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.

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.

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 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.

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.

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).

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.

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

Approximate analytical solutions in the analysis of thin elastic plates

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green's function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points.

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.

Alternating method applied to edge and surface crack problems

NASA Technical Reports Server (NTRS)

Hartranft, R. J.; Sih, G. C.

1972-01-01

The Schwarz-Neumann alternating method is employed to obtain stress intensity solutions to two crack problems of practical importance: a semi-infinite elastic plate containing an edge crack which is subjected to concentrated normal and tangential forces, and an elastic half space containing a semicircular surface crack which is subjected to uniform opening pressure. The solution to the semicircular surface crack is seen to be a significant improvement over existing approximate solutions. Application of the alternating method to other crack problems of current interest is briefly discussed.

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.

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.

Mechanical response of thick laminated beams and plates subject to out-of-plane loading

NASA Technical Reports Server (NTRS)

Hiel, C. C.; Brinson, . F.

1989-01-01

The use of simplified elasticity solutions to determine the mechanical response of thick laminated beams and plates subject to out-of-plane loading is demonstrated. Excellent results were obtained which compare favorably with theoretical, numerical and experimental analyses from other sources. The most important characteristic of the solution methodology presented is that it combines great mathematical precision with simplicity. This symbiosis has been needed for design with advanced composite materials.

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.

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.

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.

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.

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.

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

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.

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.

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.

Wave propagation in magneto-electro-elastic multilayered plates with nonlocal effect

NASA Astrophysics Data System (ADS)

Chen, Jiangyi; Guo, Junhong; Pan, Ernian

2017-07-01

In this paper, analytical solutions for propagation of time-harmonic waves in three-dimensional, transversely isotropic, magnetoelectroelastic and multilayered plates with nonlocal effect are derived. We first convert the time-harmonic wave problem into a linear eigenvalue system, from which we obtain the general solutions of the extended displacements and stresses. The solutions are then employed to derive the propagator matrix which connects the field variables at the upper and lower interfaces of each layer. Making use of the continuity conditions of the physical quantities across the interface, the global propagator relation is assembled by propagating the solutions in each layer from the bottom to the top of the layered plate. From the global propagator matrix, the dispersion equation is obtained by imposing the traction-free boundary conditions on both the top and bottom surfaces of the layered plate. Dispersion curves and mode shapes in layered plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to show the influence of the nonlocal parameter, stacking sequence, as well as the orientation of incident wave on the time-harmonic field response.

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.

An analytical and experimental study of crack extension in center-notched composites

NASA Technical Reports Server (NTRS)

Beuth, Jack L., Jr.; Herakovich, Carl T.

1987-01-01

The normal stress ratio theory for crack extension in anisotropic materials is studied analytically and experimentally. The theory is applied within a microscopic-level analysis of a single center notch of arbitrary orientation in a unidirectional composite material. The bulk of the analytical work of this study applies an elasticity solution for an infinite plate with a center line to obtain critical stress and crack growth direction predictions. An elasticity solution for an infinite plate with a center elliptical flaw is also used to obtain qualitative predictions of the location of crack initiation on the border of a rounded notch tip. The analytical portion of the study includes the formulation of a new crack growth theory that includes local shear stress. Normal stress ratio theory predictions are obtained for notched unidirectional tensile coupons and unidirectional Iosipescu shear specimens. These predictions are subsequently compared to experimental results.

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.

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.

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.

Stresses in adhesively bonded joints: A closed form solution. [plate theory

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Aydinoglu, M. N.

1980-01-01

The plane strain of adhesively bonded structures which consist of two different orthotropic adherents is considered. Assuming that the thicknesses of the adherends are constant and are small in relation to the lateral dimensions of the bonded region, the adherends are treated as plates. The transverse shear effects in the adherends and the in-plane normal strain in the adhesive are taken into account. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form. A single lap joint and a stiffened plate under various loading conditions are considered as examples. To verify the basic trend of the solutions obtained from the plate theory a sample problem is solved by using the finite element method and by treating the adherends and the adhesive as elastic continua. The plate theory not only predicts the correct trend for the adhesive stresses but also gives rather surprisingly accurate results.

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.

On approximating guided waves in plates with thin anisotropic coatings by means of effective boundary conditions

PubMed

Niklasson; Datta; Dunn

2000-09-01

In this paper, effective boundary conditions for elastic wave propagation in plates with thin coatings are derived. These effective boundary conditions are used to obtain an approximate dispersion relation for guided waves in an isotropic plate with thin anisotropic coating layers. The accuracy of the effective boundary conditions is investigated numerically by comparison with exact solutions for two different material systems. The systems considered consist of a metallic core with thin superconducting coatings. It is shown that for wavelengths long compared to the coating thickness there is excellent agreement between the approximate and exact solutions for both systems. Furthermore, numerical results presented might be used to characterize coating properties by ultrasonic techniques.

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.

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.

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

An algorithm for full parametric solution of problems on the statics of orthotropic plates by the method of boundary states with perturbations

NASA Astrophysics Data System (ADS)

Penkov, V. B.; Ivanychev, D. A.; Novikova, O. S.; Levina, L. V.

2018-03-01

The article substantiates the possibility of building full parametric analytical solutions of mathematical physics problems in arbitrary regions by means of computer systems. The suggested effective means for such solutions is the method of boundary states with perturbations, which aptly incorporates all parameters of an orthotropic medium in a general solution. We performed check calculations of elastic fields of an anisotropic rectangular region (test and calculation problems) for a generalized plane stress state.

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.

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

1973-01-01

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

Three-Dimensional Solution of the Free Vibration Problem for Metal-Ceramic Shells Using the Method of Sampling Surfaces

NASA Astrophysics Data System (ADS)

Kulikov, G. M.; Plotnikova, S. V.

2017-03-01

The possibility of using the method of sampling surfaces (SaS) for solving the free vibration problem of threedimensional elasticity for metal-ceramic shells is studied. According to this method, in the shell body, an arbitrary number of SaS parallel to its middle surface are selected in order to take displacements of these surfaces as unknowns. The SaS pass through the nodes of a Chebyshev polynomial, which improves the convergence of the SaS method significantly. As a result, the SaS method can be used to obtain analytical solutions of the vibration problem for metal-ceramic plates and cylindrical shells that asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity.

Bending analysis of a general cross-ply laminate using 3D elasticity solution and layerwise theory

NASA Astrophysics Data System (ADS)

Yazdani Sarvestani, H.; Naghashpour, A.; Heidari-Rarani, M.

2015-12-01

In this study, the analytical solution of interlaminar stresses near the free edges of a general (symmetric and unsymmetric layups) cross-ply composite laminate subjected to pure bending loading is presented based on Reddy's layerwise theory (LWT) for the first time. First, the reduced form of displacement field is obtained for a general cross-ply composite laminate subjected to a bending moment by elasticity theory. Then, first-order shear deformation theory of plates and LWT is utilized to determine the global and local deformation parameters appearing in the displacement fields, respectively. One of the main advantages of the developed solution based on the LWT is exact prediction of interlaminar stresses at the boundary layer regions. To show the accuracy of this solution, three-dimensional elasticity bending problem of a laminated composite is solved for special set of boundary conditions as well. Finally, LWT results are presented for edge-effect problems of several symmetric and unsymmetric cross-ply laminates under the bending moment. The obtained results indicate high stress gradients of interlaminar stresses near the edges of laminates.

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.

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.

Highly elastic polymer solutions under shear: Polymer migration, viscoelastic instabilities, and anomalous rheology

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

MacDonald, M.J.; Muller, S.J.

1996-12-31

The use of highly elastic polymer solutions has been remarkably successful in elucidating the behavior of polymeric materials under flowing conditions. Here, we present the results of an extensive experimental study into the shear behavior of an athermal, dilute, binary polymer solution that is believed to be free of many of these effects. Under extended shearing, we observe the migration of polymer species: after shearing for several hundred hours, concentrations that are more than double the initial uniform value can be achieved. Although the solutions are well-described by dumbbell models in shear flows on short-time scales, theoretical predictions substantially underestimatemore » the rate of migration. Flow visualization and rheometric experiments suggest that the origin of this discrepancy could be the anomalous long-time rheology of these solutions. While these fluids display the well-known elastic instability in cone and plate flow above a critical Deborah number, extended shearing reveals that the toroidal secondary flow is eventually replaced by a purely azimuthal shearing flow. In addition, when sheared below the critical condition for the instability, the solutions exhibit a slow but reversible decay in normal stresses. The shear-induced migration of polymer species has been predicted by numerous theoretical studies. However, observations on the highly elastic polymer solutions that are most likely to show polymer migration, are complicated by a number of different physical processes that occur as a result of shearing. These phenomena, which include shear-induced phase separation, elastically-induced hydrodynamic instabilities, mixed solvent effects, shear-induced aggregation, and anomalous transient shear and normal stress behavior are often observed at times earlier than and at shear rates less than those where migration is predicted to occur; hence, the experimental detection of polymer migration has been thwarted by these other physical processes.« less

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.

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.

Strength conditions for the elastic structures with a stress error

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2017-10-01

As is known, the constraints (strength conditions) for the safety factor of elastic structures and design details of a particular class, e.g. aviation structures are established, i.e. the safety factor values of such structures should be within the given range. It should be noted that the constraints are set for the safety factors corresponding to analytical (exact) solutions of elasticity problems represented for the structures. Developing the analytical solutions for most structures, especially irregular shape ones, is associated with great difficulties. Approximate approaches to solve the elasticity problems, e.g. the technical theories of deformation of homogeneous and composite plates, beams and shells, are widely used for a great number of structures. Technical theories based on the hypotheses give rise to approximate (technical) solutions with an irreducible error, with the exact value being difficult to be determined. In static calculations of the structural strength with a specified small range for the safety factors application of technical (by the Theory of Strength of Materials) solutions is difficult. However, there are some numerical methods for developing the approximate solutions of elasticity problems with arbitrarily small errors. In present paper, the adjusted reference (specified) strength conditions for the structural safety factor corresponding to approximate solution of the elasticity problem have been proposed. The stress error estimation is taken into account using the proposed strength conditions. It has been shown that, to fulfill the specified strength conditions for the safety factor of the given structure corresponding to an exact solution, the adjusted strength conditions for the structural safety factor corresponding to an approximate solution are required. The stress error estimation which is the basis for developing the adjusted strength conditions has been determined for the specified strength conditions. The adjusted strength conditions presented by allowable stresses are suggested. Adjusted strength conditions make it possible to determine the set of approximate solutions, whereby meeting the specified strength conditions. Some examples of the specified strength conditions to be satisfied using the technical (by the Theory of Strength of Materials) solutions and strength conditions have been given, as well as the examples of stress conditions to be satisfied using approximate solutions with a small error.

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.

Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory. I - Stress and displacement

NASA Technical Reports Server (NTRS)

Librescu, L.; Khdeir, A. A.

1988-01-01

A simple theory for bending of composite anisotropic plates that are laminated symmetrically about their mid-plane is presented. This theory incorporates transverse shear deformation and transverse normal stress as well as the higher-order effects and fulfills the static conditions on the external boundary planes. Further on, by using Levy-type solutions considered in conjunction with the state space concept, the state of stress and displacement of rectangular plates for a variety of edge conditions is determined and the results are compared to their first-order shear deformation and classical counterparts, obtained by using the same state-space technique.

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.

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).

The complex variable reproducing kernel particle method for bending problems of thin plates on elastic foundations

NASA Astrophysics Data System (ADS)

Chen, L.; Cheng, Y. M.

2018-07-01

In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used to form the approximation function of the deflection of the thin plates resting on elastic foundation, the Galerkin weak form of thin plates on elastic foundation is employed to obtain the discretized system equations, the penalty method is used to apply the essential boundary conditions, and Winkler and Pasternak foundation models are used to consider the interface pressure between the plate and the foundation. Then the corresponding formulae of CVRKPM for thin plates on elastic foundations are presented in detail. Several numerical examples are given to discuss the efficiency and accuracy of CVRKPM in this paper, and the corresponding advantages of the present method are shown.

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.

An improved plate theory of order (1,2) for thick composite laminates

NASA Technical Reports Server (NTRS)

Tessler, A.

1992-01-01

A new (1,2)-order theory is proposed for the linear elasto-static analysis of laminated composite plates. The basic assumptions are those concerning the distribution through the laminate thickness of the displacements, transverse shear strains and the transverse normal stress, with these quantities regarded as some weighted averages of their exact elasticity theory representations. The displacement expansions are linear for the inplane components and quadratic for the transverse component, whereas the transverse shear strains and transverse normal stress are respectively quadratic and cubic through the thickness. The main distinguishing feature of the theory is that all strain and stress components are expressed in terms of the assumed displacements prior to the application of a variational principle. This is accomplished by an a priori least-square compatibility requirement for the transverse strains and by requiring exact stress boundary conditions at the top and bottom plate surfaces. Equations of equilibrium and associated Poisson boundary conditions are derived from the virtual work principle. It is shown that the theory is particularly suited for finite element discretization as it requires simple C(sup 0)- and C(sup -1)-continuous displacement interpolation fields. Analytic solutions for the problem of cylindrical bending are derived and compared with the exact elasticity solutions and those of our earlier (1,2)-order theory based on the assumed displacements and transverse strains.

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.

A study of the effect of a boundary layer profile on the dynamic response and acoustic radiation of flat panels. Ph.D. Thesis - Virginia Univ.

NASA Technical Reports Server (NTRS)

Mixson, J. S.

1973-01-01

The response of a thin, elastic plate to a harmonic force which drives the plate from below and a compressible air stream with a viscous boundary layer flowing parallel to the upper surface along the length was investigated. Equations governing the forced response of the coupled plate-aerodynamic system are derived along with appropriate boundary conditions. Calculations of basic solution parameters for a linear velocity profile and for a Blasius profile showed that the same system response could be obtained from each profile if appropriate values of boundary layer thickness were chosen for each profile.

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.

A model of convergent plate margins based on the recent tectonics of Shikoku, Japan

NASA Technical Reports Server (NTRS)

Bischke, R. E.

1974-01-01

A viscoelastic finite element plate tectonic model is applied to displacement data for the island of Shikoku, Japan. The flow properties and geometry of the upper portions of the earth are assumed known from geophysical evidence, and the loading characteristics are determined from the model. The nature of the forces acting on the Philippine Sea plate, particularly in the vicinity of the Nankai trough, is determined. Seismic displacement data related to the 1946 Nankaido earthquake are modeled in terms of a thick elastic plate overlying a fluidlike substratum. The sequence of preseismic and seismic displacements can be explained in terms of two independent processes operating on elastic lithospheric plates: a strain accumulation process caused by vertical downward forces acting on or within the lithosphere in the vicinity of the trench, and a strain release process caused by plate failure along a preexisting zone on weakness. This is a restatement of Reid's elastic rebound theory in terms of elastic lithospheric plates.

Experimental and theoretical study of the buckling of narrow thin plates on an elastic foundation under compression

NASA Astrophysics Data System (ADS)

Kurguzov, V. D.; Demeshkin, A. G.

2016-05-01

The paper describes the processes of elastic deformation of thin films under mechanical loading. The film is modeled longitudinally by a compressed plate arranged on an elastic foundation. A computer model of the buckling of the narrow thin plate with a delamination portion located on an elastic foundation is constructed. This paper also touches upon the supercritical behavior of the plate-substrate system. The experiments on the axial compression of a metal strip adhered to a rubber plate are performed, and 2 to 7 buckling modes are obtained therein. The critical loads and buckling modes obtained in the numerical calculations are compared with the experimental data. It is shown that there is the possibility of progressive delamination of the metal plate from the foundation if the critical load is exceeded. It is found that the use of the proposed approach, which, in contrast to other approaches, accounts for the elastic deformation of the substrate, causes the dependence between the critical bending stress and the stiffness of the foundation.

Load-sharing through elastic micro-motion accelerates bone formation and interbody fusion.

