Nankai and Alaska) to 15 years (Chile). The simple model uses these values for τ to produce estimates for ζ that range from 8.4 × 1013 Pa/m/s (in Nankai) to 6.5 × 1014 Pa/m/s (in Chile). Then, the model predicts that the shear stress acting on deep creep interface averaged over the earthquake cycle ranges from 0.1 MPa (Nankai) to 1.7 MPa (Chile). These absolute stress values for the deep creep zone are slightly smaller than the great earthquake stress drops. Since the great earthquake recurrence time ( T recur) is much larger than τ for Nankai, Alaska, and Chile, the model predicts that rapid post-seismic creep should re-load the seismogenic zone to about (1/3) of the co-seismic change; geodetically observed values range from about (1/10) to more than (1/2). Also, for the case of (Trecur/τ) ≫1, the model predicts that the slip velocity across the deep creep interface during the inter-seismic phase should be about (2/3) the plate tectonic velocity (R). Thus the deep creep velocity used in Savage-type models should be less than R. Even complex 3-D models with non-linear creep laws should make a similar prediction for inter-seismic deep creep rates. At present, it seems that geodetic observations at Nankai and other subduction zones are more consistent with a deep creep rate of R rather than (2/3) R. This discrepancy is quite puzzling and is difficult to explain in the context of a 2-D steady-state earthquake cycle model. Future observational and modeling studies should examine this apparent discrepancy to gain more understanding of the earthquake cycle in subduction zones.

Topological valley transport of plate-mode waves in a homogenous thin plate with periodic stubbed surface

NASA Astrophysics Data System (ADS)

Chen, Jiu-Jiu; Huo, Shao-Yong; Geng, Zhi-Guo; Huang, Hong-Bo; Zhu, Xue-Feng

2017-11-01

The study for exotic topological effects of sound has attracted uprising interests in fundamental physics and practical applications. Based on the concept of valley pseudospin, we demonstrate the topological valley transport of plate-mode waves in a homogenous thin plate with periodic stubbed surface, where a deterministic two-fold Dirac degeneracy is form by two plate modes. We show that the topological property can be controlled by the height of stubs deposited on the plate. By adjusting the relative heights of adjacent stubs, the valley vortex chirality and band inversion are induced, giving rise to a phononic analog of valley Hall phase transition. We further numerically demonstrate the valley states of plate-mode waves with robust topological protection. Our results provide a new route to design unconventional elastic topological insulators and will significantly broaden its practical application in the engineering field.

A theory for the fracture of thin plates subjected to bending and twisting moments

NASA Technical Reports Server (NTRS)

Hui, C. Y.; Zehnder, Alan T.

1993-01-01

Stress fields near the tip of a through crack in an elastic plate under bending and twisting moments are reviewed assuming both Kirchhoff and Reissner plate theories. The crack tip displacement and rotation fields based on the Reissner theory are calculated. These results are used to calculate the J-integral (energy release rate) for both Kirchhoff and Reissner plate theories. Invoking Simmonds and Duva's (1981) result that the value of the J-integral based on either theory is the same for thin plates, a universal relationship between the Kirchhoff theory stress intensity factors and the Reissner theory stress intensity factors is obtained for thin plates. Calculation of Kirchhoff theory stress intensity factors from finite elements based on energy release rate is illustrated. It is proposed that, for thin plates, fracture toughness and crack growth rates be correlated with the Kirchhoff theory stress intensity factors.

Eulerian adaptive finite-difference method for high-velocity impact and penetration problems

NASA Astrophysics Data System (ADS)

Barton, P. T.; Deiterding, R.; Meiron, D.; Pullin, D.

2013-05-01

Owing to the complex processes involved, faithful prediction of high-velocity impact events demands a simulation method delivering efficient calculations based on comprehensively formulated constitutive models. Such an approach is presented herein, employing a weighted essentially non-oscillatory (WENO) method within an adaptive mesh refinement (AMR) framework for the numerical solution of hyperbolic partial differential equations. Applied widely in computational fluid dynamics, these methods are well suited to the involved locally non-smooth finite deformations, circumventing any requirement for artificial viscosity functions for shock capturing. Application of the methods is facilitated through using a model of solid dynamics based upon hyper-elastic theory comprising kinematic evolution equations for the elastic distortion tensor. The model for finite inelastic deformations is phenomenologically equivalent to Maxwell's model of tangential stress relaxation. Closure relations tailored to the expected high-pressure states are proposed and calibrated for the materials of interest. Sharp interface resolution is achieved by employing level-set functions to track boundary motion, along with a ghost material method to capture the necessary internal boundary conditions for material interactions and stress-free surfaces. The approach is demonstrated for the simulation of high velocity impacts of steel projectiles on aluminium target plates in two and three dimensions.

Rheology and strength of the Eurasian continental lithosphere in the foreland of the Taiwan collision belt: Constraints from seismicity, flexure, and structural styles

NASA Astrophysics Data System (ADS)