PubMed

Ledet, Eric H; Sanders, Glenn P; DiRisio, Darryl J; Glennon, Joseph C

2018-02-13

Achieving a successful spinal fusion requires the proper biological and biomechanical environment. Optimizing load-sharing in the interbody space can enhance bone formation. For anterior cervical discectomy and fusion (ACDF), loading and motion are largely dictated by the stiffness of the plate, which can facilitate a balance between stability and load-sharing. The advantages of load-sharing may be substantial for patients with comorbidities and in multilevel procedures where pseudarthrosis rates are significant. We aimed to evaluate the efficacy of a novel elastically deformable, continuously load-sharing anterior cervical spinal plate for promotion of bone formation and interbody fusion relative to a translationally dynamic plate. An in vivo animal model was used to evaluate the effects of an elastically deformable spinal plate on bone formation and spine fusion. Fourteen goats underwent an ACDF and received either a translationally dynamic or elastically deformable plate. Animals were followed up until 18 weeks and were evaluated by plain x-ray, computed tomography scan, and undecalcified histology to evaluate the rate and quality of bone formation and interbody fusion. Animals treated with the elastically deformable plate demonstrated statistically significantly superior early bone formation relative to the translationally dynamic plate. Trends in the data from 8 to 18 weeks postoperatively suggest that the elastically deformable implant enhanced bony bridging and fusion, but these enhancements were not statistically significant. Load-sharing through elastic micro-motion accelerates bone formation in the challenging goat ACDF model. The elastically deformable implant used in this study may promote early bony bridging and increased rates of fusion, but future studies will be necessary to comprehensively characterize the advantages of load-sharing through micro-motion. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Vibration Analysis of Composite Laminate Plate Excited by Piezoelectric Actuators

PubMed Central

Her, Shiuh-Chuan; Lin, Chi-Sheng

2013-01-01

Piezoelectric materials can be used as actuators for the active vibration control of smart structural systems. In this work, piezoelectric patches are surface bonded to a composite laminate plate and used as vibration actuators. A static analysis based on the piezoelectricity and elasticity is conducted to evaluate the loads induced by the piezoelectric actuators to the host structure. The loads are then employed to develop the vibration response of a simply supported laminate rectangular plate excited by piezoelectric patches subjected to time harmonic voltages. An analytical solution of the vibration response of a simply supported laminate rectangular plate under time harmonic electrical loading is obtained and compared with finite element results to validate the present approach. The effects of location and exciting frequency of piezoelectric actuators on the vibration response of the laminate plate are investigated through a parametric study. Numerical results show that modes can be selectively excited, leading to structural vibration control. PMID:23529121

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.

Behavior of a semi-infinite ice cover under periodic dynamic impact

NASA Astrophysics Data System (ADS)

Tkacheva, L. A.

2017-07-01

Oscillations of a semi-infinite ice cover in an ideal incompressible liquid of finite depth under local time-periodic axisymmetric load are considered. The ice cover is simulated by a thin elastic plate of constant thickness. An analytical solution of the problem is obtained using the Wiener-Hopf method. The asymptotic behavior of the amplitudes of oscillations of the plate and the liquid in the far field is studied. It is shown that the propagation of waves in the far field is uneven: in some directions, the waves propagate with a significantly greater amplitude.

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.

Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry.

PubMed

Malm, A V; Waigh, T A

2017-04-26

The flow instabilities of solutions of high molecular weight DNA in the entangled semi-dilute concentration regime were investigated using optical coherence tomography velocimetry, a technique that provides high spatial (probe volumes of 3.4 pL) and temporal resolution (sub μs) information on the flow behaviour of complex fluids in a rheometer. The velocity profiles of the opaque DNA solutions (high and low salt) were measured as a function of the distance across the gap of a parallel plate rheometer, and their evolution over time was measured. At lower DNA concentrations and low shear rates, the velocity fluctuations were well described by Gaussian functions and the velocity gradient was uniform across the rheometer gap, which is expected for Newtonian flows. As the DNA concentration and shear rate were increased there was a stable wall slip regime followed by an evolving wall slip regime, which is finally followed by the onset of elastic turbulence. Strain localization (shear banding) is observed on the boundaries of the flows at intermediate shear rates, but decreases in the high shear elastic turbulence regime, where bulk strain localization occurs. A dynamic phase diagram for non-linear flow was created to describe the different behaviours.

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.

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.

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.

On the solution of integral equations with a generalized Cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

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.

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.

Stability analysis of flexible wind turbine blades using finite element method

NASA Technical Reports Server (NTRS)

Kamoulakos, A.

1982-01-01

Static vibration and flutter analysis of a straight elastic axis blade was performed based on a finite element method solution. The total potential energy functional was formulated according to linear beam theory. The inertia and aerodynamic loads were formulated according to the blade absolute acceleration and absolute velocity vectors. In vibration analysis, the direction of motion of the blade during the first out-of-lane and first in-plane modes was examined; numerical results involve NASA/DOE Mod-0, McCauley propeller, north wind turbine and flat plate behavior. In flutter analysis, comparison cases were examined involving several references. Vibration analysis of a nonstraight elastic axis blade based on a finite element method solution was performed in a similar manner with the straight elastic axis blade, since it was recognized that a curved blade can be approximated by an assembly of a sufficient number of straight blade elements at different inclinations with respect to common system of axes. Numerical results involve comparison between the behavior of a straight and a curved cantilever beam during the lowest two in-plane and out-of-plane modes.

Evaluation of the use of a singularity element in finite element analysis of center-cracked plates

NASA Technical Reports Server (NTRS)

Mendelson, A.; Gross, B.; Srawley, J., E.

1972-01-01

Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.

Panel Absorber

NASA Astrophysics Data System (ADS)

MECHEL, F. P.

2001-11-01

A plane wave is incident on a simply supported elastic plate covering a back volume; the arrangement is surrounded by a hard baffle wall. The plate may be porous with a flow friction resistance; the back volume may be filled either with air or with a porous material. The back volume may be bulk reacting (i.e., with sound propagation parallel to the plate) or locally reacting. Since this arrangement is of some importance in room acoustics, Cremer in his book about room acoustics [1] has presented an approximate analysis. However, Cremer's analysis uses a number of assumptions which make his solution, in his own estimate, unsuited for low frequencies, where, on the other hand, the arrangement mainly is applied. This paper presents a sound field description which uses modal analysis. It is applicable not only in the far field, but also near the absorber. Further, approximate solutions are derived, based on simplifying assumptions like Cremer has used. The modal analysis solution is of interest not only as a reference for approximations but also for practical applications, because the aspect of computing time becomes more and more unimportant (the 3D-plots presented below for the sound field were evaluated with modal analysis in about 6 s).

Contact stresses in pin-loaded orthotropic plates

NASA Technical Reports Server (NTRS)

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

1984-01-01

The effects of pin elasticity, friction, and clearance on the stresses near the hole in a pin-loaded orthotropic plate are described. The problem is modeled as a contact elasticity problem using complex variable theory, the pin and the plate being two elastic bodies interacting through contact. This modeling is in contrast to previous works which assumed that the pin is rigid or that it exerts a known cosinusoidal radial traction on the hole boundary. Neither of these approaches explicitly involves a pin. A collocation procedure and iteration were used to obtain numerical results for a variety of plate and pin elastic properties and various levels of friction and clearance. Collocation was used to enforce the boundary and iteration was used to find the contact and no-slip regions on the boundary. Details of the numerical scheme are discussed.

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.

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.

Stress-strain state on non-thin plates and shells. Generalized theory (survey)

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

Nemish, Yu.N.; Khoma, I.Yu.

1994-05-01

In the first part of this survey, we examined exact and approximate analytic solutions of specific problems for thick shells and plates obtained on the basis of three-dimensional equations of the mathematical theory of elasticity. The second part of the survey, presented here, is devoted to systematization and analysis of studies made in regard to a generalized theory of plates and shells based on expansion of the sought functions into Fourier series in Legendre polynomials of the thickness coordinate. Methods are described for constructing systems of differential equations in the coefficients of the expansions (as functions of two independent variablesmore » and time), along with the corresponding boundary and initial conditions. Matters relating to substantiation of the given approach and its generalizations are also discussed.« less

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.

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.

Time-Varying Upper-Plate Deformation during the Megathrust Subduction Earthquake Cycle

NASA Astrophysics Data System (ADS)

Furlong, Kevin P.; Govers, Rob; Herman, Matthew

2015-04-01

Over the past several decades of the WEGENER era, our abilities to observe and image the deformational behavior of the upper plate in megathrust subduction zones has dramatically improved. Several intriguing inferences can be made from these observations including apparent lateral variations in locking along subduction zones, which differs from interseismic to coseismic periods; the significant magnitude of post-earthquake deformation (e.g. following the 20U14 Mw Iquique, Chile earthquake, observed on-land GPS post-EQ displacements are comparable to the co-seismic displacements); and incompatibilities between rates of slip deficit accumulation and resulting earthquake co-seismic slip (e.g. pre-Tohoku, inferred rates of slip deficit accumulation on the megathrust significantly exceed slip amounts for the ~ 1000 year recurrence.) Modeling capabilities have grown from fitting simple elastic accumulation/rebound curves to sparse data to having spatially dense continuous time series that allow us to infer details of plate boundary coupling, rheology-driven transient deformation, and partitioning among inter-earthquake and co-seismic displacements. In this research we utilize a 2D numerical modeling to explore the time-varying deformational behavior of subduction zones during the earthquake cycle with an emphasis on upper-plate and plate interface behavior. We have used a simplified model configuration to isolate fundamental processes associated with the earthquake cycle, rather than attempting to fit details of specific megathrust zones. Using a simple subduction geometry, but realistic rheologic layering we are evaluating the time-varying displacement and stress response through a multi-earthquake cycle history. We use a simple model configuration - an elastic subducting slab, an elastic upper plate (shallower than 40 km), and a visco-elastic upper plate (deeper than 40 km). This configuration leads to an upper plate that acts as a deforming elastic beam at inter-earthquake loading times and rates with a viscously relaxed regime at depths greater than 40 km. Analyses of our preliminary model results lead to the following: 1. Co-seismic stress transfer from the unloading elastic layer (shallow) into an elastically loading visco-elastic layer (deeper) - extends ~ 100 km inboard of locked zone. This stress transfer affects both coseismic and post-seismic surface displacements. 2. Post-seismic response of upper plate involves seaward motion for initial 10-20 years (~ 2 Maxwell times) after EQ. This occurs in spite of there being no slip on locked plate boundary - i.e. this is not plate boundary after-slip but rather is a consequence of stress relaxation in co-seismically loaded visco-elastic layer. However standard inversions of the surface displacement field would indicate significant after-slip along the locked plate interface. 3. By approximately 80 years (8 Maxwell times) system has returned to simple linear displacement pattern - the expected behavior for a shortening elastic beam. Prior to that time, the surface (observable) displacement pattern changes substantially over time and would result in an apparent temporal variation in coupling - from near-zero coupling to fully locked over ~ 80 years post-earthquake. These preliminary results indicate that care is needed in interpreting observed surface displacement fields from GPS, InSAR, etc. during the interseismic period. temporal variations in crustal deformation observed in regions such as the recent Tohoku, Maule, and Iquique megathrust events which are ascribed to fault plane after-slip may in fact reflect processes associated with re-equilibration of the visco-elastic subduction system.

General analytical approach for sound transmission loss analysis through a thick metamaterial plate

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

Oudich, Mourad; Zhou, Xiaoming; Badreddine Assouar, M., E-mail: Badreddine.Assouar@univ-lorraine.fr

We report theoretically and numerically on the sound transmission loss performance through a thick plate-type acoustic metamaterial made of spring-mass resonators attached to the surface of a homogeneous elastic plate. Two general analytical approaches based on plane wave expansion were developed to calculate both the sound transmission loss through the metamaterial plate (thick and thin) and its band structure. The first one can be applied to thick plate systems to study the sound transmission for any normal or oblique incident sound pressure. The second approach gives the metamaterial dispersion behavior to describe the vibrational motions of the plate, which helpsmore » to understand the physics behind sound radiation through air by the structure. Computed results show that high sound transmission loss up to 72 dB at 2 kHz is reached with a thick metamaterial plate while only 23 dB can be obtained for a simple homogeneous plate with the same thickness. Such plate-type acoustic metamaterial can be a very effective solution for high performance sound insulation and structural vibration shielding in the very low-frequency range.« less

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.

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)

Vibration control of multiferroic fibrous composite plates using active constrained layer damping

NASA Astrophysics Data System (ADS)

Kattimani, S. C.; Ray, M. C.

2018-06-01

Geometrically nonlinear vibration control of fiber reinforced magneto-electro-elastic or multiferroic fibrous composite plates using active constrained layer damping treatment has been investigated. The piezoelectric (BaTiO3) fibers are embedded in the magnetostrictive (CoFe2O4) matrix forming magneto-electro-elastic or multiferroic smart composite. A three-dimensional finite element model of such fiber reinforced magneto-electro-elastic plates integrated with the active constrained layer damping patches is developed. Influence of electro-elastic, magneto-elastic and electromagnetic coupled fields on the vibration has been studied. The Golla-Hughes-McTavish method in time domain is employed for modeling a constrained viscoelastic layer of the active constrained layer damping treatment. The von Kármán type nonlinear strain-displacement relations are incorporated for developing a three-dimensional finite element model. Effect of fiber volume fraction, fiber orientation and boundary conditions on the control of geometrically nonlinear vibration of the fiber reinforced magneto-electro-elastic plates is investigated. The performance of the active constrained layer damping treatment due to the variation of piezoelectric fiber orientation angle in the 1-3 Piezoelectric constraining layer of the active constrained layer damping treatment has also been emphasized.

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.

Elasticity Solution of an Adhesively Bonded Cover Plate of Various Geometries

NASA Technical Reports Server (NTRS)

Aksel, G. N.; Erdogan, F.

1985-01-01

The plane strain of adhesively bonded structures consisting of two different isotropic adherends is considered. By expressing the x-y components of the displacements in terms of Fourier integrals and using the corresponding boundary and continuity conditions, the integral equations for the general problem are obtained and solved numerically by applying Gauss-Chebyshev integration scheme. The shear and the normal stresses in the adhesive are calculated for various geometries and material properties for a stiffened plate under uniaxial tension. Numerical results involving the stress intensity factors and the strain energy release rate are presented. The closed-form expressions for the Fredholm kernels are provided to obtain the solution for an arbitrary geometry and material properties. For the general geometry, the contribution of the normal stress is quite significant, while for symmetric geometries, the shear stress is dominant, the normal stress vanishes if the adherends are of the same material and the same thickness.

A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects.

PubMed

Gao, X-L; Zhang, G Y

2016-07-01

A non-classical model for a Mindlin plate resting on an elastic foundation is developed in a general form using a modified couple stress theory, a surface elasticity theory and a two-parameter Winkler-Pasternak foundation model. It includes all five kinematic variables possible for a Mindlin plate. The equations of motion and the complete boundary conditions are obtained simultaneously through a variational formulation based on Hamilton's principle, and the microstructure, surface energy and foundation effects are treated in a unified manner. The newly developed model contains one material length-scale parameter to describe the microstructure effect, three surface elastic constants to account for the surface energy effect, and two foundation parameters to capture the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the new model includes the Mindlin plate models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases, recovers the Kirchhoff plate model incorporating the microstructure, surface energy and foundation effects, and degenerates to the Timoshenko beam model including the microstructure effect. To illustrate the new Mindlin plate model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulae derived.

A non-classical Mindlin plate model incorporating microstructure, surface energy and foundation effects

PubMed Central

Zhang, G. Y.

2016-01-01

A non-classical model for a Mindlin plate resting on an elastic foundation is developed in a general form using a modified couple stress theory, a surface elasticity theory and a two-parameter Winkler–Pasternak foundation model. It includes all five kinematic variables possible for a Mindlin plate. The equations of motion and the complete boundary conditions are obtained simultaneously through a variational formulation based on Hamilton's principle, and the microstructure, surface energy and foundation effects are treated in a unified manner. The newly developed model contains one material length-scale parameter to describe the microstructure effect, three surface elastic constants to account for the surface energy effect, and two foundation parameters to capture the foundation effect. The current non-classical plate model reduces to its classical elasticity-based counterpart when the microstructure, surface energy and foundation effects are all suppressed. In addition, the new model includes the Mindlin plate models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases, recovers the Kirchhoff plate model incorporating the microstructure, surface energy and foundation effects, and degenerates to the Timoshenko beam model including the microstructure effect. To illustrate the new Mindlin plate model, the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulae derived. PMID:27493578

Action of a Local Time-Periodic Load on an Ice Sheet with a Crack

NASA Astrophysics Data System (ADS)

Tkacheva, L. A.

2017-11-01

The problem of vibrations of an ice sheet with a rectilinear crack on the surface of an ideal incompressible fluid of finite depth under the action of a time-periodic local load is solved analytically using the Wiener-Hopf technique. Ice cover is simulated by two thin elastic semi-infinite plates of constant thickness. The thickness of the plates may be different on the opposite sides of the crack. Various boundary conditions on the edges of the plates are considered. For the case of contact of plates of the same thickness, a solution in explicit form is obtained. The asymptotics of the deflection of the plates in the far field is studied. It is shown that in the case of contact of two plates of different thickness, predominant directions of wave propagation at an angle to the crack can be identified in the far field. In the case of contact of plates of the same thickness with free edges and with free overlap, an edge waveguide mode propagating along the crack is excited. It is shown that the edge mode propagates with maximum amplitude if the vertical wall is in contact with the plate. Examples of calculations are given.

Applications of FEM and BEM in two-dimensional fracture mechanics problems

NASA Technical Reports Server (NTRS)

Min, J. B.; Steeve, B. E.; Swanson, G. R.

1992-01-01

A comparison of the finite element method (FEM) and boundary element method (BEM) for the solution of two-dimensional plane strain problems in fracture mechanics is presented in this paper. Stress intensity factors (SIF's) were calculated using both methods for elastic plates with either a single-edge crack or an inclined-edge crack. In particular, two currently available programs, ANSYS for finite element analysis and BEASY for boundary element analysis, were used.

An experimental-theoretical study of free vibrations of plates on elastic point supports

NASA Technical Reports Server (NTRS)

Leuner, T. R.

1972-01-01

A theoretical and experimental study is made to investigate the effect on plate vibrations of varying the stiffness of corner elastic point supports. A theoretical model is developed using a Rayleigh-Ritz analysis which approximates the plate mode shapes as products of free-free beam modes. The elastic point supports are modelled both as massless translational springs, and springs with tip masses. The tip masses are included to better represent the experimental supports. An experiment is constructed using the bending stiffness of horizontal beams to support a square plate at its four corners. The stiffness of these supports can be varied over such a range that the plate fundamental frequency is lowered to 40% of the rigid support frequency. The variation with support stiffness of the frequencies of the first eight plate modes is measured, and compared with the theoretical results. The plate mode shapes for rigid supports are analyzed using holographic interferometry. There is excellent agreement between the theoretical and experimental results, except for high plate modes where the theoretical model is demonstrated to be inadequate.

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.

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.

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.

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.

Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending

PubMed Central

Jun, Ding; Song, Chen; Wei-Bin, Wen; Shao-Ming, Luo; Xia, Huang

2014-01-01

A novel numerical manifold method was derived from the cubic B-spline basis function. The new interpolation function is characterized by high-order coordination at the boundary of a manifold element. The linear elastic-dynamic equation used to solve the bending vibration of thin plates was derived according to the principle of minimum instantaneous potential energy. The method for the initialization of the dynamic equation and its solution process were provided. Moreover, the analysis showed that the calculated stiffness matrix exhibited favorable performance. Numerical results showed that the generalized degrees of freedom were significantly fewer and that the calculation accuracy was higher for the manifold method than for the conventional finite element method. PMID:24883403

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.

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.

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.

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

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.

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.

Estimates of elastic plate thicknesses beneath large volcanos on Venus

NASA Technical Reports Server (NTRS)

Mcgovern, Patrick J.; Solomon, Sean C.

1992-01-01

Megellan radar imaging and topography data are now available for a number of volcanos on Venus greater than 100 km in radius. These data can be examined to reveal evidence of the flexural response of the lithosphere to the volcanic load. On Earth, flexure beneath large hotspot volcanos results in an annual topographic moat that is partially to completely filled in by sedimentation and mass wasting from the volcano's flanks. On Venus, erosion and sediment deposition are considered to be negligible at the resolution of Magellan images. Thus, it may be possible to observe evidence of flexure by the ponding of recent volcanic flows in the moat. We also might expect to find topographic signals from unfilled moats surrounding large volcanos on Venus, although these signals may be partially obscured by regional topography. Also, in the absence of sedimentation, tectonic evidence of deformation around large volcanos should be evident except where buried by very young flows. We use analytic solutions in axisymmetric geometry for deflections and stresses resulting from loading of a plate overlying an inviscid fluid. Solutions for a set of disk loads are superimposed to obtain a solution for a conical volcano. The deflection of the lithosphere produces an annular depression or moat, the extent of which can be estimated by measuring the distance from the volcano's edge to the first zero crossing or to the peak of the flexural arch. Magellan altimetry data records (ARCDRs) from data cycle 1 are processed using the GMT mapping and graphics software to produce topographic contour maps of the volcanos. We then take topographic profiles that cut across the annular and ponded flows seen on the radar images. By comparing the locations of these flows to the predicted moat locations from a range of models, we estimate the elastic plate thickness that best fits the observations, together with the uncertainty in that estimate.

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.

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

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

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.

Constitutive error based parameter estimation technique for plate structures using free vibration signatures

NASA Astrophysics Data System (ADS)

Guchhait, Shyamal; Banerjee, Biswanath

2018-04-01

In this paper, a variant of constitutive equation error based material parameter estimation procedure for linear elastic plates is developed from partially measured free vibration sig-natures. It has been reported in many research articles that the mode shape curvatures are much more sensitive compared to mode shape themselves to localize inhomogeneity. Complying with this idea, an identification procedure is framed as an optimization problem where the proposed cost function measures the error in constitutive relation due to incompatible curvature/strain and moment/stress fields. Unlike standard constitutive equation error based procedure wherein a solution of a couple system is unavoidable in each iteration, we generate these incompatible fields via two linear solves. A simple, yet effective, penalty based approach is followed to incorporate measured data. The penalization parameter not only helps in incorporating corrupted measurement data weakly but also acts as a regularizer against the ill-posedness of the inverse problem. Explicit linear update formulas are then developed for anisotropic linear elastic material. Numerical examples are provided to show the applicability of the proposed technique. Finally, an experimental validation is also provided.

[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.

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.

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.

Programming of the complex logarithm function in the solution of the cracked anisotropic plate loaded by a point force

NASA Astrophysics Data System (ADS)

Zaal, K. J. J. M.

1991-06-01

In programming solutions of complex function theory, the complex logarithm function is replaced by the complex logarithmic function, introducing a discontinuity along the branch cut into the programmed solution which was not present in the mathematical solution. Recently, Liaw and Kamel presented their solution of the infinite anisotropic centrally cracked plate loaded by an arbitrary point force, which they used as Green's function in a boundary element method intended to evaluate the stress intensity factor at the tip of a crack originating from an elliptical home. Their solution may be used as Green's function of many more numerical methods involving anisotropic elasticity. In programming applications of Liaw and Kamel's solution, the standard definition of the logarithmic function with the branch cut at the nonpositive real axis cannot provide a reliable computation of the displacement field for Liaw and Kamel's solution. Either the branch cut should be redefined outside the domain of the logarithmic function, after proving that the domain is limited to a part of the plane, or the logarithmic function should be defined on its Riemann surface. A two dimensional line fractal can provide the link between all mesh points on the plane essential to evaluate the logarithm function on its Riemann surface. As an example, a two dimensional line fractal is defined for a mesh once used by Erdogan and Arin.

Small bending and stretching of sandwich-type shells

NASA Technical Reports Server (NTRS)

Reissner, Eric

1950-01-01

A theory has been developed for small bending and stretching of sandwich-type shells. This theory is an extension of the known theory of homogeneous thin elastic shells. It was found that two effects are important in the present problem, which are not normally of importance in the theory of curved shells: (1) the effect of transverse shear deformation and (2) the effect of transverse normal stress deformation. The first of these two effects has been known to be of importance in the theory of plates and beams. The second effect was found to occur in a manner which is typical for shells and has no counterpart in flat-plate theory. The general results of this report have been applied to the solution of problems concerning flat plates, circular rings, circular cylindrical shells, and spherical shells. In each case numerical examples have been given, illustrating the magnitude of the effects of transverse shear and normal stress deformation.

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.

Structure-property relations of orthorhombic [(CH3)3NCH2COO]2(CuCl2)3 · 2H2 O

NASA Astrophysics Data System (ADS)

Haussühl, Eiken; Schreuer, Jürgen; Wiehl, Leonore; Paulsen, Natalia

2014-04-01

Large single crystals of orthorhombic [(CH3)3NCH2COO]2(CuCl2)3 · 2H2 O with dimensions up to 40×40×30 mm3 were grown from aqueous solutions. The elastic and piezoelastic coefficients were derived from ultrasonic resonance frequencies and their shifts upon variation of pressure, respectively, using the plate-resonance technique. Additionally, the coefficients of thermal expansion were determined between 95 K and 305 K by dilatometry. The elastic behaviour at ambient conditions is dominated by the 2-dimensional network of strong hydrogen bonds within the (001) plane leading to a corresponding pseudo-tetragonal anisotropy of the longitudinal elastic stiffness. The variation of elastic properties with pressure, however, as well as the thermal expansion shows strong deviations from the pseudo-tetragonal symmetry. These deviations are probably correlated with tilts of the elongated tri-nuclear betaine-CuCl2-water complexes. Neither the thermal expansion nor the specific heat capacity gives any hint on a phase transition in the investigated temperature range.

A mechanism for tectonic deformation on Venus

NASA Technical Reports Server (NTRS)

Phillips, Roger J.

1986-01-01

In the absence of identifiable physiographic features directly associated with plate tectonics, alternate mechanisms are sought for the intense tectonic deformation observed in radar images of Venus. One possible mechanism is direct coupling into an elastic lithosphere of the stresses associated with convective flow in the interior. Spectral Green's function solutions have been obtained for stresses in an elastic lithosphere overlying a Newtonian interior with an exponential depth dependence of viscosity, and a specified surface-density distribution driving the flow. At long wavelengths and for a rigid elastic/fluid boundary condition, horizontal normal stresses in the elastic lid are controlled by the vertical shear stress gradient and are directly proportional to the depth of the density disturbance in the underlying fluid. The depth and strength of density anomalies in the Venusian interior inferred by analyses of long wavelength gravity data suggest that stresses in excess of 100 MPa would be generated in a 10 km thick elastic lid unless a low viscosity channel occurring beneath the lid or a positive viscosity gradient uncouples the flow stresses. The great apparent depth of compensation of topographic features argues against this, however, thus supporting the importance of the coupling mechanism. If there is no elastic lid, stresses will also be very high near the surface, providing also that the viscosity gradient is negative.

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.

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.

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

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

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).

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.

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.

Identification of material properties of orthotropic composite plate using experimental frequency response function data

NASA Astrophysics Data System (ADS)

Tam, Jun Hui; Ong, Zhi Chao; Ismail, Zubaidah; Ang, Bee Chin; Khoo, Shin Yee

2018-05-01

The demand for composite materials is increasing due to their great superiority in material properties, e.g., lightweight, high strength and high corrosion resistance. As a result, the invention of composite materials of diverse properties is becoming prevalent, and thus, leading to the development of material identification methods for composite materials. Conventional identification methods are destructive, time-consuming and costly. Therefore, an accurate identification approach is proposed to circumvent these drawbacks, involving the use of Frequency Response Function (FRF) error function defined by the correlation discrepancy between experimental and Finite-Element generated FRFs. A square E-glass epoxy composite plate is investigated under several different configurations of boundary conditions. It is notable that the experimental FRFs are used as the correlation reference, such that, during computation, the predicted FRFs are continuously updated with reference to the experimental FRFs until achieving a solution. The final identified elastic properties, namely in-plane elastic moduli, Ex and Ey, in-plane shear modulus, Gxy, and major Poisson's ratio, vxy of the composite plate are subsequently compared to the benchmark parameters as well as with those obtained using modal-based approach. As compared to the modal-based approach, the proposed method is found to have yielded relatively better results. This can be explained by the direct employment of raw data in the proposed method that avoids errors that might incur during the stage of modal extraction.

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.

Deformations of a pre-stretched elastic membrane driven by non-uniform electroosmotic flow

NASA Astrophysics Data System (ADS)

Bercovici, Moran; Boyko, Evgeniy; Gat, Amir

2016-11-01

We study viscous-elastic dynamics of fluid confined between a rigid plate and a pre-stretched elastic membrane subjected to non-uniform electroosmotic flow, and focus on the case of a finite-size membrane clamped at its boundaries. Considering small deformations of a strongly pre-stretched membrane, and applying the lubrication approximation for the flow, we derive a linearized leading-order non-homogenous 4th order diffusion equation governing the deformation and pressure fields. We derive a time-dependent Green's function for a rectangular domain, and use it to obtain several basic solutions for the cases of constant and time varying electric fields. In addition, defining an asymptotic expansion where the small parameter is the ratio of the induced to prescribed tension, we obtain a set of four one-way coupled equations providing a first order correction for the deformation field. Funded by the European Research Council (ERC) under the Horizon 2020 Research and Innovation Programme, Grant agreement No. 678734 (MetamorphChip).

Experimental study and finite element analysis based on equivalent load method for laser ultrasonic measurement of elastic constants.

PubMed

Zhan, Yu; Liu, Changsheng; Zhang, Fengpeng; Qiu, Zhaoguo

2016-07-01

The laser ultrasonic generation of Rayleigh surface wave and longitudinal wave in an elastic plate is studied by experiment and finite element method. In order to eliminate the measurement error and the time delay of the experimental system, the linear fitting method of experimental data is applied. The finite element analysis software ABAQUS is used to simulate the propagation of Rayleigh surface wave and longitudinal wave caused by laser excitation on a sheet metal sample surface. The equivalent load method is proposed and applied. The pulsed laser is equivalent to the surface load in time and space domain to meet the Gaussian profile. The relationship between the physical parameters of the laser and the load is established by the correction factor. The numerical solution is in good agreement with the experimental result. The simple and effective numerical and experimental methods for laser ultrasonic measurement of the elastic constants are demonstrated. Copyright © 2016. Published by Elsevier B.V.

Stress-intensity factor calculations using the boundary force method

NASA Technical Reports Server (NTRS)

Tan, P. W.; Raju, I. S.; Newman, J. C., Jr.

1987-01-01

The Boundary Force Method (BFM) was formulated for the three fundamental problems of elasticity: the stress boundary value problem, the displacement boundary value problem, and the mixed boundary value problem. Because the BFM is a form of an indirect boundary element method, only the boundaries of the region of interest are modeled. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, unlike other boundary element methods, here the crack face need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing a center-cracked specimen subjected to mixed boundary conditions and a three-hole cracked configuration subjected to traction boundary conditions. The results obtained are in good agreement with accepted numerical solutions. The method is then used to generate stress-intensity solutions for two common cracked configurations: an edge crack emanating from a semi-elliptical notch, and an edge crack emanating from a V-notch. The BFM is a versatile technique that can be used to obtain very accurate stress intensity factors for complex crack configurations subjected to stress, displacement, or mixed boundary conditions. The method requires a minimal amount of modeling effort.

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.

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.

Approximate analytical solutions in the analysis of elastic structures of complex geometry

NASA Astrophysics Data System (ADS)

Goloskokov, Dmitriy P.; Matrosov, Alexander V.

2018-05-01

A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

Geophysical Age Dating of Seamounts using Dense Core Flexure Model

NASA Astrophysics Data System (ADS)

Hwang, Gyuha; Kim, Seung-Sep

2016-04-01

Lithospheric flexure of oceanic plate is thermo-mechanical response of an elastic plate to the given volcanic construct (e.g., seamounts and ocean islands). If the shape and mass of such volcanic loads are known, the flexural response is governed by the thickness of elastic plate, Te. As the age of oceanic plate increases, the elastic thickness of oceanic lithosphere becomes thicker. Thus, we can relate Te with the age of plate at the time of loading. To estimate the amount of the driving force due to seamounts on elastic plate, one needs to approximate their density structure. The most common choice is uniform density model, which utilizes constant density value for a seamount. This approach simplifies computational processes for gravity prediction and error estimates. However, the uniform density model tends to overestimate the total mass of the seamount and hence produces more positive gravitational contributions from the load. Minimization of gravity misfits using uniform density, therefore, favors thinner Te in order to increase negative contributions from the lithospheric flexure, which can compensate for the excessive positives from the seamount. An alternative approach is dense core model, which approximate the heterogeneity nature of seamount density as three bodies of infill sediment, edifice, and dense core. In this study, we apply the dense core model to the Louisville Seamount Chain for constraining flexural deformation. We compare Te estimates with the loading time of the examined seamounts to redefine empirical geophysical age dating of seamounts.

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 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.

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.

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...

Stress concentrations for straight-shank and countersunk holes in plates subjected to tension, bending, and pin loading

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Newman, J. C., Jr.

1992-01-01

A three dimensional stress concentration analysis was conducted on straight shank and countersunk (rivet) holes in a large plate subjected to various loading conditions. Three dimensional finite element analysis were performed with 20 node isoparametric elements. The plate material was assumed to be linear elastic and isotropic, with a Poisson ratio of 0.3. Stress concentration along the bore of the hole were computed for several ratios of hole radius to plate thickness (0.1 to 2.5) and ratios of countersink depth to plate thickness (0.25 to 1). The countersink angles were varied from 80 to 100 degrees in some typical cases, but the angle was held constant at 100 degrees for most cases. For straight shank holes, three types of loading were considered: remote tension, remote bending, and wedge loading in the hole. Results for remote tension and wedge loading were used to estimate stress concentration for simulated rivet in pin loading. For countersunk holes only remote tension and bending were considered. Based on the finite element results, stress concentration equations were developed. Whenever possible, the present results were compared with other numerical solutions and experimental results from the literature.

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.

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.

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.