Mouthereau, FréDéRic; Petit, Carole

2003-11-01

Deformation in western Taiwan is characterized by variable depth-frequency distribution of crustal earthquakes which are closely connected with along-strike variations of tectonic styles (thin or thick skinned) around the Peikang High, a major inherited feature of the Chinese margin. To fit the calculated high crustal geotherm and the observed distribution of the crustal seismic activity, a Qz-diorite and granulite composition for the upper and the lower crust is proposed. We then model the plate flexure, through Te estimates, using brittle-elastic-ductile plate rheology. Flexure modeling shows that the best fit combination of Te-boundary condition is for thrust loads acting at the belt front. The calculated Te vary in the range of ˜15-20 km. These values are primarily a reflection of the thermal state of the rifted Chinese margin inherited from the Oligocene spreading in the South China Sea. However, other mechanical properties such as the degree of crust/mantle coupling and the thickness of the mechanically competent crust and mantle are considered. South of the Peikang High, flexure modeling reveals lower Te associated with thinner mechanically strong layers. Variable stress/strain distribution associated with a higher degree of crust/mantle decoupling is examined to explain plate weakening. We first show that plate curvature cannot easily explain strength reduction and observed seismic activity. Additional plate-boundary forces arising from the strong coupling induced by more frontal subduction of a buoyant crustal asperity, i.e., the Peikang High, with the overriding plate are required. Favorably oriented inherited features in the adjacent Tainan basin produce acceleration of strain rates in the upper crust and hence facilitate the crust/mantle decoupling as attested by high seismic activity and thick-skinned deformation. The relative weakening of the lower crust and mantle then leads to weaken the lithosphere. By contrast, to the north, more oblique collision and the lack of inherited features keep the lithosphere stronger. This study suggests that when the Eurasian plate enters the Taiwan collision, tectonic inheritance of the continental margin exerts a strong control on the plate deformation by modifying its strength.

Modeling Analysis of a Six-axis Force/Tactile Sensor for Robot Fingers and a Method for Decreasing Error

NASA Astrophysics Data System (ADS)

Luo, Minghua; Shimizu, Etsuro; Zhang, Feifei; Ito, Masanori

This paper describes a six-axis force/tactile sensor for robot fingers. A mathematical model of this sensor is proposed. By this model, the grasping force and its moments, and touching position of robot finger for holding an object can be calculated. A new sensor is fabricated based on this model, where the elastic sensing unit of the sensor is made of a brazen plate. A new compensating method for decreasing error is proposed. Furthermore, the performance of this sensor is examined. The test results present approximate relationship between theoretical input and output of the sensor. It is obvious that the performance of the new sensor is better than the sensor with no compensation.

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

NASA Technical Reports Server (NTRS)

Wang, P. K. C.; Hadaegh, F. Y.

1996-01-01

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures

NASA Astrophysics Data System (ADS)

Rafii-Tabar, Hashem; Ghavanloo, Esmaeal; Fazelzadeh, S. Ahmad

2016-06-01

Insight into the mechanical characteristics of nanoscopic structures is of fundamental interest and indeed poses a great challenge to the research communities around the world. These structures are ultra fine in size and consequently performing standard experiments to measure their various properties is an extremely difficult and expensive endeavor. Hence, to predict the mechanical characteristics of the nanoscopic structures, different theoretical models, numerical modeling techniques, and computer-based simulation methods have been developed. Among several proposed approaches, the nonlocal continuum-based modeling is of particular significance because the results obtained from this modeling for different nanoscopic structures are in very good agreement with the data obtained from both experimental and atomistic-based studies. A review of the essentials of this model together with its applications is presented here. Our paper is a self contained presentation of the nonlocal elasticity theory and contains the analysis of the recent works employing this model within the field of nanoscopic structures. In this review, the concepts from both the classical (local) and the nonlocal elasticity theories are presented and their applications to static and dynamic behavior of nanoscopic structures with various morphologies are discussed. We first introduce the various nanoscopic structures, both carbon-based and non carbon-based types, and then after a brief review of the definitions and concepts from classical elasticity theory, and the basic assumptions underlying size-dependent continuum theories, the mathematical details of the nonlocal elasticity theory are presented. A comprehensive discussion on the nonlocal version of the beam, the plate and the shell theories that are employed in modeling of the mechanical properties and behavior of nanoscopic structures is then provided. Next, an overview of the current literature discussing the application of the nonlocal models of nanoscopic carbon allotropes is presented. We then discuss the application of the models to the investigation of the properties of nanoscopic structures from different materials and with different types of morphologies. Furthermore, we also present recent developments in the application of the nonlocal models. Finally, conclusions and discussions regarding the potentiality of these models for future research are provided.

Unveiling Extreme Anisotropy in Elastic Structured Media

NASA Astrophysics Data System (ADS)

Lefebvre, G.; Antonakakis, T.; Achaoui, Y.; Craster, R. V.; Guenneau, S.; Sebbah, P.

2017-06-01

Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones, and saddle points; identifying these and the nature of the associated modes from a direct reading of the dispersion surfaces is not straightforward, especially in three dimensions or at high frequencies when several dispersion surfaces fold back in the Brillouin zone. A recently proposed asymptotic high-frequency homogenization theory is applied to a challenging time-domain experiment with elastic waves in a pinned metallic plate. The prediction of a narrow high-frequency spectral region where the effective medium tensor dramatically switches from positive definite to indefinite is confirmed experimentally; a small frequency shift of the pulse carrier results in two distinct types of highly anisotropic modes. The underlying effective equation mirrors this behavior with a change in form from elliptic to hyperbolic exemplifying the high degree of wave control available and the importance of a simple and effective predictive model.

Analysis of gravity and topography in the GLIMPSE study region: Isostatic compensation and uplift of the Sojourn and Hotu Matua Ridge systems

USGS Publications Warehouse

Harmon, N.; Forsyth, D.W.; Scheirer, D.S.