Finite Element Analysis of a Dynamically Loaded Flat Laminated Plate

DTIC Science & Technology

1980-07-01

and the elements are stacked in the thickness direction to represent various material layers. This analysis allows for orthotropic, elastic- plastic or...INCREMENTS 27 V. PLASTICITY 34 Orthotropic Elastic- Plastic Yielding 34 Orthotropic Elastic-Viscoplastic Yielding 37 VI. ELEMENT EQUILIBRIUM...with time, consequently the materials are assumed to be represented by elastic- plastic and elastic-viscoplastic models. The finite element model

Elastic interactions of a fatigue crack with a micro-defect by the mixed boundary integral equation method

NASA Technical Reports Server (NTRS)

Lua, Yuan J.; Liu, Wing K.; Belytschko, Ted

1993-01-01

In this paper, the mixed boundary integral equation method is developed to study the elastic interactions of a fatigue crack and a micro-defect such as a void, a rigid inclusion or a transformation inclusion. The method of pseudo-tractions is employed to study the effect of a transformation inclusion. An enriched element which incorporates the mixed-mode stress intensity factors is applied to characterize the singularity at a moving crack tip. In order to evaluate the accuracy of the numerical procedure, the analysis of a crack emanating from a circular hole in a finite plate is performed and the results are compared with the available numerical solution. The effects of various micro-defects on the crack path and fatigue life are investigated. The results agree with the experimental observations.

Deformations of a pre-stretched and lubricated finite elastic membrane driven by non-uniform external forcing

NASA Astrophysics Data System (ADS)

Boyko, Evgeniy; Gat, Amir; Bercovici, Moran

2017-11-01

We study viscous-elastic dynamics of a fluid confined between a rigid plate and a finite pre-stretched circular elastic membrane, pinned at its boundaries. The membrane is subjected to forces acting either directly on the membrane or through a pressure distribution in the fluid. Under the assumptions of strong pre-stretching and small deformations of the elastic sheet, and by applying the lubrication approximation for the flow, we derive the Green's function for the resulting linearized 4th order diffusion equation governing the deformation field in cylindrical coordinates. In addition, defining an asymptotic expansion with the ratio of the induced to prescribed tension serving as the small parameter, we reduce the coupled Reynolds and non-linear von-Karman equations to a set of three one-way coupled linear equations. The solutions to these equations provide insight onto the effects of induced tension, and enable simplified prediction of the correction for the deformation field. Funded by the European Research Council (ERC) under the European Union'sHorizon 2020 Research and Innovation Programme, Grant Agreement No. 678734 (MetamorphChip). E.B. is supported by the Adams Fellowship Program.

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.

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

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.

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.

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

A closed form large deformation solution of plate bending with surface effects.

PubMed

Liu, Tianshu; Jagota, Anand; Hui, Chung-Yuen

2017-01-04

We study the effect of surface stress on the pure bending of a finite thickness plate under large deformation. The surface is assumed to be isotropic and its stress consists of a part that can be interpreted as a residual stress and a part that stiffens as the surface increases its area. Our results show that residual surface stress and surface stiffness can both increase the overall bending stiffness but through different mechanisms. For sufficiently large residual surface tension, we discover a new type of instability - the bending moment reaches a maximum at a critical curvature. Effects of surface stress on different stress components in the bulk of the plate are discussed and the possibility of self-bending due to asymmetry of the surface properties is also explored. The results of our calculations provide insights into surface stress effects in the large deformation regime and can be used as a test for implementation of finite element methods for surface elasticity.

A simple and efficient shear-flexible plate bending element

NASA Technical Reports Server (NTRS)

Chaudhuri, Reaz A.

1987-01-01

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

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.

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.

Thermo-Elastic Analysis of Internally Cooled Structures Using a Higher Order Theory

NASA Technical Reports Server (NTRS)

Arnold, Steven M.; Bednarcyk, Brett A.; Aboudi, Jacob

2001-01-01

This paper presents the results of a study on the thermomechanical behavior of internally cooled silicon nitride structures. Silicon nitride is under consideration for elevated temperature aerospace engine applications. and techniques for lowering the operating temperature of structures composed of this material are under development. Lowering the operating temperature provides a large payoff in terms of fatigue life and may be accomplished through the use of thermal barrier coatings (TBC's) and the novel concept of included cooling channels. Herein, an in-depth study is performed on the behavior of a flame-impinged silicon nitride plate with a TBC and internal channels cooled by forced air. The analysis is performed using the higher order theory for functionally graded materials (HOTFGM), which has been developed through NASA Glenn Research Center funding over the past several years. HOTFGM was chosen over the traditional finite element approach as a prelude to an examination of functionally graded silicon nitride structures for which HOTFGM is ideally suited. To accommodate the analysis requirement% of the internally cooled plate problem, two crucial enhancements were made to the two-dimensional Cartesian-based version of HOTFGM. namely, incorporation of internal boundary capabilities and incorporation of convective boundary conditions. Results indicate the viability and large benefits of cooling the plate via forced air through cooling channels. Furthermore, cooling can positively impact the stress and displacement fields present in the plate, yielding an additional payoff in terms of fatigue life. Finally, a spin-off capability resulted from inclusion of internal boundaries within HOTFGM; the ability to simulate the thermo-elastic response of structures with curved surfaces. This new capability is demonstrated, and through comparison with an analytical solution, shown to be viable and accurate.

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.

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

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.

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.

Gravity-Assist Mechanical Simulator for Outreach

NASA Technical Reports Server (NTRS)

Doody, David F.; White, Victor E.; Schaff, Mitch D.

2012-01-01

There is no convenient way to demonstrate mechanically, as an outreach (or inreach) topic, the angular momentum trade-offs and the conservation of angular momentum associated with gravityassist interplanetary trajectories. The mechanical concepts that underlie gravity assist are often misunderstood or confused, possibly because there is no mechanical analog to it in everyday experience. The Gravity Assist Mech - anical Simulator is a hands-on solution to this longstanding technical communications challenge. Users intuitively grasp the concepts, meeting specific educational objectives. A manually spun wheel with high angular mass and low-friction bearings supplies momentum to an attached spherical neodymium magnet that represents a planet orbiting the Sun. A steel bearing ball following a trajectory across a glass plate above the wheel and magnet undergoes an elastic collision with the revolving magnet, illustrating the gravitational elastic collision between spacecraft and planet on a gravity-assist interplanetary trajectory. Manually supplying the angular momentum for the elastic collision, rather than observing an animation, intuitively conveys the concepts, meeting nine specific educational objectives. Many NASA and JPL interplanetary missions are enabled by the gravity-assist technique.

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.

Nonlinear problems of the theory of heterogeneous slightly curved shells

NASA Technical Reports Server (NTRS)

Kantor, B. Y.

1973-01-01

An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

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

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.

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.

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.

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.

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.

Flexural edge waves generated by steady-state propagation of a loaded rectilinear crack in an elastically supported thin plate

NASA Astrophysics Data System (ADS)

Nobili, Andrea; Radi, Enrico; Lanzoni, Luca

2017-08-01

The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The full-field solution is obtained and the spotlight is set on flexural edge wave generation. Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist. These waves are characterized by a novel dispersion relation and fade off from the crack line in an oscillatory manner, whence they play an important role in the far field behaviour. Dynamic stress intensity factors are obtained and, for speed close to the critical speed, they show a resonant behaviour which expresses the most efficient way to channel external work into the crack. Indeed, this behaviour is justified through energy considerations regarding the work of the applied load and the energy release rate. Results might be useful in a wide array of applications, ranging from fracturing and machining to acoustic emission and defect detection.

Flexural edge waves generated by steady-state propagation of a loaded rectilinear crack in an elastically supported thin plate.

PubMed

Nobili, Andrea; Radi, Enrico; Lanzoni, Luca

2017-08-01

The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The full-field solution is obtained and the spotlight is set on flexural edge wave generation. Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist. These waves are characterized by a novel dispersion relation and fade off from the crack line in an oscillatory manner, whence they play an important role in the far field behaviour. Dynamic stress intensity factors are obtained and, for speed close to the critical speed, they show a resonant behaviour which expresses the most efficient way to channel external work into the crack. Indeed, this behaviour is justified through energy considerations regarding the work of the applied load and the energy release rate. Results might be useful in a wide array of applications, ranging from fracturing and machining to acoustic emission and defect detection.

Viscoelastic deformation near active plate boundaries

NASA Technical Reports Server (NTRS)

Ward, S. N.

1986-01-01

Model deformations near the active plate boundaries of Western North America using space-based geodetic measurements as constraints are discussed. The first six months of this project were spent gaining familarity with space-based measurements, accessing the Crustal Dynamics Data Information Computer, and building time independent deformation models. The initial goal was to see how well the simplest elastic models can reproduce very long base interferometry (VLBI) baseline data. From the Crustal Dynamics Data Information Service, a total of 18 VLBI baselines are available which have been surveyed on four or more occasions. These data were fed into weighted and unweighted inversions to obtain baseline closure rates. Four of the better quality lines are illustrated. The deformation model assumes that the observed baseline rates result from a combination of rigid plate tectonic motions plus a component resulting from elastic strain build up due to a failure of the plate boundary to slip at the full plate tectonic rate. The elastic deformation resulting from the locked plate boundary is meant to portray interseismic strain accumulation. During and shortly after a large interplate earthquake, these strains are largely released, and points near the fault which were previously retarded suddenly catch up to the positions predicted by rigid plate models. Researchers judge the quality of fit by the sum squares of weighted residuals, termed total variance. The observed baseline closures have a total variance of 99 (cm/y)squared. When the RM2 velocities are assumed to model the data, the total variance increases to 154 (cm/y)squared.

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.

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)

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.

Asymptotic derivation of nonlocal plate models from three-dimensional stress gradient elasticity

NASA Astrophysics Data System (ADS)

Hache, F.; Challamel, N.; Elishakoff, I.

2018-01-01

This paper deals with the asymptotic derivation of thin and thick nonlocal plate models at different orders from three-dimensional stress gradient elasticity, through the power series expansions of the displacements in the thickness ratio of the plate. Three nonlocal asymptotic approaches are considered: a partial nonlocality following the thickness of the plate, a partial nonlocality following the two directions of the plates and a full nonlocality (following all the directions). The three asymptotic approaches lead at the zeroth order to a nonlocal Kirchhoff-Love plate model, but differ in the expression of the length scale. The nonlocal asymptotic models coincide at this order with the stress gradient Kirchhoff-Love plate model, only when the nonlocality is following the two directions of the plate and expressed through a nabla operator. This asymptotic model also yields the nonlocal truncated Uflyand-Mindlin plate model at the second order. However, the two other asymptotic models lead to equations that differ from the current existing nonlocal engineering models (stress gradient engineering plate models). The natural frequencies for an all-edges simply supported plate are obtained for each model. It shows that the models provide similar results for low orders of frequencies or small thickness ratio or nonlocal lengths. Moreover, only the asymptotic model with a partial nonlocality following the two directions of the plates is consistent with a stress gradient plate model, whatever the geometry of the plate.

An asymptotic Reissner-Mindlin plate model

NASA Astrophysics Data System (ADS)

Licht, Christian; Weller, Thibaut

2018-06-01

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner-Mindlin plate model.

Reconstruction of structural damage based on reflection intensity spectra of fiber Bragg gratings

NASA Astrophysics Data System (ADS)

Huang, Guojun; Wei, Changben; Chen, Shiyuan; Yang, Guowei

2014-12-01

We present an approach for structural damage reconstruction based on the reflection intensity spectra of fiber Bragg gratings (FBGs). Our approach incorporates the finite element method, transfer matrix (T-matrix), and genetic algorithm to solve the inverse photo-elastic problem of damage reconstruction, i.e. to identify the location, size, and shape of a defect. By introducing a parameterized characterization of the damage information, the inverse photo-elastic problem is reduced to an optimization problem, and a relevant computational scheme was developed. The scheme iteratively searches for the solution to the corresponding direct photo-elastic problem until the simulated and measured (or target) reflection intensity spectra of the FBGs near the defect coincide within a prescribed error. Proof-of-concept validations of our approach were performed numerically and experimentally using both holed and cracked plate samples as typical cases of plane-stress problems. The damage identifiability was simulated by changing the deployment of the FBG sensors, including the total number of sensors and their distance to the defect. Both the numerical and experimental results demonstrate that our approach is effective and promising. It provides us with a photo-elastic method for developing a remote, automatic damage-imaging technique that substantially improves damage identification for structural health monitoring.

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.

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.

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.

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.

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 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.

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.

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.

Subcritical crack growth of selected aerospace pressure vessel materials

NASA Technical Reports Server (NTRS)

Hall, L. R.; Bixler, W. D.

1972-01-01

This experimental program was undertaken to determine the effects of combined cyclic/sustained loads, stress level, and crack shape on the fatigue crack growth rate behavior of cracks subjected to plane strain conditions. Material/environment combinations tested included: 2219-T87 aluminum plate in gaseous helium, room air, and 3.5% NaCl solution at room temperature, liquid nitrogen, and liquid hydrogen; 5Al-2.5 Sn (ELI) titanium plate in liquid nitrogen and liquid hydrogen and 6AL-4V (ELI) STA titanium plate in gaseous helium and methanol at room temperature. Most testing was accomplished using surface flawed specimens instrumented with a clip gage to continuously monitor crack opening displacements at the specimen surface. Tapered double cantilever beam specimens were also tested. Static fracture and ten hour sustained load tests were conducted to determine fracture toughness and apparent threshold stress intensity values. Cyclic tests were performed using sinusoidal loading profiles at 333 MHz (20 cpm) and trapezoidal loading profiles at both 8.3 MHz (0.5 cpm) and 3.3 MHz (0.2 cpm). Data were evaluated using modified linear elastic fracture mechanics parameters.

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.

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.

A weak-coupling immersed boundary method for fluid-structure interaction with low density ratio of solid to fluid

NASA Astrophysics Data System (ADS)

Kim, Woojin; Lee, Injae; Choi, Haecheon

2018-04-01

We present a weak-coupling approach for fluid-structure interaction with low density ratio (ρ) of solid to fluid. For accurate and stable solutions, we introduce predictors, an explicit two-step method and the implicit Euler method, to obtain provisional velocity and position of fluid-structure interface at each time step, respectively. The incompressible Navier-Stokes equations, together with these provisional velocity and position at the fluid-structure interface, are solved in an Eulerian coordinate using an immersed-boundary finite-volume method on a staggered mesh. The dynamic equation of an elastic solid-body motion, together with the hydrodynamic force at the provisional position of the interface, is solved in a Lagrangian coordinate using a finite element method. Each governing equation for fluid and structure is implicitly solved using second-order time integrators. The overall second-order temporal accuracy is preserved even with the use of lower-order predictors. A linear stability analysis is also conducted for an ideal case to find the optimal explicit two-step method that provides stable solutions down to the lowest density ratio. With the present weak coupling, three different fluid-structure interaction problems were simulated: flows around an elastically mounted rigid circular cylinder, an elastic beam attached to the base of a stationary circular cylinder, and a flexible plate, respectively. The lowest density ratios providing stable solutions are searched for the first two problems and they are much lower than 1 (ρmin = 0.21 and 0.31, respectively). The simulation results agree well with those from strong coupling suggested here and also from previous numerical and experimental studies, indicating the efficiency and accuracy of the present weak coupling.

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

A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S.; Klang, Eric C.

2001-01-01

The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.

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.

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.

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.

Buckling of a circular plate made of a shape memory alloy due to a reverse thermoelastic martensite transformation

NASA Astrophysics Data System (ADS)

Movchan, A. A.; Sil'chenko, L. G.

2008-02-01

We solve the axisymmetric buckling problem for a circular plate made of a shape memory alloy undergoing reverse martensite transformation under the action of a compressing load, which occurs after the direct martensite transformation under the action of a generally different (extending or compressing) load. The problem was solved without any simplifying assumptions concerning the transverse dimension of the supplementary phase transition region related to buckling. The mathematical problem was reduced to a nonlinear eigenvalue problem. An algorithm for solving this problem was proposed. It was shown that the critical buckling load under the reverse transition, which is obtained by taking into account the evolution of the phase strains, can be many times lower than the same quantity obtained under the assumption that the material behavior is elastic even for the least (martensite) values of the elastic moduli. The critical buckling force decreases with increasing modulus of the load applied at the preliminary stage of direct transition and weakly depends on whether this load was extending or compressing. In shape memory alloys (SMA), mutually related processes of strain and direct (from the austenitic into the martensite phase) or reverse thermoelastic phase transitions may occur. The direct transition occurs under cooling and (or) an increase in stresses and is accompanied by a significant decrease (nearly by a factor of three in titan nickelide) of the Young modulus. If the direct transition occurs under the action of stresses with nonzero deviator, then it is accompanied by accumulation of macroscopic phase strains, whose intensity may reach 8%. Under the reverse transition, which occurs under heating and (or) unloading, the moduli increase and the accumulated strain is removed. For plates compressed in their plane, in the case of uniform temperature distribution over the thickness, one can separate trivial processes under which the strained plate remains plane and the phase ratio has a uniform distribution over the thickness. For sufficiently high compressing loads, the trivial process of uniform compression may become unstable in the sense that, for small perturbations of the plate deflection, temperature, the phase ratio, or the load, the difference between the corresponding perturbed process and the unperturbed process may be significant. The results of several experiments concerning the buckling of SMA elements are given in [1, 2], and the statement and solution of the corresponding boundary value problems can be found in [3-11]. The experimental studies [2] and several analytic solutions obtained for the Shanley column [3, 4], rods [5-7], rectangular plates under direct [8] and reverse [9] transitions showed that the processes of thermoelastic phase transitions can significantly (by several times) decrease the critical buckling loads compared with their elastic values calculated for the less rigid martensite state of the material. Moreover, buckling does not occur in the one-phase martensite state in which the elastic moduli are minimal but in the two-phase state in which the values of the volume fractions of the austenitic and martensite phase are approximately equal to each other. This fact is most astonishing for buckling, studied in the present paper, under the reverse transition in which the Young modulus increases approximately half as much from the beginning of the phase transition to the moment of buckling. In [3-9] and in the present paper, the static buckling criterion is used. Following this criterion, the critical load is defined to be the load such that a nontrivial solution of the corresponding quasistatic problem is possible under the action of this load. If, in the problems of stability of rods and SMA plates, small perturbations of the external load are added to small perturbations of the deflection (the critical force is independent of the amplitude of the latter), then the critical forces vary depending on the value of perturbations of the external load [5, 8, 9]. Thus, in the case of small perturbations of the load, the problem of stability of SMA elements becomes indeterminate. The solution of the stability problem for SMA elements also depends on whether the small perturbations of the phase ratio and the phase strain tensor are taken into account. According to this, the problem of stability of SMA elements can be solved in the framework of several statements (concepts, hypotheses) which differ in the set of quantities whose perturbations are admissible (taken into account) in the process of solving the problem. The variety of these statements applied to the problem of buckling of SMA elements under direct martensite transformation is briefly described in [4, 5]. But, in the problem of buckling under the reverse transformation, some of these statements must be changed. The main question which we should answer when solving the problem of stability of SMA elements is whether small perturbations of the phase ratio (the volume fraction of the martensite phase q) are taken into account, because an appropriate choice significantly varies the results of solving the stability problem. If, under the transition to the adjacent form of equilibrium, the phase ratio of all points of the body is assumed to remain the same, then we deal with the "fixed phase atio" concept. The opposite approach can be classified as the "supplementary phase transition" concept (which occurs under the transition to the adjacent form of equilibrium). It should be noted that, since SMA have temperature hysteresis, the phase ratio in SMA can endure only one-sided small variations. But if we deal with buckling under the inverse transformation, then the variation in the volume fraction of the martensite phase cannot be positive. The phase ratio is not an independent variable, like loads or temperature, but, due to the constitutive relations, its variations occur together with the temperature variations and, in the framework of connected models for a majority of SMA, together with variations in the actual stresses. Therefore, the presence or absence of variations in q is determined by the presence or absence of variations in the temperature, deflection, and load, as well as by the system of constitutive relations used in this particular problem. In the framework of unconnected models which do not take the influence of actual stresses on the phase ratio into account, the "fixed phase ratio" concept corresponds to the case of absence of temperature variations. The variations in the phase ratio may also be absent in connected models in the case of specially chosen values of variations in the temperature and (or) in the external load, as well as in the case of SMA of CuMn type, for which the influence of the actual stresses on the phase compound is absent or negligible. In the framework of the "fixed phase ratio" hypothesis, the stability problem for SMA elements has a solution coinciding in form with the solution of the corresponding elastic problem, with the elastic moduli replaced by the corresponding functions of the phase ratio. In the framework of the supplementary phase transition" concept, the result of solving the stability problem essentially depends on whether the small perturbations of the external loads are taken into account in the process of solving the problem. The point is that, when solving the problem in the connected setting, the supplementary phase transition region occupies, in general, not the entire cross-section of the plate but only part of it, and the location of the boundary of this region depends on the existence and the value of these small perturbations. More precisely, the existence of arbitrarily small perturbations of the actual load can result in finite changes of the configuration of the supplementary phase transition region and hence in finite change of the critical values of the load. Here we must distinguish the "fixed load" hypothesis where no perturbations of the external loads are admitted and the "variable load" hypothesis in the opposite case. The conditions that there no variations in the external loads imply additional equations for determining the boundary of the supplementary phase transition region. If the "supplementary phase transition" concept and the "fixed load" concept are used together, then the solution of the stability problem of SMA is uniquely determined in the same sense as the solution of the elastic stability problem under the static approach. In the framework of the "variable load" concept, the result of solving the stability problem for SMA ceases to be unique. But one can find the upper and lower bounds for the critical forces which correspond to the cases of total absence of the supplementary phase transition: the upper bound corresponds to the critical load coinciding with that determined in the framework of the "fixed phase ratio" concept, and the lower bound corresponds to the case where the entire cross-section of the plate experiences the supplementary phase transition. The first version does not need any additional name, and the second version can be called as the "all-round supplementary phase transition" hypothesis. In the present paper, the above concepts are illustrated by examples of solving problems about axisymmetric buckling of a circular freely supported or rigidly fixed plate experiencing reverse martensite transformation under the action of an external force uniformly distributed over the contour. We find analytic solutions in the framework of all the above-listed statements except for the case of free support in the "fixed load" concept, for which we obtain a numerical solution.

Ab initio calculations of the lattice parameter and elastic stiffness coefficients of bcc Fe with solutes

DOE PAGES

Fellinger, Michael R.; Hector, Louis G.; Trinkle, Dallas R.

2016-10-28

Here, we present an efficient methodology for computing solute-induced changes in lattice parameters and elastic stiffness coefficients Cij of single crystals using density functional theory. We also introduce a solute strain misfit tensor that quantifies how solutes change lattice parameters due to the stress they induce in the host crystal. Solutes modify the elastic stiffness coefficients through volumetric changes and by altering chemical bonds. We compute each of these contributions to the elastic stiffness coefficients separately, and verify that their sum agrees with changes in the elastic stiffness coefficients computed directly using fully optimized supercells containing solutes. Computing the twomore » elastic stiffness contributions separately is more computationally efficient and provides more information on solute effects than the direct calculations. We compute the solute dependence of polycrystalline averaged shear and Young's moduli from the solute dependence of the single-crystal Cij. We then apply this methodology to substitutional Al, B, Cu, Mn, Si solutes and octahedral interstitial C and N solutes in bcc Fe. Comparison with experimental data indicates that our approach accurately predicts solute-induced changes in the lattice parameter and elastic coefficients. The computed data can be used to quantify solute-induced changes in mechanical properties such as strength and ductility, and can be incorporated into mesoscale models to improve their predictive capabilities.« less

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

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.

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.

Elasto-plastic deformation and plate weakening due to normal faulting in the subducting plate along the Mariana Trench

NASA Astrophysics Data System (ADS)

Zhou, Zhiyuan; Lin, Jian

2018-06-01

We investigated variations in the elasto-plastic deformation of the subducting plate along the Mariana Trench through an analysis of flexural bending and normal fault characteristics together with geodynamic modeling. Most normal faults were initiated at the outer-rise region and grew toward the trench axis with strikes mostly subparallel to the local trench axis. The average trench relief and maximum fault throws were measured to be significantly greater in the southern region (5 km and 320 m, respectively) than the northern and central regions (2 km and 200 m). The subducting plate was modeled as an elasto-plastic slab subjected to tectonic loading at the trench axis. The calculated strain rates and velocities revealed an array of normal fault-like shear zones in the upper plate, resulting in significant faulting-induced reduction in the deviatoric stresses. We then inverted for solutions that best fit the observed flexural bending and normal faulting characteristics, revealing normal fault penetration to depths of 21, 20, and 32 km beneath the seafloor for the northern, central, and southern regions, respectively, which is consistent with the observed depths of the relocated normal faulting earthquakes in the central Mariana Trench. The calculated deeper normal faults of the southern region might lead to about twice as much water being carried into the mantle per unit trench length than the northern and central regions. We further calculated that normal faulting has reduced the effective elastic plate thickness Te by up to 52% locally in the southern region and 33% in both the northern and central regions. The best-fitting solutions revealed a greater apparent angle of the pulling force in the southern region (51-64°) than in the northern (22-35°) and central (20-34°) regions, which correlates with a general southward increase in the seismically-determined dip angle of the subducting slab along the Mariana Trench.

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.

Processing and evaluation of long fiber thermoplastic composite plates for internal fixation

NASA Astrophysics Data System (ADS)

Warren, Paul B.

The metallic plates used in internal fracture fixation may have up to ten times the elastic modulus of normal bone tissue, causing stress shielding-induced osteopenia in healed bone that can lead to re-fracture after plate removal and prolonged and painful recovery. Thermoplastic polymer matrix composites reinforced with long carbon fiber are promising alternative materials for internal fixation plates because they may be produced with relative ease and be tailored to have specific mechanical properties, alleviating the stress shielding problem. Long carbon fiber-reinforced polyetheretherketone (LCF PEEK) plates were produced using the extrusion / compression molding process. Static flexural testing determined that LCF PEEK plates with rectangular cross-section had an average flexural modulus of 12 GPa, or 23% of the flexural modulus of a stainless steel plate. The LCF PEEK plates also experienced negligible (14.7%, 14.5%, and 16.7%) reductions in modulus after fatigue testing at applied moments of 2.5, 3.0, and 3.5 N•m, respectively, over 106 load cycles. Aging the plates in 0.9% NaCl solution for four and eight weeks caused 0.34% and 0.28% increases in plate mass, respectively. No significant decrease of flexural properties due to aging was detected. Differential scanning calorimetry (DSC) revealed the PEEK matrix of the plates to be 24.5% crystalline, which is lower than typical PEEK crystallinity values of 30-35%. Scanning electron microscopy (SEM) revealed three times as many fiber pullout areas in LCF PEEK fracture surfaces as in fracture surfaces of long carbon fiber-reinforced polyphenylenesulfide (LCF PPS), another plate material tested. DSC and SEM data suggest that improvements in processing conditions and fiber/matrix bonding, along with higher carbon fiber fractions, would enhance LCF PEEK plate performance. LCF PEEK remains a promising alternative to stainless steel for internal fixation plates.

DYCAST: A finite element program for the crash analysis of structures

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Winter, R.; Ogilvie, P.

1987-01-01

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

Phononic Crystal Waveguide Transducers for Nonlinear Elastic Wave Sensing.

PubMed

Ciampa, Francesco; Mankar, Akash; Marini, Andrea

2017-11-07

Second harmonic generation is one of the most sensitive and reliable nonlinear elastic signatures for micro-damage assessment. However, its detection requires powerful amplification systems generating fictitious harmonics that are difficult to discern from pure nonlinear elastic effects. Current state-of-the-art nonlinear ultrasonic methods still involve impractical solutions such as cumbersome signal calibration processes and substantial modifications of the test component in order to create material-based tunable harmonic filters. Here we propose and demonstrate a valid and sensible alternative strategy involving the development of an ultrasonic phononic crystal waveguide transducer that exhibits both single and multiple frequency stop-bands filtering out fictitious second harmonic frequencies. Remarkably, such a sensing device can be easily fabricated and integrated on the surface of the test structure without altering its mechanical and geometrical properties. The design of the phononic crystal structure is supported by a perturbative theoretical model predicting the frequency band-gaps of periodic plates with sinusoidal corrugation. We find our theoretical findings in excellent agreement with experimental testing revealing that the proposed phononic crystal waveguide transducer successfully attenuates second harmonics caused by the ultrasonic equipment, thus demonstrating its wide range of potential applications for acousto/ultrasonic material damage inspection.

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).

Elastic Properties and Internal Friction of Two Magnesium Alloys at Elevated Temperatures

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

Freels, M.; Liaw, P. K.; Garlea, E.

2011-06-01

The elastic properties and internal friction of two magnesium alloys were studied from 25 C to 450 C using Resonant Ultrasound Spectroscopy (RUS). The Young's moduli decrease with increasing temperature. At 200 C, a change in the temperature dependence of the elastic constants is observed. The internal friction increases significantly with increasing temperature above 200 C. The observed changes in the temperature dependence of the elastic constants and the internal friction are the result of anelastic relaxation by grain boundary sliding at elevated temperatures. Elastic properties govern the behavior of a materials subjected to stress over a region of strainmore » where the material behaves elastically. The elastic properties, including the Young's modulus (E), shear modulus (G), bulk modulus (B), and Poisson's ratio (?), are of significant interest to many design and engineering applications. The choice of the most appropriate material for a particular application at elevated temperatures therefore requires knowledge of its elastic properties as a function of temperature. In addition, mechanical vibration can cause significant damage in the automotive, aerospace, and architectural industries and thus, the ability of a material to dissipate elastic strain energy in materials, known as damping or internal friction, is also important property. Internal friction can be the result of a wide range of physical mechanisms, and depends on the material, temperature, and frequency of the loading. When utilized effectively in engineering applications, the damping capacity of a material can remove undesirable noise and vibration as heat to the surroundings. The elastic properties of materials can be determined by static or dynamic methods. Resonant Ultrasound Spectroscopy (RUS), used in this study, is a unique and sophisticated non-destructive dynamic technique for determining the complete elastic tensor of a solid by measuring the resonant spectrum of mechanical resonance for a sample of known geometry, dimensions, and mass. In addition, RUS allows determination of internal friction, or damping, at different frequencies and temperatures. Polycrystalline pure magnesium (Mg) exhibits excellent high damping properties. However, the poor mechanical properties limit the applications of pure Mg. Although alloying can improve the mechanical properties of Mg, the damping properties are reduced with additions of alloying elements. Therefore, it becomes necessary to study and develop Mg-alloys with simultaneous high damping capacity and improved mechanical properties. Moreover, studies involving the high temperature dynamic elastic properties of Mg alloys are limited. In this study, the elastic properties and internal friction of two magnesium alloys were studied at elevated temperatures using RUS. The effect of alloy composition and grain size was investigated. The wrought magnesium alloys AZ31 and ZK60 were employed. Table 1 gives the nominal chemical compositions of these two alloys. The ZK60 alloy is a commercial extruded plate with a T5 temper, i.e. solution-treated at 535 C for two hours, quenched in hot water, and aged at 185 C for 24 hours. The AZ31 alloy is a commercial rolled plate with a H24 temper, i.e. strain hardened and partially annealed.« less

Nonlinear behavior of shells of revolution under cyclic loading

NASA Technical Reports Server (NTRS)

Levine, H. S.; Armen, H., Jr.; Winter, R.; Pifko, A.

1972-01-01

A large deflection elastic-plastic analysis is presented, applicable to orthotropic axisymmetric plates and shells of revolution subjected to monotonic and cyclic loading conditions. The analysis is based on the finite-element method. It employs a new higher order, fully compatible, doubly curved orthotropic shell-of-revolution element using cubic Hermitian expansions for both meridional and normal displacements. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening theory, which predicts an ideal Bauschinger effect. Numerous sample problems involving monotonic and cyclic loading conditions are analyzed. The monotonic results are compared with other theoretical solutions.

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.

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.

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.

Nano and micro mechanical properties of uncross-linked and cross-linked chitosan films

PubMed Central

Aryaei, Ashkan; Jayatissa, Ahalapitiya H.; Jayasuriya, A. Champa

2016-01-01

The aim of this study is to determine the nano and micro mechanical properties for uncross-linked and cross-linked chitosan films. Specifically, we looked at nanoindentation hardness, microhardness, and elastic modulus. It is important to study the nano and microscale mechanical properties of chitosan since chitosan has been widely used for biomedical applications. Using the solvent-cast method, the chitosan films were prepared at room temperature on the cleaned glass plates. The chitosan solution was prepared by dissolving chitosan in acetic acid 1% (v/v). Tripolyphosphate (TPP) was used to create the cross-links between amine groups in chitosan and phosphate groups in TPP. In this study, atomic force microscopy was used to measure the nanoindentation hardness and surface topography of the uncross-linked and cross-linked chitosan films. Elastic modulus was then calculated from the nanoindentation results. The effective elastic modulus was determined by microhardness with some modifications to previous theories. The microhardness of the chitosan films were measured using Vicker’s hardness meter under three different loads. Our results show that the microhardness and elastic modulus for cross-linked chitosan films are higher than the uncross-linked films. However, the cross-linked chitosan films show increased brittleness when compared to uncross-linked films. By increasing the load magnitude, the microhardness increases for both uncross-linked and cross-linked chitosan films. PMID:22100082

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.

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.

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

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

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.

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.

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.

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.

Numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity

NASA Astrophysics Data System (ADS)

Korepanov, V. V.; Matveenko, V. P.; Fedorov, A. Yu.; Shardakov, I. N.

2013-07-01

An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions. Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity.

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.

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.

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.

Determining linear vibration frequencies of a ferromagnetic shell

NASA Astrophysics Data System (ADS)

Bagdoev, A. G.; Vardanyan, A. V.; Vardanyan, S. V.; Kukudzhanov, V. N.