2006-01-01

The Gravity Lieations Intraplate Melting Petrologic and Seismic Expedition (GLIMPSE) Experiment investigated the formation of a series of non-hot spot, intraplate volcanic ridges in the South Pacific and their relationship to cross-grain gravity lineaments detected by satellite altimetry. Using shipboard gravity measurements and a simple model of surface loading of a thin elastic plate, we estimate effective elastic thicknesses ranging from ???2 km beneath the Sojourn Ridge to a maximum of 10 km beneath the Southern Cross Seamount. These elastic thicknesses are lower than predicted for the 3-9 Ma seafloor on which the volcanoes lie, perhaps due to reheating and thinning of the plate during emplacement. Anomalously low apparent densities estimated for the Matua and Southern Cross seamounts 2050 and 2250 kg m-3, respectively, probably are artifacts caused by the assumption of only surface loading, ignoring the presence of subsurface loading in the form of underplated crust and/or low-density mantle. Using satellite free-air gravity and shipboard bathymetry, we calculate the age-detrended, residual mantle Bouguer anomaly (rMBA). The rMBA corrects the free-air anomaly for the direct effects of topography, including the thickening of the crust beneath the seamounts and volcanic ridges due to surface loading of the volcanic edifices. There are broad, negative rMBA anomalies along the Sojourn and Brown ridges and the Hotu Matua seamount chain that extend nearly to the East Pacific Rise. These negative rMBA anomalies connect to negative free-air anomalies in the western part of the study area that have been recognized previously as the beginnings of the cross-grain gravity lineaments. Subtracting the topographic effects of surface loading by the ridges and seamounts from the observed topography reveals that the ridges are built on broad bands of anomalously elevated seafloor. This swell topography and the negative rMBA anomalies contradict the predictions of lithospheric cracking models for the origin of gravity lineaments and associated volcanic ridges, favoring models with a dynamic mantle component such as small-scale convection or channelized asthenospheric return flow. Copyright 2006 by the American Geophysical Union.

Elastic stability of laminated, flat and curved, long rectangular plates subjected to combined inplane loads

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Tamekuni, M.; Baker, L. L.

1974-01-01

A method is presented to predict theoretical buckling loads of long, rectangular flat and curved laminated plates with arbitrary orientation of orthotropic axes each lamina. The plate is subjected to combined inplane normal and shear loads. Arbitrary boundary conditions may be stipulated along the longitudinal sides of the plate. In the absence of inplane shear loads and extensional-shear coupling, the analysis is also applicable to finite length plates. Numerical results are presented for curved laminated composite plates with boundary conditions and subjected to various loadings. These results indicate some of the complexities involved in the numerical solution of the analysis for general laminates. The results also show that the reduced bending stiffness approximation when applied to buckling problems could lead to considerable error in some cases and therefore must be used with caution.

Designing Glass Panels for Economy and Reliability

NASA Technical Reports Server (NTRS)

Moore, D. M.

1983-01-01

Analytical method determines probability of failure of rectangular glass plates subjected to uniformly distributed loads such as those from wind, earthquake, snow, and deadweight. Developed as aid in design of protective glass covers for solar-cell arrays and solar collectors, method is also useful in estimating the reliability of large windows in buildings exposed to high winds and is adapted to nonlinear stress analysis of simply supported plates of any elastic material.

Enhancing acoustic signal response and absorption of an underwater coated plate by embedding periodical inhomogeneities.

PubMed

Zhang, Yanni; Pan, Jie

2017-12-01

An underwater structure is proposed for simultaneous detection and stealth purposes by embedding periodic signal conditioning plates (SCPs) at the interface of two elastic coatings attached to an elastic plate. Results show that the embedded SCPs can enhance sound absorption at frequencies below the coincidence frequency of the plate (f c ). Significantly enhanced absorption occurs at five peaks, of which the peak due to excited localized bending resonance in the outer coating between SCPs is the most significant. When the dilatational velocity of the outer coating equals that of the inner coating, nearly total absorption occurs in a wideband, owing to strong coupling between the localized waveguide resonance in the outer coating and that in the inner coating, and the diffraction waves by the SCPs. Meanwhile, an amplified acoustic signal of over 14 dB is observed at most frequencies within 0 ∼ f c at the coatings' interface close to the SCPs' edges, owing to focused stress formed there. Peaks in the signal response at maximal 30 dB are also observed. These peak frequencies are coincident with or close to the peak frequencies of absorption, demonstrating that significantly enhanced acoustic signal and absorption can be achieved simultaneously through the use of embedded periodic SCPs.

Modeling ocean wave propagation under sea ice covers

NASA Astrophysics Data System (ADS)

Zhao, Xin; Shen, Hayley H.; Cheng, Sukun

2015-02-01

Operational ocean wave models need to work globally, yet current ocean wave models can only treat ice-covered regions crudely. The purpose of this paper is to provide a brief overview of ice effects on wave propagation and different research methodology used in studying these effects. Based on its proximity to land or sea, sea ice can be classified as: landfast ice zone, shear zone, and the marginal ice zone. All ice covers attenuate wave energy. Only long swells can penetrate deep into an ice cover. Being closest to open water, wave propagation in the marginal ice zone is the most complex to model. The physical appearance of sea ice in the marginal ice zone varies. Grease ice, pancake ice, brash ice, floe aggregates, and continuous ice sheet may be found in this zone at different times and locations. These types of ice are formed under different thermal-mechanical forcing. There are three classic models that describe wave propagation through an idealized ice cover: mass loading, thin elastic plate, and viscous layer models. From physical arguments we may conjecture that mass loading model is suitable for disjoint aggregates of ice floes much smaller than the wavelength, thin elastic plate model is suitable for a continuous ice sheet, and the viscous layer model is suitable for grease ice. For different sea ice types we may need different wave ice interaction models. A recently proposed viscoelastic model is able to synthesize all three classic models into one. Under suitable limiting conditions it converges to the three previous models. The complete theoretical framework for evaluating wave propagation through various ice covers need to be implemented in the operational ocean wave models. In this review, we introduce the sea ice types, previous wave ice interaction models, wave attenuation mechanisms, the methods to calculate wave reflection and transmission between different ice covers, and the effect of ice floe breaking on shaping the sea ice morphology. Laboratory experiments, field measurements and numerical simulations supporting the fundamental research in wave-ice interaction models are discussed. We conclude with some outlook of future research needs in this field.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Elastic fibre organization in the intervertebral discs of the bovine tail