2007-10-01

The problems of determining the roots of dispersion equations for free bending vibrations of thin magnetoelastic plates and shells are of both theoretical and practical interest, in particular, in studying vibrations of metallic structures used in controlled thermonuclear reactors. These problems were solved on the basis of the Kirchhoff hypothesis in [1-5]. In [6], an exact spatial approach to determining the vibration frequencies of thin plates was suggested, and it was shown that it completely agrees with the solution obtained according to the Kirchhoff hypothesis. In [7-9], this exact approach was used to solve the problem on vibrations of thin magnetoelastic plates, and it was shown by cumbersome calculations that the solutions obtained according to the exact theory and the Kirchhoff hypothesis differ substantially except in a single case. In [10], the equations of the dynamic theory of elasticity in the axisymmetric problem are given. In [11], the equations for the vibration frequencies of thin ferromagnetic plates with arbitrary conductivity were obtained in the exact statement. In [12], the Kirchhoff hypothesis was used to obtain dispersion relations for a magnetoelastic thin shell. In [5, 13-16], the relations for the Maxwell tensor and the ponderomotive force for magnetics were presented. In [17], the dispersion relations for thin ferromagnetic plates in the transverse field in the spatial statement were studied analytically and numerically. In the present paper, on the basis of the exact approach, we study free bending vibrations of a thin ferromagnetic cylindrical shell. We obtain the exact dispersion equation in the form of a sixth-order determinant, which can be solved numerically in the case of a magnetoelastic thin shell. The numerical results are presented in tables and compared with the results obtained by the Kirchhoff hypothesis. We show a large number of differences in the results, even for the least frequency.

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.

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.

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.

Static bending deflection and free vibration analysis of moderate thick symmetric laminated plates using multidimensional wave digital filters

NASA Astrophysics Data System (ADS)

Tseng, Chien-Hsun

2018-06-01

This paper aims to develop a multidimensional wave digital filtering network for predicting static and dynamic behaviors of composite laminate based on the FSDT. The resultant network is, thus, an integrated platform that can perform not only the free vibration but also the bending deflection of moderate thick symmetric laminated plates with low plate side-to-thickness ratios (< = 20). Safeguarded by the Courant-Friedrichs-Levy stability condition with the least restriction in terms of optimization technique, the present method offers numerically high accuracy, stability and efficiency to proceed a wide range of modulus ratios for the FSDT laminated plates. Instead of using a constant shear correction factor (SCF) with a limited numerical accuracy for the bending deflection, an optimum SCF is particularly sought by looking for a minimum ratio of change in the transverse shear energy. This way, it can predict as good results in terms of accuracy for certain cases of bending deflection. Extensive simulation results carried out for the prediction of maximum bending deflection have demonstratively proven that the present method outperforms those based on the higher-order shear deformation and layerwise plate theories. To the best of our knowledge, this is the first work that shows an optimal selection of SCF can significantly increase the accuracy of FSDT-based laminates especially compared to the higher order theory disclaiming any correction. The highest accuracy of overall solution is compared to the 3D elasticity equilibrium one.

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.

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...

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.

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.

Effect of quenching medium on the microstructure of hot rolled Ti-6Al-6Nb alloy for medical application

NASA Astrophysics Data System (ADS)

Sutowo, Cahya; Alhamidi, A. Ali; Basir, Muh. Idrus Abdul; Rokhmanto, Fendy

2018-05-01

The Ti-6Al-6Nb alloy has been used as bone plate in biomedical application. But, its modulus elasticity still lies above its cortical-bone, which causes stress shielding. An alternative process for reduce modulus of elasticity by means of treatment solutions with heating β-transus temperature follows with rapid cooling for obtaining high % intensity of β-phase fractions. In this study the Ti-6Al-6Nb as-cast alloys were homogenized at 1050 °C for 12 hours, then hot-rolled with a reduction 60% (from 10mm to 4 mm thickness) at 1000 °C and then dissolved at 1100 °C for 2 hours and then cooled by water, oil and air. The microstructural observations were performed with OM and SEM-EDS. The phase analyzes were observed by XRD test and mechanical properties observed by Ultrasonic test. The observation result shows the elasticity modulus value in alloys which being ST with cooling is 106,71 GPa. This is consistent with the observation of the microstructure that the presence of β-transformed and it is also in accordance with the XRD analysis and the intensity of the phase fraction, where the peak and% intensity of the β (35%) phase fraction increase in alloys which ST and oil quench.

Elastic constants and pressure derivative of elastic constants of Si1-xGex solid solution

NASA Astrophysics Data System (ADS)

Jivani, A. R.; Baria, J. K.; Vyas, P. S.; Jani, A. R.

2013-02-01

Elastic properties of Si1-xGex solid solution with arbitrary (atomic) concentration (x) are studied using the pseudo-alloy atom model based on the pseudopotential theory and on the higher-order perturbation scheme with the application of our own proposed model potential. We have used local-field correction function proposed by Sarkar et al to study Si-Ge system. The Elastic constants and pressure derivatives of elastic constants of the solid solution is investigated with different concentration x of Ge. It is found in the present study that the calculated numerical values of the aforesaid physical properties of Si-Ge system are function of x. The elastic constants (C11, C12 and C44) decrease linearly with increase in concentration x and pressure derivative of elastic constants (C11, C12 and C44) increase with the concentration x of Ge. This study provides better set of theoretical results for such solid solution for further comparison either with theoretical or experimental results.

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.

Scaling, elasticity, and CLPT

NASA Technical Reports Server (NTRS)

Brunelle, Eugene J.

1994-01-01

The first few viewgraphs describe the general solution properties of linear elasticity theory which are given by the following two statements: (1) for stress B.C. on S(sub sigma) and zero displacement B.C. on S(sub u) the altered displacements u(sub i)(*) and the actual stresses tau(sub ij) are elastically dependent on Poisson's ratio nu alone: thus the actual displacements are given by u(sub i) = mu(exp -1)u(sub i)(*); and (2) for zero stress B.C. on S(sub sigma) and displacement B.C. on S(sub u) the actual displacements u(sub i) and the altered stresses tau(sub ij)(*) are elastically dependent on Poisson's ratio nu alone: thus the actual stresses are given by tau(sub ij) = E tau(sub ij)(*). The remaining viewgraphs describe the minimum parameter formulation of the general classical laminate theory plate problem as follows: The general CLT plate problem is expressed as a 3 x 3 system of differential equations in the displacements u, v, and w. The eighteen (six each) A(sub ij), B(sub ij), and D(sub ij) system coefficients are ply-weighted sums of the transformed reduced stiffnesses (bar-Q(sub ij))(sub k); the (bar-Q(sub ij))(sub k) in turn depend on six reduced stiffnesses (Q(sub ij))(sub k) and the material and geometry properties of the k(sup th) layer. This paper develops a method for redefining the system coefficients, the displacement components (u,v,w), and the position components (x,y) such that a minimum parameter formulation is possible. The pivotal steps in this method are (1) the reduction of (bar-Q(sub ij))(sub k) dependencies to just two constants Q(*) = (Q(12) + 2Q(66))/(Q(11)Q(22))(exp 1/2) and F(*) - (Q(22)/Q(11))(exp 1/2) in terms of ply-independent reference values Q(sub ij); (2) the reduction of the remaining portions of the A, B, and D coefficients to nondimensional ply-weighted sums (with 0 to 1 ranges) that are independent of Q(*) and F(*); and (3) the introduction of simple coordinate stretchings for u, v, w and x,y such that the process is neatly completed.

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.

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

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.

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.

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.

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.

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).

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

Physics of heat pipe rewetting

NASA Technical Reports Server (NTRS)

Chan, S. H.

1992-01-01

Although several studies have been made to determine the rewetting characteristics of liquid films on heated rods, tubes, and flat plates, no solutions are yet available to describe the rewetting process of a hot plate subjected to a uniform heating. A model is presented to analyze the rewetting process of such plates with and without grooves. Approximate analytical solutions are presented for the prediction of the rewetting velocity and the transient temperature profiles of the plates. It is shown that the present rewetting velocity solution reduces correctly to the existing solution for the rewetting of an initially hot isothermal plate without heating from beneath the plate. Numerical solutions have also been obtained to validate the analytical solutions.

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.

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.

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.

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.

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.

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)

Bulk solitary waves in elastic solids

NASA Astrophysics Data System (ADS)

Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.

2015-10-01

A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the duct-like polymer shell and proved, that there is no tensile area behind the wave, the bulk soliton propagates on a distance many times longer than its wave length, while both its shape and amplitude remain unchanged. We demonstrated recently how the strain solitons can be used for non-destructive testing (NDT) of laminated composites, used nowadays for various applications, e.g., in microelectronics, aerospace and automotive industries, and bulk strain solitons are among prospective instruments for NDT. Being aimed to propose the bulk strain solitons as an instrument for NDT in solids, we studied numerically the evolution of them in various wave guides with local defects, and shown that the strain soliton undergoes changes in amplitude, phase shift and the shape, that are distinctive and can be estimated. To sum up, now we are able to propose a new NDT technique, based on bulk strain soliton propagation in structural elements.

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.

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.

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.

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.

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.

Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felício B.

2017-12-01

Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

Rigidity of Major Plates and Microplates Estimated From GPS Solution GPS2006.0

NASA Astrophysics Data System (ADS)

Kogan, M. G.; Steblov, G. M.

2006-05-01

Here we analyze the rigidity of eight major lithospheric plates using our global GPS solution GPS2006.0. We included all daily observations in interval 1995.0 to 2006.0 collected at IGS stations, as well as observations at many important stations not included in IGS. Loose multiyear solution GPS2006.0 is based on daily solutions by GAMIT software, performed at SOPAC and at Columbia University; those daily solutions were combined by Kalman filter (GLOBK software) into a loose multiyear solution. The constrained solution for station positions and velocities was obtained without a conventional reference frame; instead, we applied translation and rotation in order to best fit the zero velocities of 76 stations in stable plate cores excluding the regions of postglacial rebound. Simultaneously, we estimated relative plate rotation vectors (RV) and the origin translation rate (OTR), and then corrected station velocities for it. Therefore, the velocities in GPS2006.0 are unaffected by the OTR error of ITRF2000 conventionally used to constrain a loose solution. The 1-sigma plate-residual velocity in a stable plate core is less than 1 mm/yr for the plates: Eurasia, Pacific, North and South Americas, Nubia, Australia, and Antarctica; it is 1.4 mm/yr for the Indian plate, most probably because of poorer data quality. Plate-residuals at other established plates (Arabia, Nazca, Caribbean, Philippine) were not assessed for lack of observations. From our analysis, an upper bound for the mobility of the plate inner area is 1 mm/yr. Plate- residual GPS velocities for several hypothesized microplates in east Asia, such as Okhotsk, Amuria, South China, are 3-4 times higher; corresponding strain rates for these microplates are an order of magnitude higher than for Eurasia, North America, and other large plates.

An overview of self-consistent methods for fiber-reinforced composites

NASA Technical Reports Server (NTRS)

Gramoll, Kurt C.; Freed, Alan D.; Walker, Kevin P.

1991-01-01

The Walker et al. (1989) self-consistent method to predict both the elastic and the inelastic effective material properties of composites is examined and compared with the results of other self-consistent and elastically based solutions. The elastic part of their method is shown to be identical to other self-consistent methods for non-dilute reinforced composite materials; they are the Hill (1965), Budiansky (1965), and Nemat-Nasser et al. (1982) derivations. A simplified form of the non-dilute self-consistent method is also derived. The predicted, elastic, effective material properties for fiber reinforced material using the Walker method was found to deviate from the elasticity solution for the v sub 31, K sub 12, and mu sub 31 material properties (fiber is in the 3 direction) especially at the larger volume fractions. Also, the prediction for the transverse shear modulus, mu sub 12, exceeds one of the accepted Hashin bounds. Only the longitudinal elastic modulus E sub 33 agrees with the elasticity solution. The differences between the Walker and the elasticity solutions are primarily due to the assumption used in the derivation of the self-consistent method, i.e., the strain fields in the inclusions and the matrix are assumed to remain constant, which is not a correct assumption for a high concentration of inclusions.

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.

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.

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.

Elasticity Theory Solution of the Problem on Plane Bending of a Narrow Layered Cantilever Beam by Loads at Its Free End

NASA Astrophysics Data System (ADS)

Goryk, A. V.; Koval'chuk, S. B.

2018-05-01

An exact elasticity theory solution for the problem on plane bending of a narrow layered composite cantilever beam by tangential and normal loads distributed on its free end is presented. Components of the stress-strain state are found for the whole layers package by directly integrating differential equations of the plane elasticity theory problem by using an analytic representation of piecewise constant functions of the mechanical characteristics of layer materials. The continuous solution obtained is realized for a four-layer beam with account of kinematic boundary conditions simulating the rigid fixation of its one end. The solution obtained allows one to predict the strength and stiffness of composite cantilever beams and to construct applied analytical solutions for various problems on the elastic bending of layered beams.

Structure–property relations of orthorhombic [(CH{sub 3}){sub 3}NCH{sub 2}COO]{sub 2}(CuCl{sub 2}){sub 3}·2H{sub 2}O

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

Haussühl, Eiken, E-mail: haussuehl@kristall.uni-frankfurt.de; Schreuer, Jürgen; Wiehl, Leonore

2014-04-01

Large single crystals of orthorhombic [(CH{sub 3}){sub 3}NCH{sub 2}COO]{sub 2}(CuCl{sub 2}){sub 3}·2H{sub 2}O with dimensions up to 40×40×30 mm{sup 3} were grown from aqueous solutions. The elastic and piezoelastic coefficients were derived from ultrasonic resonance frequencies and their shifts upon variation of pressure, respectively, using the plate-resonance technique. Additionally, the coefficients of thermal expansion were determined between 95 K and 305 K by dilatometry. The elastic behaviour at ambient conditions is dominated by the 2-dimensional network of strong hydrogen bonds within the (001) plane leading to a corresponding pseudo-tetragonal anisotropy of the longitudinal elastic stiffness. The variation of elastic propertiesmore » with pressure, however, as well as the thermal expansion shows strong deviations from the pseudo-tetragonal symmetry. These deviations are probably correlated with tilts of the elongated tri-nuclear betaine–CuCl{sub 2}–water complexes. Neither the thermal expansion nor the specific heat capacity gives any hint on a phase transition in the investigated temperature range. - Graphical abstract: Single crystal of orthorhombic [(CH{sub 3}){sub 3}NCH{sub 2}COO]{sub 2}(CuCl{sub 2}){sub 3}·2H{sub 2}O. - Highlights: • Large single crystals (40 ×40 ×30 mm{sup 3}) of [(CH{sub 3}){sub 3}NCH{sub 2}COO]{sub 2}(CuCl{sub 2}){sub 3}·2H{sub 2}O were grown. • The elastic and piezoelastic coefficients were derived from ultrasonic resonance frequencies. • Thermal expansion (95 K–305 K) and heat capacity (113 K–323 K) were determined. • The orthorhombic structure shows pseudo-tetragonal elastic anisotropy at ambient conditions. • The crystal structure is stable in the investigated range (1–1600 bar, 95–303 K)« less

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 new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

NASA Astrophysics Data System (ADS)

Yi, Dake; Wang, TzuChiang

2018-06-01

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J( z), the stress intensity factor K( z) and the tri-axial stress constraint level T z ( z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J( z) and T z ( z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

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.

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.

Analysis of laminated plates under thermal environment

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

Iyenger, N.G.R.; Shankara, C.A.

1995-12-31

Use of composites in advanced aircrafts and spacecraft structures calls for a thorough understanding of their behaviour under various types of loads. In the present paper, an attempt has been made to study the effect of thermal loads on the flexural response of composite laminated plates. Most of the studies in this area are either based on Classical Lamination Theory or First Order Shear Deformation Theory. In the present investigation, analysis has been carried out using a Higher Order Shear Deformation Theory, that allows for a parabolic variation of transverse shear stress through the thickness. The displacement model presented bymore » Reddy has been transformed so that only C{degrees} continuous element is required. This, however, increases the Degree of freedom per node from 5 to 7. Nine-noded isoparametric Legrangian elements are used for computing the results. The results were found to be very stable and comparable with those of exact elasticity solutions. The temperature is assumed to remain constant or vary linearly through the thickness. However, it varies sinusoidally in the plane of the plate. Effect of various parameters like material, fiber orientation, number of layers and boundary conditions on the response of the laminate has been investigated. The present study indicates that the flexural behaviour of laminates under thermal loads is very much different from that when subjected only to mechanical loads. Further, the variation of plate deflection with increase in temperature is not linear.« less

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.

Role of surface elasticity in the drainage of soap films

NASA Astrophysics Data System (ADS)

Sonin, A. A.; Bonfillon, A.; Langevin, D.

1993-10-01

We present measurements of the thinning velocity of circular horizontal soap films made from dilute surfactant solutions (around the critical micellar concentration). We have solved numerically the hydrodynamic equations for the drainage process. After data fitting, we deduce the values of the elasticities of the surfactant monolayer that stabilizes the soap film. These elasticity values have been compared to elasticities obtained independently from the study of waves at the surface of the solution. The comparison reveals the importance of surface convection in the drainage process and demonstrates the important role of surface elasticity.