PubMed Central

Yu, Jing; Peter, C; Roberts, Sally; Urban, Jill PG

2002-01-01

Elastic fibres have been revealed by both elastin immunostaining and conventional histological orcein-staining in the intervertebral discs of the bovine tail. These fibres are distributed in all regions of the disc but their organization varies from region to region. In the centre of the nucleus, long (>150 μm) elastic fibres are orientated radially. In the transitional region between nucleus and annulus, the orientation of the elastic fibres changes, producing a criss-cross pattern. In the annulus itself, elastic fibres appear densely distributed in the region between the lamellae and also in ‘bridges’ across the lamellae, particularly in the adult. Elastic fibres are apparent within the lamellae, orientated parallel to the collagen fibres of each lamella, particularly in the young (12-day-old) discs. In the region between the disc and the cartilaginous endplate, elastic fibres appear to anchor into the plate and terminate there. The results of this study suggest that elastic fibres contribute to the mechanical functioning of the intervertebral disc. The varying organization of the elastic fibres in the different regions of the disc is likely to relate to the different regional loading patterns PMID:12489758

The effect of transverse shear in a cracked plate under skew-symmetric loading

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1979-01-01

The problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered. By using a bending theory which allows the satisfaction of the boundary conditions on the crack surface regarding the normal and the twisting moments and the transverse shear load separately, it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems. The problem is solved for uniformly distributed or concentrated twisting moment or transverse shear load and the normalized Mode II and Mode III stress-intensity factors are tabulated. The results also include the effect of the Poisson's ratio and material orthotropy for specially orthotropic materials on the stress-intensity factors.

Some Problems of the Lithosphere (Augustus Love Medal Lecture)

NASA Astrophysics Data System (ADS)

Houseman, Gregory A.

2015-04-01

In 1911 Augustus Love published a monograph: Some Problems of Geodynamics which in part dealt with the problem of isostasy and the support of mountain belts. In doing so he was one of the first authors to use the concept of the lithosphere. Although his analysis used the framework of linear elasticity, he clearly recognised that the evident structural heterogeneity of the Earth's crust could not simply be interpreted in terms of elastic displacement, and he had no simple explanation for what processes had produced the major topographic features of the Earth: continents, oceans and mountain belts. Today we have a far more complete understanding of those processes, but there are still unresolved problems. In this presentation I will focus on two of those problems that are of particular interest in understanding the geological evolution of the continents: the relationship of near-surface faults and ductile deformation in the lithosphere, and the stability of continental lithosphere in actively deforming zones. While the lithosphere certainly manifests elastic strain, most notably in the context of earthquakes and seismic waves, the large strains that have shaped the continents result from diffuse ductile strain at the deeper levels, coupled with movement on fault planes in the upper crust. Although plates in many regions move coherently with little internal deformation, the stresses that act on different parts of a plate may cause broad deformation zones to develop within a plate interior. Plate boundaries that cross continental regions also typically involve broadly distributed deformation. In recent years the distribution of deformation in such regions is measured accurately using GPS, and in general is explained well by a model in which the lithosphere behaves as a thin viscous sheet, albeit with a non-linear temperature-dependent viscosity law. Such models are broadly consistent with laboratory deformation experiments on small rock samples. However, the relationship between faulting and earthquake activity and the continuous deformation field below the seismogenic layer continues to be poorly understood. Prominent surface faults may be a natural consequence of the localization of strain caused by processes within the ductile layer such as shear heating, grain-size reduction, or simply the interaction of non-Newtonian constitutive law and irregular geometry. Where intra-plate convergence occurs the lithosphere must thicken, and the question naturally arises as to whether the thickened lithosphere will remain stable or somehow be removed by convective overturn with underlying asthenophere. Such overturn is expected of a viscous lithospheric layer that is denser than the asthenosphere; it will be denser because it is colder, unless there is some compositional contrast which makes it intrinsically buoyant. A relatively low viscosity is required, however, in order that the instability can grow at a sufficiently fast rate to overcome diffusive stabilisation of the temperature field. The high stresses created by plate convergence may provide the mechanism that activates the viscosity (and explains why the lithosphere elsewhere is generally stable). High-resolution tomographic investigations find convincing evidence of small-scale mantle drips occurring beneath recently active orogenic zones such as the western USA and the SE Carpathians. However, seismic observations of thickened lithosphere remaining beneath Tibet apparently contradict the interpretation of mantle overturn suggested by recent volcanism and uplift. Although the Tibetan mantle lithosphere may be relatively buoyant, the possibility that this layer has overturned internally may allow these conflicting interpretations to be reconciled.

170-MHz electrodeless quartz crystal microbalance biosensor: capability and limitation of higher frequency measurement.

PubMed

Ogi, Hirotsugu; Nagai, Hironao; Naga, Hironao; Fukunishi, Yuji; Hirao, Masahiko; Nishiyama, Masayoshi

2009-10-01

We develop a highly sensitive quartz crystal microbalance (QCM) biosensor with a fundamental resonance frequency of 170 MHz. A naked AT-cut quartz plate of 9.7 microm thick is set in a sensor cell. Its shear vibration is excited by the line wire, and the vibration signals are detected by the other line wire, achieving the noncontacting measurement of the resonance frequency. The mass sensitivity of the 170 MHz QCM biosensor is 15 pg/(cm2 Hz), which is better than that of a conventional 5 MHz QCM by 3 orders of magnitude. Its high sensitivity is confirmed by detecting human immunoglobulin G (hIgG) via Staphylococcus protein A immobilized nonspecifically on both surfaces of the quartz plate. The detection limit is 0.5 pM. Limitation of the high-frequency QCM measurement is then theoretically discussed with a continuum mechanics model for a plate with point masses connected by elastic springs. The result indicates that a QCM measurement will break down at frequencies one-order-of-magnitude higher than the local resonance frequency at specific binding cites.

Birefringence and incipient plastic deformation in elastically overdriven [100] CaF2 under shock compression

NASA Astrophysics Data System (ADS)

Li, Y.; Zhou, X. M.; Cai, Y.; Liu, C. L.; Luo, S. N.

2018-04-01

[100] CaF2 single crystals are shock-compressed via symmetric planar impact, and the flyer plate-target interface velocity histories are measured with a laser displacement interferometry. The shock loading is slightly above the Hugoniot elastic limit to investigate incipient plasticity and its kinetics, and its effects on optical properties and deformation inhomogeneity. Fringe patterns demonstrate different features in modulation of fringe amplitude, including birefringence and complicated modulations. The birefringence is attributed to local lattice rotation accompanying incipient plasticity. Spatially resolved measurements show inhomogeneity in deformation, birefringence, and fringe pattern evolutions, most likely caused by the inhomogeneity associated with lattice rotation and dislocation slip. Transiently overdriven elastic states are observed, and the incubation time for incipient plasticity decreases inversely with increasing overdrive by the elastic shock.

The application of continuum damage mechanics to solve problems in geodynamics

NASA Astrophysics Data System (ADS)

Manaker, David Martin

Deformation within the Earth's lithosphere is largely controlled by the rheology of the rock. Ductile behavior in rocks is often associated with plasticity due to dislocation motion or diffusion under high pressures and temperatures. However, ductile behavior can also occur in brittle materials. An example would be cataclastic flow associated with folding at shallow crustal levels, steep subduction zones, and large-scale deformation at plate boundaries. Engineers utilize damage mechanics to model the continuum deformation of brittle materials. We utilize a modified form of damage mechanics where damage represents a reduction in frictional strength and includes a yield stress. We use this empirical approach to simulate the bending of the lithosphere. We use numerical simulations to obtain elastostatic solutions for plate bending and where the stress exceeds a yield stress, we apply damage to reduce the elastic moduli. Damage is calculated at each time step by a power-law relationship of the ratio of the yield stress to stress and the yield strain to the strain. To test our method, we apply our damage rheology to a plate deforming under applied shear, a constant bending moment, and a constant load. We simulate a wide range of behaviors from slow relaxation to instantaneous failure, over timescales that span six orders of magnitude. Stress relaxation produces elastic-perfectly plastic behavior in cases where failure does not occur. For cases of failure, we observe a rapid increase in damage leading to failure. The changes in the rate of damage accumulation in failure cases are similar to the changes in b-values of acoustic emissions observed in triaxial compression tests of fractured rock and b-value changes prior to some large earthquakes. Thus continuum damage mechanics can simulate ductile behavior due to brittle mechanisms as well as observations of laboratory experiments and seismicity.

Geodetic results in Afar: The rifting episode of November 1978 in the Asal-Ghoubbet rift

NASA Astrophysics Data System (ADS)

Kasser, M.; Lepine, J. C.; Ruegg, J. C.; Tarantula, A.

1981-01-01

A seismo-tectonic and volcanic crisis occurred in November 1978 in the Asal-Ghoubbet rift, first subaerial section of the accreting plate boundary between the African and Arabian plates (Allard et al., 1979; Abdallah et al., 1979; Le Dain et al., 1980). The activity was located in the center of a geodetic network set up in the winter 1972-1973 by the Institut Géographique National in collaboration with the Institut de Physique du Globe de Paris. Simultaneously, a precise levelling line of about 100 km was established across the area (I.G.N., 1973). The resurveying of both the geodetic network and the levelling line was carried out after the crisis, between November 1978 and March 1979. Extensions up to 2.4 m and vertical displacements up to 0.7 m were measured. Operating techniques and results of the resurveying are described in Kasser et al. (1979) and Ruegg et al. (1979). Figure 1 shows the horizontal displacements (relating to point B and to the direction BT) and figure 2 shows the vertical displacements relating to the two external points. Tarantola et al. (1979, 1980) have shown that these results can be geodynamically interpreted by a mechanism of sudden breaking and elastic rebound after an elastic stretching of the crust due to the relative drift of the plates. The breaking is triggered by magmatic fracturing of the crust, with dykes injection from a magmatic chamber which has fed the basaltic fissurai eruption. The horizontal and vertical displacements outside the broken zone of the Inner Floor are predicted by a numerical model based on this interpretation which fit very well the experimental data.

Geological and mechanical properties on the 3-D fault patch of the rapid creeping Chihshang Fault: a plate suture between Luzon arc and Eurasia in eastern Taiwan

NASA Astrophysics Data System (ADS)

Lee, J. C.; Mu, C. H.; Huang, W. J.; Liu, Z. Y. C.; Shirzaei, M.