Electrochemical Assay of Gold-Plating Solutions

NASA Technical Reports Server (NTRS)

Chiodo, R.

1982-01-01

Gold content of plating solution is assayed by simple method that required only ordinary electrochemical laboratory equipment and materials. Technique involves electrodeposition of gold from solution onto electrode, the weight gain of which is measured. Suitable fast assay methods are economically and practically necessary in electronics and decorative-plating industries. If gold content in plating bath is too low, poor plating may result, with consequent economic loss to user.

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....

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

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.

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.

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.

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

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.…

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.

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.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Stress fields around two pores in an elastic body: exact quadrature domain solutions.

PubMed

Crowdy, Darren

2015-08-08

Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky-Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores.

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

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

Elasticity solutions for a class of composite laminate problems with stress singularities

NASA Technical Reports Server (NTRS)

Wang, S. S.

1983-01-01

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

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.

Shock wave emission from laser-induced cavitation bubbles in polymer solutions.

PubMed

Brujan, Emil-Alexandru

2008-09-01

The role of extensional viscosity on the acoustic emission from laser-induced cavitation bubbles in polymer solutions and near a rigid boundary is investigated by acoustic measurements. The polymer solutions consist of a 0.5% polyacrylamide (PAM) aqueous solution with a strong elastic component and a 0.5% carboxymethylcellulose (CMC) aqueous solution with a weak elastic component. A reduction of the maximum amplitude of the shock wave pressure and a prolongation of the oscillation period of the bubble were found in the elastic PAM solution. It might be caused by an increased resistance to extensional flow which is conferred upon the liquid by the polymer additive. In both polymer solutions, however, the shock pressure decays proportionally to r(-1) with increasing distance r from the emission centre.

Exact Analytical Solutions for Elastodynamic Impact

DTIC Science & Technology

2015-11-30

corroborated by derivation of exact discrete solutions from recursive equations for the impact problems. 15. SUBJECT TERMS One-dimensional impact; Elastic...wave propagation; Laplace transform; Floor function; Discrete solutions 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...impact Elastic wave propagation Laplace transform Floor function Discrete solutionsWe consider the one-dimensional impact problem in which a semi

Closed solutions to a differential-difference equation and an associated plate solidification problem.

PubMed

Layeni, Olawanle P; Akinola, Adegbola P; Johnson, Jesse V

2016-01-01

Two distinct and novel formalisms for deriving exact closed solutions of a class of variable-coefficient differential-difference equations arising from a plate solidification problem are introduced. Thereupon, exact closed traveling wave and similarity solutions to the plate solidification problem are obtained for some special cases of time-varying plate surface temperature.

Does maltose influence on the elasticity of SOPC membrane?

NASA Astrophysics Data System (ADS)

Genova, J.; Zheliaskova, A.; Mitov, M. D.

2010-11-01

Thermally induced shape fluctuations of giant quasi-spherical lipid vesicles are used to study the influence of the disaccharide maltose, dissolved in the aqueous solution, on the curvature elasticity kc of a lipid membrane. The influence of the carbohydrate solute is investigated throughout a considerably wide interval of concentrations. The values of the bending elastic modulus for 200 mM and 400 mM of maltose in the water solution are obtained. The data for kc in presence of maltose is compared with previously obtained results for this constant for the most popular hydrocarbons: monosaccharides glucose and fructose and disaccharides sucrose and trehalose. It is shown that the presence of maltose, dissolved in the aqueous phase surrounding the membrane does not influence on the bending elasticity with the increase of its concentration in the aqueous solution. Up to our knowledge this is the first sugar that does not show decrease of the bending elastic modulus of the lipid membrane, when present in the water surrounding it in concentration up to 400mM.

Method for regeneration of electroless nickel plating solution

DOEpatents

Eisenmann, Erhard T.

1997-01-01

An electroless nickel(EN)/hypophosphite plating bath is provided employing acetic acid/acetate as a buffer and which is, as a result, capable of perpetual regeneration while avoiding the production of hazardous waste. A regeneration process is provided to process the spent EN plating bath solution. A concentrated starter and replenishment solution is provided for ease of operation of the plating bath. The regeneration process employs a chelating ion exchange system to remove nickel cations from spent EN plating solution. Phosphites are then removed from the solution by precipitation. The nickel cations are removed from the ion exchange system by elution with hypophosphorous acid and the nickel concentration of the eluate adjusted by addition of nickel salt. The treated solution and adjusted eluate are combined, stabilizer added, and the volume of resulting solution reduced by evaporation to form the bath starter and replenishing solution.

Method for regeneration of electroless nickel plating solution

DOEpatents

Eisenmann, E.T.

1997-03-11

An electroless nickel(EN)/hypophosphite plating bath is provided employing acetic acid/acetate as a buffer and which is, as a result, capable of perpetual regeneration while avoiding the production of hazardous waste. A regeneration process is provided to process the spent EN plating bath solution. A concentrated starter and replenishment solution is provided for ease of operation of the plating bath. The regeneration process employs a chelating ion exchange system to remove nickel cations from spent EN plating solution. Phosphites are then removed from the solution by precipitation. The nickel cations are removed from the ion exchange system by elution with hypophosphorus acid and the nickel concentration of the eluate adjusted by addition of nickel salt. The treated solution and adjusted eluate are combined, stabilizer added, and the volume of resulting solution reduced by evaporation to form the bath starter and replenishing solution. 1 fig.

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.

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.

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.

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change: Elasticity and Approximate Solutions

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Cooper, D. E.; Cohen, D.

1985-01-01

The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.

Elastic and piezoelectric fields around a quantum wire of zincblende heterostructures with interface elasticity effect

NASA Astrophysics Data System (ADS)

Ye, Wei; Liu, Yifei

2018-04-01

This work formulates the solutions to the elastic and piezoelectric fields around a quantum wire (QWR) with interface elasticity effect. Closed-form solutions to the piezoelectric potential field of zincblende QWR/matrix heterostructures grown along [111] crystallographic orientation are found and numerical results of InAs/InP heterostructures are provided as an example. The piezoelectric potential in the matrix depends on the interface elasticity, the radius and stiffness of the QWR. Our results indicate that interface elasticity can significantly alter the elastic and piezoelectric fields near the interface. Additionally, when the elastic property of the QWR is considered to be anisotropic in contrary to the common isotropic assumption, piezoelectric potentials are found to be distinct near the interface, but the deviations are negligible at positions far away from the interface.

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

[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.

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.

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.

Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources.

PubMed

Frank, Scott D; Collis, Jon M; Odom, Robert I

2015-06-01

Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.

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.

On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach

NASA Astrophysics Data System (ADS)

Gerstmayr, Johannes; Irschik, Hans

2008-12-01

In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant-Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation.

Shocks in oscillated granular layers

NASA Astrophysics Data System (ADS)

Bougie, J.; Moon, Sung Joon; Swift, J. B.; Swinney, Harry L.

2001-11-01

We study shock formation in vertically oscillated granular layers, where shock waves form with each collision between the layer and the bottom plate of the container. We use both three-dimensional numerical solutions of continuum equations developed by Jenkins and Richman (J.T. Jenkins and M.W. Richman, Arch. Rat. Mech. Anal. 87), 355 (1985) for smooth and nearly elastic hard spheres, and previously validated molecular dynamics (MD) simulations (C. Bizon, M.D. Shattuck, J.B. Swift, W.D. McCormick, and H.L. Swinney, Phys. Rev. Lett. 80), 57 (1998). Both methods capture the shock formation, and the two methods agree quantitatively for small dissipation. We also investigate the effect of inelasticity on shock formation, and use both smooth and rough hard-sphere MD simulations to investigate the effect of friction in this system.

Control of large flexible spacecraft by the independent modal-space control method

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Shenar, J.

1984-01-01

The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes.

Review on failure prediction techniques of composite single lap joint

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

Ab Ghani, A.F., E-mail: ahmadfuad@utem.edu.my; Rivai, Ahmad, E-mail: ahmadrivai@utem.edu.my

2016-03-29

Adhesive bonding is the most appropriate joining method in construction of composite structures. The use of reliable design and prediction technique will produce better performance of bonded joints. Several papers from recent papers and journals have been reviewed and synthesized to understand the current state of the art in this area. It is done by studying the most relevant analytical solutions for composite adherends with start of reviewing the most fundamental ones involving beam/plate theory. It is then extended to review single lap joint non linearity and failure prediction and finally on the failure prediction on composite single lap joint.more » The review also encompasses the finite element modelling part as tool to predict the elastic response of composite single lap joint and failure prediction numerically.« less

Sound transmission through lined, composite panel structures: Transversely isotropic poro-elastic model

NASA Astrophysics Data System (ADS)

Kim, Jeong-Woo

A joint experimental and analytical investigation of the sound transmission loss (STL) and two-dimensional free wave propagation in composite sandwich panels is presented here. An existing panel, a Nomex honeycomb sandwich panel, was studied in detail. For the purpose of understanding the typical behavior of sandwich panels, a composite structure comprising two aluminum sheets with a relatively soft, poro-elastic foam core was also constructed and studied. The cores of both panels were modeled using an anisotropic (transversely isotropic) poro-elastic material theory. Several estimation methods were used to obtain the material properties of the honeycomb core and the skin plates to be used in the numerical calculations. Appropriate values selected from among the estimates were used in the STL and free wave propagation models. The prediction model was then verified in two ways: first, the calculated wave speeds and STL of a single poro-elastic layer were numerically verified by comparison with the predictions of a previously developed isotropic model. Secondly, to physically validate the transversely isotropic model, the measured STL and the phase speeds of the sandwich panels were compared with their predicted values. To analyze the actual treatment of a fuselage structure, multi-layered configurations, including a honeycomb panel and several layers such as air gaps, acoustic blankets and membrane partitions, were formulated. Then, to find the optimal solution for improving the sound barrier performance of an actual fuselage system, air layer depth and glass fiber lining effects were investigated by using these multi-layer models. By using the free wave propagation model, the first anti-symmetric and symmetric modes of the sandwich panels were characterized to allow the identification of the coincidence frequencies of the sandwich panel. The behavior of the STL could then be clearly explained by comparison with the free wave propagation solutions. By performing a parameter study based both on the STL and free wave propagation speeds, the mass, stiffness and damping-controlled regions of the STL were identified. The structural factors that can be adjusted to improve STL performance were also identified.

Elastic parabolic equation solutions for underwater acoustic problems using seismic sources.

PubMed

Frank, Scott D; Odom, Robert I; Collis, Jon M

2013-03-01

Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.

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.

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.

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.

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.

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

Scanning nozzle plating system. [for etching or plating metals on substrates without masking

NASA Technical Reports Server (NTRS)

Oliver, G. D. (Inventor)

1974-01-01

A plating system is described in which a substrate to be plated is supported on a stationary platform. A nozzle assembly with a small nozzle is supplied with a plating solution under high pressure, so that a constant-flow stream of solution is directed to the substrate. The nozzle assembly is moved relative to the substrate at a selected rate and movement pattern. A potential difference (voltage) is provided between the substrate and the solution in the assembly. The voltage amplitude is modulated so that only when the amplitude is above a minimum known value plating takes place.

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.

Analytical close-form solutions to the elastic fields of solids with dislocations and surface stress

NASA Astrophysics Data System (ADS)

Ye, Wei; Paliwal, Bhasker; Ougazzaden, Abdallah; Cherkaoui, Mohammed

2013-07-01

The concept of eigenstrain is adopted to derive a general analytical framework to solve the elastic field for 3D anisotropic solids with general defects by considering the surface stress. The formulation shows the elastic constants and geometrical features of the surface play an important role in determining the elastic fields of the solid. As an application, the analytical close-form solutions to the stress fields of an infinite isotropic circular nanowire are obtained. The stress fields are compared with the classical solutions and those of complex variable method. The stress fields from this work demonstrate the impact from the surface stress when the size of the nanowire shrinks but becomes negligible in macroscopic scale. Compared with the power series solutions of complex variable method, the analytical solutions in this work provide a better platform and they are more flexible in various applications. More importantly, the proposed analytical framework profoundly improves the studies of general 3D anisotropic materials with surface effects.

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

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

A new finite element code for the study of strain-localization under strike-slip faults

NASA Astrophysics Data System (ADS)

Rodríguez-González, J.; Montesi, L.

2016-12-01

Shear localization under strike-slip faults in ductile conditions remains a matter of debate. The rheology of rocks in the ductile regime is fundamentally strain-rate hardening, which complicates the understanding of the formation of narrow shear zones. Localized shear zones are present in a variety of scales, including kilometric structures at plate boundaries. To compensate for strain-rate hardening, shear zones must be weaker than their surroundings thanks to some weakening mechanism that works at multiple length scales. Mechanisms as shear heating or grain size reduction have been invoked to explain localization of deformation, but none of these mechanisms can work in scales that range from 1 to 1000 km. Layered fabric development has been suggested as a candidate to develop localized shear zones at multiple scales. To test this hypothesis, we have developed a new software that uses the Finite Element Method library deal.II written in C++. We solve the elasticity equations for elastic and Maxwell visco-elastic mediums. A key component required to study strain localization is adaptive mesh refinement. The code automatically identifies those regions in which the deformation is being localized and will increase the resolution. We benchmark the code and test its accuracy using analytical solutions of strike-slip deformation with different boundary conditions. We simulate the instantaneous deformation caused by two kinds of dislocations: a free fault subject to a far field traction and fault with an imposed displacement. We also simulate the visco-elastic relaxation following a strike-slip dislocation. We show that deal.II is a flexible library, suitable for different problems, which will prove useful to study the mechanisms that can lead to strain localization.

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.

Elastic-plastic finite-element analyses of thermally cycled single-edge wedge specimens

NASA Technical Reports Server (NTRS)

Kaufman, A.

1982-01-01

Elastic-plastic stress-strain analyses were performed for single-edge wedge alloys subjected to thermal cycling in fluidized beds. Three cases (NASA TAZ-8A alloy under one cycling condition and 316 stainless steel alloy under two cycling conditions) were analyzed by using the MARC nonlinear, finite-element computer program. Elastic solutions from MARC showed good agreement with previously reported solutions that used the NASTRAN and ISO3DQ computer programs. The NASA TAZ-8A case exhibited no plastic strains, and the elastic and elastic-plastic analyses gave identical results. Elastic-plastic analyses of the 316 stainless steel alloy showed plastic strain reversal with a shift of the mean stresses in the compressive direction. The maximum equivalent total strain ranges for these cases were 13 to 22 percent greater than that calculated from elastic analyses.

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.

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.

Solution of the Eshelby problem in gradient elasticity for multilayer spherical inclusions

NASA Astrophysics Data System (ADS)

Volkov-Bogorodskii, D. B.; Lurie, S. A.

2016-03-01

We consider gradient models of elasticity which permit taking into account the characteristic scale parameters of the material. We prove the Papkovich-Neuber theorems, which determine the general form of the gradient solution and the structure of scale effects. We derive the Eshelby integral formula for the gradient moduli of elasticity, which plays the role of the closing equation in the self-consistent three-phase method. In the gradient theory of deformations, we consider the fundamental Eshelby-Christensen problem of determining the effective elastic properties of dispersed composites with spherical inclusions; the exact solution of this problem for classical models was obtained in 1976. This paper is the first to present the exact analytical solution of the Eshelby-Christensen problem for the gradient theory, which permits estimating the influence of scale effects on the stress state and the effective properties of the dispersed composites under study.We also analyze the influence of scale factors.

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.

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.

ELASTIC NET FOR COX'S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM.

PubMed

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox's proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox's proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems.

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.

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.

Adhesive-bonded double-lap joints. [analytical solutions for static load carrying capacity

NASA Technical Reports Server (NTRS)

Hart-Smith, L. J.

1973-01-01

Explicit analytical solutions are derived for the static load carrying capacity of double-lap adhesive-bonded joints. The analyses extend the elastic solution Volkersen and cover adhesive plasticity, adherend stiffness imbalance and thermal mismatch between the adherends. Both elastic-plastic and bi-elastic adhesive representations lead to the explicit result that the influence of the adhesive on the maximum potential bond strength is defined uniquely by the strain energy in shear per unit area of bond. Failures induced by peel stresses at the ends of the joint are examined. This failure mode is particularly important for composite adherends. The explicit solutions are sufficiently simple to be used for design purposes

Application of laser ranging and VLBI data to a study of plate tectonic driving forces. [finite element method

NASA Technical Reports Server (NTRS)

Solomon, S. C.

1980-01-01

The measurability of changes in plate driving or resistive forces associated with plate boundary earthquakes by laser rangefinding or VLBI is considered with emphasis on those aspects of plate forces that can be characterized by such measurements. Topics covered include: (1) analytic solutions for two dimensional stress diffusion in a plate following earthquake faulting on a finite fault; (2) two dimensional finite-element solutions for the global state of stress at the Earth's surface for possible plate driving forces; and (3) finite-element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting.

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.