2017-12-01

The 35-km-long Chihshang Fault is a rapidly creeping thrust at plate suture between the converging Philippine and Eurasian plates in eastern Taiwan. We combined geological investigation, geodetic data, seismological information, and a rate-dependant friction model, to illustrate the mechanical frictional properties and their variations along the strike and the depth (30-km-deep) of the fault. During the interseismic period, the Chihshang Fault is characterized by three different slip behaviours at different depths: 1) abundant micro-seismicity and semi-continuous rapid slip at the depth of 10-20 km seismogenic zone; 2) visco-elastic aseismic slip zone beneath 25 km; 3) seasonal locked/creep switch at depth of 0-2 km. Using elastic dislocation model, 1-D diffusion model, Coulomb stress criterion, and rate-dependent frictional law, we simulate the surface creep curves from the creep meters data. The result shows a rate-strengthening zone with positive frictional property (a-b) in the upper 500 meters of fault, which appears to be locked during the dry season. We tend to interpret it as a result of 300-500 m thick of unconsolidated gravels layers in the footwall of the Chihshang Fault. We also implement an inverse dynamic modeling scheme to estimate the frictional parameter () in depths by taking into account pre-seismic stress and coulomb stress changes associated with co- and post-seismic deformation of the 2003 Mw 6.5 Chengkung earthquake. Model parameters are determined from fitting the transient post-seismic geodetic signal measured at 12 continuous GPS stations. We apply a non-linear optimization algorithm, Genetic Algorithm (GA), to search for the optimum parameters. The optimum is 1.4 ×10-2 along the shallow part of the fault (0-10 km depth) and 1.2 × 10-2 in 22-28 km depth. The inferred frictional parameters are consistent with the laboratory measurements on clay rich fault zone gouges comparable to the Lichi mélange, considering the main rock composition of the Chihshang fault. Our results indicate a possibly strong influence from the surface cover of a few hundreds meter thick unconsolidated deposits (i.e., late Quaternary gravel) and the clay rich fault gouge (i.e. the Lichi Melange) on frictional properties.

An analysis of hypercritical states in elastic and inelastic systems

NASA Astrophysics Data System (ADS)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

Present-Day Kinematics of the Dead Sea Transform and Internal Deformation within the Sinai and Arabian Plates

NASA Astrophysics Data System (ADS)

Gomez, F. G.; Yassminh, R.; Cochran, W. J.; Reilinger, R. E.; Barazangi, M.

2015-12-01

An updated GPS velocity field along the Dead Sea Fault (DSF) provides a basis for assessing off-transform strain within the Sinai and Arabian plates along entire length of this left-lateral, continental transform. As one of the main tectonic elements in the eastern Mediterranean region, an improved kinematic view of the DSF elucidates the broader understanding of the regional tectonic framework, as well as contributes to refining the earthquake hazard assessment. Reconciling short-term (geodetic) measurements of crustal strain with neotectonic data on fault movements can yield insight into the mechanical and rheological properties of crustal deformation associated with transform tectonics. In addition to regional continuous GPS stations, this study assembles results from campaign GPS networks in Syria, Lebanon, and Jordan spanning more than a decade. 1-sigma uncertainties on velocities range from less than 0.4 mm/yr (continuous stations and older GPS survey sites) to about 1.0 mm/yr (newer survey sites). Analyses using elastic block models suggest slip rates of 4.0 - 5.0 mm/yr along the southern and central DSF and slip rates of 2.0 - 3.0 mm/yr along the northern DSF, and fault locking depths also vary along strike of the transform. Furthermore, the spatial distribution of GPS observations permits analyzing residual strains within the adjacent plates, after plate boundary strain is removed. A key observation is horizontal stretching within the Sinai plate, which may be related to pull by the subducted slab of the Sinai plate. Within the Arabian plate, areas of horizontal stretching generally correlate with locations of Quaternary volcanism.

A Novel Shape Memory Plate Osteosynthesis for Noninvasive Modulation of Fixation Stiffness in a Rabbit Tibia Osteotomy Model

PubMed Central

Müller, Christian W.; Pfeifer, Ronny; Meier, Karen; Decker, Sebastian; Reifenrath, Janin; Gösling, Thomas; Wesling, Volker; Krettek, Christian; Krämer, Manuel

2015-01-01

Nickel-titanium shape memory alloy (NiTi-SMA) implants might allow modulating fracture healing, changing their stiffness through alteration of both elastic modulus and cross-sectional shape by employing the shape memory effect (SME). Hypotheses: a novel NiTi-SMA plate stabilizes tibia osteotomies in rabbits. After noninvasive electromagnetic induction heating the alloy exhibits the SME and the plate changes towards higher stiffness (inverse dynamization) resulting in increased fixation stiffness and equal or better bony healing. In 14 rabbits, 1.0 mm tibia osteotomies were fixed with our experimental plate. Animals were randomised for control or induction heating at three weeks postoperatively. Repetitive X-ray imaging and in vivo measurements of bending stiffness were performed. After sacrifice at 8 weeks, macroscopic evaluation, µCT, and post mortem bending tests of the tibiae were carried out. One death and one early implant dislocation occurred. Following electromagnetic induction heating, radiographic and macroscopic changes of the implant proved successful SME activation. All osteotomies healed. In the treatment group, bending stiffness increased over time. Differences between groups were not significant. In conclusion, we demonstrated successful healing of rabbit tibia osteotomies using our novel NiTi-SMA plate. We demonstrated shape-changing SME in-vivo through transcutaneous electromagnetic induction heating. Thus, future orthopaedic implants could be modified without additional surgery. PMID:26167493

The effect of dynamic topography and gravity on lithospheric effective elastic thickness estimation: a case study

NASA Astrophysics Data System (ADS)

Bai, Yongliang; Dong, Dongdong; Kirby, Jon F.; Williams, Simon E.; Wang, Zhenjie

2018-04-01

Lithospheric effective elastic thickness (Te), a proxy for plate strength, is helpful for the understanding of subduction characteristics. Affected by curvature, faulting and magma activity, lithospheric strength near trenches should be weakened but some regional inversion studies have shown much higher Te values along some trenches than in their surroundings. In order to improve Te estimation accuracy, here we discuss the long-wavelength effect of dynamic topography and gravity on Te estimation by taking the Izu-Bonin-Mariana (IBM) Trench as a case study area. We estimate the long-wavelength influence of the density and negative buoyancy of the subducting slab on observed gravity anomalies and seafloor topography. The residual topography and gravity are used to map Te using the fan-wavelet coherence method. Maps of Te, both with and without the effects of dynamic topography and slab gravity anomaly, contain a band of high-Te values along the IBM Trench, though these values and their errors are lower when slab effects are accounted for. Nevertheless, tests show that the Te map is relatively insensitive to the choice of slab-density modelling method, even though the dynamic topography and slab-induced gravity anomaly vary considerably when the slab density is modelled by different methods. The continued presence of a high-Te band along the trench after application of dynamic corrections shows that, before using 2D inversion methods to estimate Te variations in subduction zones, there are other factors that should be considered besides the slab dynamic effects on the overriding plate.

Rheology of the lithosphere inferred from postseismic uplift following the 1959 Hebgen Lake earthquake

USGS Publications Warehouse

Nishimura, T.; Thatcher, W.

2003-01-01

We have modeled the broad postseismic uplift measured by geodetic leveling in the epicentral area of the 1959 Mw = 7.3 Hebgen Lake, Montana earthquake, a normal faulting event in the northern Basin and Range province. To fit the observed uplift we calculate synthetic postseismic deformation using the relaxation response of a gravitational viscoelastic Earth to the earthquake. For a model with an elastic plate overlying a viscoelastic half-space, we find that the elastic thickness is 38 ?? 8 km, which isclose to the local crustal thickness. The half-space viscosity is estimated at 4 ?? 1018??0.5 Pa s. The leveling data do not require a viscous lower crust but permit a lower bound viscosity of 1020 Pa s. The observed broad uplift cannot be explained by physically plausible afterslip on and below the coseismic fault. However, local deformation across the coseismic surface rupture requires shallow afterslip reaching the surface. The postseismic deformation induced by the estimated viscoelastic structure decays exponentially with a time constant of ???15 years. Because of coupling between the elastic layer and the viscoelastic substrate, this relaxation time is significantly longer than the 2 year Maxwell relaxation time of the viscous half-space itself. Our result suggests the importance of postseismic relaxation in interpreting high-precision global positioning system velocities. For example, our model results suggest that postseismic transient velocities from both the 1959 Hebgen Lake and the 1983 Mw = 6.9 Borah Peak earthquakes are currently as large as 1-2 mm/yr.

The relationship between the instantaneous velocity field and the rate of moment release in the lithosphere

USGS Publications Warehouse

Pollitz, F.F.

2003-01-01

Instantaneous velocity gradients within the continental lithosphere are often related to the tectonic driving forces. This relationship is direct if the forces are secular, as for the case of loading of a locked section of a subduction interface by the downgoing plate. If the forces are static, as for the case of lateral variations in gravitational potential energy, then velocity gradients can be produced only if the lithosphere has, on average, zero strength. The static force model may be related to the long-term velocity field but not the instantaneous velocity field (typically measured geodetically over a period of several years) because over short time intervals the upper lithosphere behaves elastically. In order to describe both the short- and long-term behaviour of an (elastic) lithosphere-(viscoelastic) asthenosphere system in a self-consistent manner, I construct a deformation model termed the expected interseismic velocity (EIV) model. Assuming that the lithosphere is populated with faults that rupture continually, each with a definite mean recurrence time, and that the Earth is well approximated as a linear elastic-viscoelastic coupled system, I derive a simple relationship between the instantaneous velocity field and the average rate of moment release in the lithosphere. Examples with synthetic fault networks demonstrate that velocity gradients in actively deforming regions may to a large extent be the product of compounded viscoelastic relaxation from past earthquakes on hundreds of faults distributed over large ( ≥106 km2) areas.

Sensitivity studies of pediatric material properties on juvenile lumbar spine responses using finite element analysis.

PubMed

Jebaseelan, D Davidson; Jebaraj, C; Yoganandan, Narayan; Rajasekaran, S; Kanna, Rishi M

2012-05-01

The objective of the study was to determine the sensitivity of material properties of the juvenile spine to its external and internal responses using a finite element model under compression, and flexion-extension bending moments. The methodology included exercising the 8-year-old juvenile lumbar spine using parametric procedures. The model included the vertebral centrum, growth plates, laminae, pedicles, transverse processes and spinous processes; disc annulus and nucleus; and various ligaments. The sensitivity analysis was conducted by varying the modulus of elasticity for various components. The first simulation was done using mean material properties. Additional simulations were done for each component corresponding to low and high material property variations. External displacement/rotation and internal stress-strain responses were determined under compression and flexion-extension bending. Results indicated that, under compression, disc properties were more sensitive than bone properties, implying an elevated role of the disc under this mode. Under flexion-extension moments, ligament properties were more dominant than the other components, suggesting that various ligaments of the juvenile spine play a key role in modulating bending behaviors. Changes in the growth plate stress associated with ligament properties explained the importance of the growth plate in the pediatric spine with potential implications in progressive deformities.

Lithospheric flexure revealed by Pleistocene emerged marine terraces on the southern Hawaiian Islands

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jones, A.T.

1992-01-01

New field and geochronological data from emerged marine deposits in the southern Hawaiian Islands suggest uplift of the islands of Molokai, Lanai and Oahu. Corals from these islands were dated by ESR. The accumulated dose for aragonitic coral at ESR signal, g = 2.0007, was determined by the additive dose method. The environmental dose rate was estimated from the Uranium concentration in corals and by using an estimate of 2.5 rad/a for the cosmic ray dose. The ESR ages of the highest terraces on Molokai are 290 [+-] 31 ka (30 m), on Lanai 217 [+-] 19 ka (50 m)more » and on Oahu 468 [+-] 36 ka (28 m). The age and elevation of the marine terraces are interpreted to imply uplift during the Late Quaternary. Lithospheric flexure combined with horizontal plate motion is proposed as a mechanism to describe the pattern of uplifted terraces on these islands. Using two-dimensional elastic plate models, the height of maximum bulge is approximately 4% to 7% of the maximum deflection for a continuous or broken plate model. Drowned reefs off Hawaii indicate subsidence of 1 km since 340 ka. Thus, the magnitude of observed uplift (30--50 m) is consistent with theoretical maximum bulge heights derived from numerical results.« less

Crust-Lithosphere-Asthenosphere Dynamics in Mantle Plume Provinces with Emphasis on the Galapagos =

NASA Astrophysics Data System (ADS)

Orellana, Felipe

Hotspot tracks, which most geoscientists attribute to the effects of mantle plumes on the overlying lithospheric plates, are characterized by distinct bathymetry, gravity signatures, structural geology, volcanology, petrology, and geochemistry; motivating us to try to understand the dynamics behind the space-time-histories of these systems. Making use of classical geodynamic paradigms, such as highly-viscous fluids (Stokes flow, for the mantle and/or lithosphere), elastic plate behavior, and heat flow, we develop conceptual frameworks to explain a number of distinct hotspot track features, and present quantitative models aimed at elucidating their origins. There is much diversity among the population of mantle plume hotspot tracks on the Earth's oceanic crust. For example, there are marked differences in the style of their bathymetry, as well as in their gravimetric signals, and also in the isotopic signature of extruded lavas. At the same time, important underlying differences are given by the age of the lithospheric plates under which the mantle plumes are impinging, lithospheric elastic thickness, the heat (or buoyancy) flux of individual mantle plumes, their melt production, crustal thickening, the proximity of spreading centers, etc. In the first chapter of this dissertation, making use of scaling theory, we show that for most oceanic hotspot tracks, the character of bathymetric expression (primarily rough vs. smooth topography) can be explained by three independent primary underlying factors - plate thickness, or equivalently plate age; plate speed; and plume buoyancy flux - combined into a single parameter, R, the ratio of plume heat flux to the effective thermal capacity of the moving plate overlying the plume. The Galapagos archipelago (off the west coast of equatorial South America), part of a >20 Ma old hotspot track formed by the underlying Galapagos mantle plume, currently exhibits a broad geographic distribution of volcanic centers of surprisingly variable age, unusual spatial patterns of geochemical enrichment, spectacular and enigmatic bathymetric features, important lithospheric and elastic thickness discontinuities, pronounced regional faults, the presence of the Nazca-Cocos spreading center nearby, and a Nazca plate - Galapagos hotspot relative velocity that varied through time. These factors have combined to create what is arguably the most complex mantle plume province on Earth, rivaled in this regard perhaps only by the Reunion and the Kerguelen-Ninetyeast hotspot provinces. The present-day Galapagos archipelago sits over a broad massive platform that has been formed primarily by intrusion and secondarily by extrusion, and that exhibits remarkable bathymetric gradients (comparable to those on the Hawaiian hotspot track). In the second chapter of this dissertation we show that some of these bathymetric features may be reasonably explained in the context of thermo-mechanical processes occurring on locally-weak crust/lithosphere, responding to internal gradients in lithostatic stresses, and that these processes of Quaternary history continue to the present day. Studies in evolutionary biology, dating back to Darwin's famous discoveries, have shown that many of the endemic Galapagos species (flora and fauna) must have evolved from species derived largely from South and Central America. Thus there is much scientific incentive to complement current phylogenetic knowledge regarding the origins of these endemic Galapagos species, with state-of-the-art geophysical models for the emergence and subsidence of the islands habitat on which these species must have evolved, most of which is no longer above sea level ! The third chapter of this dissertation represents a preliminary effort in this direction, combining multiple sources of dynamic topography during and following the formation of the Carnegie/Cocos ridges, which were constructed by the Galapagos mantle plume. We show that plate tectonic reconstructions, mantle plume dynamics, and crustal processes combined can reasonably account for changes in elevation along the Carnegie Ridge, that strongly support the idea that seamounts along most of this ridge were above sea level. In the regard, we note the irony that many Galapagos species, such as the famous marine iguanas, are older than the Galapagos Islands themselves, an observation explained perhaps by understanding the dynamic history of the Galapagos-Carnegie hotspot track through time, conforming to a spatio-temporal progression defined by the Nazca plate - Galapagos hotspot relative motion. These findings coming purely from geophysics, support a likely hypothesis/scenario of South American species migrating over now-submerged paleo-archipelagos along the Carnegie Ridge, finally giving rise to the present-day Galapagos flora and fauna.

Nonlocal modeling and buckling features of cracked nanobeams with von Karman nonlinearity

NASA Astrophysics Data System (ADS)

Akbarzadeh Khorshidi, Majid; Shaat, Mohamed; Abdelkefi, Abdessattar; Shariati, Mahmoud

2017-01-01

Buckling and postbuckling behaviors of cracked nanobeams made of single-crystalline nanomaterials are investigated. The nonlocal elasticity theory is used to model the nonlocal interatomic effects on the beam's performance accounting for the beam's axial stretching via von Karman nonlinear theory. The crack is then represented as torsional spring where the crack severity factor is derived accounting for the nonlocal features of the beam. By converting the beam into an equivalent infinite long plate with an edge crack subjected to a tensile stress at the far field, the crack energy release rate, intensity factor, and severity factor are derived according to the nonlocal elasticity theory. An analytical solution for the buckling and the postbuckling responses of cracked nonlocal nanobeams accounting for the beam axial stretching according to von Karman nonlinear theory of kinematics is derived. The impacts of the nonlocal parameter on the critical buckling loads and the static nonlinear postbuckling responses of cracked nonlocal nanobeams are studied. The results indicate that the buckling and postbuckling behaviors of cracked nanobeams are strongly affected by the crack location, crack depth, nonlocal parameter, and length-to-thickness ratio.