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.

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).

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.

Elastic-plastic finite-element analyses of thermally cycled double-edge wedge specimens

NASA Technical Reports Server (NTRS)

Kaufman, A.; Hunt, L. E.

1982-01-01

Elastic-plastic stress-strain analyses were performed for double-edge wedge specimens subjected to thermal cycling in fluidized beds at 316 and 1088 C. Four cases involving different nickel-base alloys (IN 100, Mar M-200, NASA TAZ-8A, and Rene 80) were analyzed by using the MARC nonlinear, finite element computer program. Elastic solutions from MARC showed good agreement with previously reported solutions obtained by using the NASTRAN and ISO3DQ computer programs. Equivalent total strain ranges at the critical locations calculated by elastic analyses agreed within 3 percent with those calculated from elastic-plastic analyses. The elastic analyses always resulted in compressive mean stresses at the critical locations. However, elastic-plastic analyses showed tensile mean stresses for two of the four alloys and an increase in the compressive mean stress for the highest plastic strain case.

Influence of isotopic disorder on solid state amorphization and polyamorphism in solid H2O -D2O solutions

NASA Astrophysics Data System (ADS)

Gromnitskaya, E. L.; Danilov, I. V.; Lyapin, A. G.; Brazhkin, V. V.

2015-10-01

We present a low-temperature and high-pressure ultrasonic study of elastic properties of isotopic H2O-D2O solid solutions, comparing their properties with those of the isotopically pure H2O and D2O ices. Measurements were carried out for solid state amorphization (SSA) from 1h to high-density amorphous (HDA) ice upon compression up to 1.8 GPa at 77 K and for the temperature-induced (77 -190 K ) u-HDA (unrelaxed HDA) → e-HDA (expanded HDA) → low-density amorphous (LDA )→1 c cascade of ice transformations near room pressure. There are many similarities in the elasticity behaviour of H2O ,D2O , and H2O-D2O solid solutions, including the softening of the shear elastic modulus as a precursor of SSA and the HDA →LDA transition. We have found significant isotopic effects during H/D substitution, including elastic softening of H2O -D2O solid solutions with respect to the isotopically pure ices in the case of the bulk moduli of ices 1c and 1h and for both bulk and shear elastic moduli of HDA ice at high pressures (>1 GPa ) . This softening is related to the configurational isotopic disorder in the solid solutions. At low pressures, the isotope concentration dependence of the elastic moduli of u-HDA ice changes remarkably and becomes monotonic with pronounced change of the bulk modulus (≈20 %) .

The Riemann problem for longitudinal motion in an elastic-plastic bar

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

Trangenstein, J.A.; Pember, R.B.

In this paper the analytical solution to the Riemann problem for the Antman-Szymczak model of longitudinal motion in an elastic-plastic bar is constructed. The model involves two surfaces corresponding to plastic yield in tension and compression, and exhibits the appropriate limiting behavior for total compressions. The solution of the Riemann problem involves discontinuous changes in characteristic speeds due to transitions from elastic to plastic response. Illustrations are presented, in both state-space and self-similar coordinates, of the variety of possible solutions to the Riemann problem for possible use with numerical algorithms.

Thermo-magnetic field effects on the wave propagation behavior of smart magnetostrictive sandwich nanoplates

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Dabbagh, Ali

2018-03-01

In this paper, a three-variable plate model is utilized to explore the wave propagation problem of smart sandwich nanoplates made of a magnetostrictive core and ceramic face sheets while subjected to thermo-magnetic loading. Herein, the magnetostriction effect is considered and controlled via a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak elastic substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small-scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations are derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of the propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of the presented model are verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

A phase-plane analysis of localized frictional waves

NASA Astrophysics Data System (ADS)

Putelat, T.; Dawes, J. H. P.; Champneys, A. R.

2017-07-01

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick-slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.

A phase-plane analysis of localized frictional waves

PubMed Central

Dawes, J. H. P.; Champneys, A. R.

2017-01-01

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick–slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types. PMID:28804255

A phase-plane analysis of localized frictional waves.

PubMed

Putelat, T; Dawes, J H P; Champneys, A R

2017-07-01

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick-slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.

Purity test for copper-plating solutions

NASA Technical Reports Server (NTRS)

Mansfeld, F. B.

1977-01-01

Electrode configuration can be used to measure extent of impurities in acid-copper plating solution. It can be inserted into any plating tank and will show whether bath is clean or contaminated, within fifteen minutes.

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.

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.

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.

Method for making thin polypropylene film

DOEpatents

Behymer, R.D.; Scholten, J.A.

1985-11-21

An economical method is provided for making uniform thickness polypropylene film as thin as 100 Angstroms. A solution of polypropylene dissolved in xylene is formed by mixing granular polypropylene and xylene together in a flask at an elevated temperature. A substrate, such as a glass plate or microscope slide is immersed in the solution. When the glass plate is withdrawn from the solution at a uniform rate, a thin polypropylene film forms on a flat surface area of the glass plate as the result of xylene evaporation. The actual thickness of the polypropylene film is functional of the polypropylene in xylene solution concentration, and the particular withdrawal rate of the glass plate from the solution. After formation, the thin polypropylene film is floated from the glass plate onto the surface of water, from which it is picked up with a wire hoop.

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.

Boundary-integral methods in elasticity and plasticity. [solutions of boundary value problems

NASA Technical Reports Server (NTRS)

Mendelson, A.

1973-01-01

Recently developed methods that use boundary-integral equations applied to elastic and elastoplastic boundary value problems are reviewed. Direct, indirect, and semidirect methods using potential functions, stress functions, and displacement functions are described. Examples of the use of these methods for torsion problems, plane problems, and three-dimensional problems are given. It is concluded that the boundary-integral methods represent a powerful tool for the solution of elastic and elastoplastic problems.

Eikonal solutions to optical model coupled-channel equations

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Khandelwal, Govind S.; Maung, Khin M.; Townsend, Lawrence W.; Wilson, John W.

1988-01-01

Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first and second order optical model solutions for elastic and inelastic scattering of H-1 and He-4 on C-12. The effects of bound-state excitations on total and reaction cross sections are also estimated.

Contribution to defining a geodetic reference frame for Africa (AFREF): Geodynamics implications

NASA Astrophysics Data System (ADS)

Saria, Elifuraha E.

African Reference Frame (AFREF) is the proposed regional three-dimensional standard frame, which will be used to reference positions and velocities for geodetic sites in Africa and surrounding. This frame will play a crucial role in scientific application for example plate motion and crustal deformation studies, and also in mapping when it involves for example national boundary surveying, remote sensing, GIS, engineering projects and other development programs in Africa. To contribute to the definition of geodetic reference frame for Africa and provide the first continent-wide position/velocity solution for Africa, we processed and analyzed 16 years of GPS and 17 years of DORIS data at 133 GPS sites and 9 DORIS sites continuously operating geodetic sites in Africa and surroundings to describe the present-day kinematics of the Nubian and Somalian plates and constrain relative motions across the East African Rift. We use the resulting horizontal velocities to determine the level of rigidity of Nubia and updated a plate motion model for the East African Rift and revise the counter clockwise rotation of the Victoria plate and clockwise rotation of the Rovuma plate with respect to Nubia. The vertical velocity ranges from -2 to +2 mm/yr, close to their uncertainties with no clear geographical pattern. This study provides the first continent-wide position/velocity solution for Africa, expressed in International Terrestrial Reference Frame (ITRF2008), a contribution to the upcoming African Reference Frame (AFREF). In the next step we used the substantial increase in the geologic, geophysical and geodetic data in Africa to improve our understanding of the rift geometry and the block kinematics of the EAR. We determined the best-fit fault structure of the rift in terms of the locking depth and dip angle and use a block modeling approach where observed velocities are described as the contribution of rigid block rotation and strain accumulation on locked faults. Our results show a better fit with three sub-plates (Victoria, Rovuma and Lwandle) between the major plates Nubia and Somalia. We show that the earthquake slip vectors provide information that is consistent with the GPS velocities and significantly help reduce the uncertainties in plate angular velocity estimates. However, we find that 3.16 My average spreading rates along the Southwest Indian Ridge (SWIR) from MORVEL model are systematically faster than GPS-derived motions across that ridge, possibly reflecting the need to revise the MORVEL outward displacement correction. In the final step, we attempt to understand the hydrological loading in Africa, which may affect our geodetic estimates, particularly the uplift rates. In this work, we analyze 10 years (2002 - 2012) of continuous GPS measurements operating in Africa, and compare with the modeled hydrological loading deformation inferred from the Gravity Recovery and Climate Experiment (GRACE) at the same GPS location and for the same time period. We estimated hydrological loading deformation based on the Equivalent Water Height (EWH) derived from the 10-days interval reprocessed GRACE solution second release (RL02). We took in to account in both GPS and GRACE the systematic errors from atmospheric pressure and non-tidal ocean loading effects and model the Earth as perfect elastic and compute the deformation using appropriate Greens function. We analyze the strength of association between the observation (GPS) and the model (GRACE) in terms of annual amplitude and phase as well as the original data (time-series). We find a good correlation mainly in regions associated with strong seasonal hydrological variations. To improve the correlation between the two solutions, we subtract the GRACE-derived vertical displacement from GPS-observed time series and determine the variance reduction. Our solution shows average variance between the model and the observation reduced to ~40%. (Abstract shortened by UMI.)

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

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.

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.

Octanol reduces end-plate channel lifetime

PubMed Central

Gage, Peter W.; McBurney, Robert N.; Van Helden, Dirk

1978-01-01

1. Post-synaptic effects of n-octanol at concentrations of 0·1-1 mM were examined in toad sartorius muscles by use of extracellular and voltage-clamp techniques. 2. Octanol depressed the amplitude and duration of miniature end-plate currents and hence depressed neuromuscular transmission. 3. The decay of miniature end-plate currents remained exponential in octanol solutions even when the time constant of decay (τD) was decreased by 80-90%. 4. The lifetime of end-plate channels, obtained by analysis of acetylcholine noise, was also decreased by octanol. The average lifetime measured from noise spectra agreed reasonably well with the time constant of decay of miniature end-plate currents, both in control solution and in octanol solutions. 5. Octanol caused a reduction in the conductance of end-plate channels. Single channel conductance was on average about 25 pS in control solution and 20 pS in octanol. 6. In most cells the normal voltage sensitivity of the decay of miniature end-plate currents was retained in octanol solutions. The lifetime of end-plate channels measured from acetylcholine noise also remained voltage-sensitive in octanol solutions. In some experiments in which channel lifetime was exceptionally reduced the voltage sensitivity was less than normal. 7. In octanol solutions, τD was still very sensitive to temperature changes in most cells although in some the temperature sensitivity of τD was clearly reduced. Changes in τD with temperature could generally be fitted by the Arrhenius equation suggesting that a single step reaction controlled the decay of currents both in control and in octanol solutions. In some cells in which τD became less than 0·3 ms, the relationship between τD and temperature became inconsistent with the Arrhenius equation. 8. As the decay of end-plate currents in octanol solutions remains exponential, and the voltage and temperature sensitivity can be unchanged even when τD is significantly reduced, it seems likely that octanol decreases τD by increasing the rate of the reaction which normally controls the lifetime of end-plate channels. PMID:203674

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.

Asymptotically Exact Solution of the Problem of Harmonic Vibrations of an Elastic Parallelepiped

NASA Astrophysics Data System (ADS)

Papkov, S. O.

2017-11-01

An asymptotically exact solution of the classical problem of elasticity about the steadystate forced vibrations of an elastic rectangular parallelepiped is constructed. The general solution of the vibration equations is constructed in the form of double Fourier series with undetermined coefficients, and an infinite system of linear algebraic equations is obtained for determining these coefficients. An analysis of the infinite system permits determining the asymptotics of the unknowns which are used to convolve the double series in both equations of the infinite systems and the displacement and stress components. The efficiency of this approach is illustrated by numerical examples and comparison with known solutions. The spectrum of the parallelepiped symmetric vibrations is studied for various ratios of its sides.

Study on rheological properties of CMC/Eu-Tb solutions with different concentrations

NASA Astrophysics Data System (ADS)

Fu, Z. C.; Ye, J.; Xiong, J.

2018-05-01

The rheological properties of polymer solution are sensitive to variations in the polymer structure. Carboxymethyl cellulose (CMC) aqueous solution has been used in many fields, such as food, medicine and paper industry. In this paper, the effects of different concentrations (2% - 6%) of CMC/Eu-Tb on their rheological properties were investigeted, including steady-state flow and viscoelastic response. The results show that, the viscosity of CMC/Eu-Tb is lower than that of CMC, at the same concentrations; the products solutions present a nearly Newtonian behavior at the low concentrations (2% - 3%); while at the higher concentrations (4% - 6%), the products solutions present a pseudoplastic behavior; shear-thinning behavior is due to the polymer chains unravel under the action of flow and the molecular chains are oriented in the flow direction. The results also show that the viscosity of the solutions decreases with increasing temperature. Dynamic rheological tests show that CMC/Eu-Tb has viscoelasticity in the concentrations of 2% - 6%. At lower concentrations, the elastic modulus G‧ is slightly higher than the viscous modulus G″, and as the concentrations increase, the elastic modulus G‧ is significantly higher than the viscous modulus G″. It means that at the lower solution concentrations, the solutions tend to be less elastic and easier to flow. Most of the energies are lost through the viscous flow. As the solution concentrations increase, the solutions tend to be more elastic, and the system tends to form a gel.

Critical and post-critical behaviour of two-degree-of-freedom flutter-based generators

NASA Astrophysics Data System (ADS)

Pigolotti, Luca; Mannini, Claudio; Bartoli, Gianni; Thiele, Klaus

2017-09-01

Energy harvesting from flow-induced vibrations is a recent research field, which considers a diverse range of systems, among which two-degree-of-freedom flutter-based solutions were individuated as good candidates to obtain high energy performance. In the present work, numerical linear analyses and wind-tunnel tests were conducted on a flat-plate sectional model. The aim is to identify some design guidelines for generators exploiting the classical-flutter instability, through the investigation of the critical condition and the response during the post-critical regime. Many sets of governing parameters of interest from the energy-harvesting point of view were considered, including high levels of heaving damping to simulate the operation of a conversion apparatus. In particular, eccentricity of the elastic centre and small downstream mass unbalance can be introduced as solutions aiming at optimal operative ranges. The collected results suggest the high potentiality of flutter-based generators, and a significant enhancement of performance can be envisaged. Moreover, they contribute to improve the knowledge of the flutter excitation mechanism and to widen the dataset of measurements in the post-critical regime.

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.

Plating Processes Utilizing High Intensity Acoustic Beams

NASA Technical Reports Server (NTRS)

Oeftering, Richard C. (Inventor); Denofrio, Charles (Inventor)

2002-01-01

A system and a method for selective plating processes are disclosed which use directed beams of high intensity acoustic waves to create non-linear effects that alter and improve the plating process. The directed beams are focused on the surface of an object, which in one embodiment is immersed in a plating solution, and in another embodiment is suspended above a plating solution. The plating processes provide precise control of the thickness of the layers of the plating, while at the same time, in at least some incidents, eliminates the need for masking.

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

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.

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.

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.

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.

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

NASA Technical Reports Server (NTRS)

Szabo, Barna A.; Actis, Ricardo L.; Holzer, Stefan M.

1993-01-01

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

The role of material flexibility on the drying transition of water between hydrophobic objects: A thermodynamic analysis

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

Altabet, Y. Elia; Debenedetti, Pablo G., E-mail: pdebene@princeton.edu

2014-11-14

Liquid water confined between hydrophobic objects of sufficient size becomes metastable with respect to its vapor at separations smaller than a critical drying distance. Macroscopic thermodynamic arguments predicting this distance have been restricted to the limit of perfectly rigid confining materials. However, no material is perfectly rigid and it is of interest to account for this fact in the thermodynamic analysis. We present a theory that combines the current macroscopic theory with the thermodynamics of elasticity to derive an expression for the critical drying distance for liquids confined between flexible materials. The resulting expression is the sum of the well-knownmore » drying distance for perfectly rigid confining materials and a new term that accounts for flexibility. Thermodynamic arguments show that this new term is necessarily positive, meaning that flexibility increases the critical drying distance. To study the expected magnitude and scaling behavior of the flexible term, we consider the specific case of water and present an example of drying between thin square elastic plates that are simply supported along two opposite edges and free at the remaining two. We find that the flexible term can be the same order of magnitude or greater than the rigid solution for materials of biological interest at ambient conditions. In addition, we find that when the rigid solution scales with the characteristic size of the immersed objects, the flexible term is independent of size and vice versa. Thus, the scaling behavior of the overall drying distance will depend on the relative weights of the rigid and flexible contributions.« less

ELASTIC NET FOR COX’S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM

PubMed Central

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox’s proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox’s proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems. PMID:23226932

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.

A unified theory for laminated plates

NASA Astrophysics Data System (ADS)

Guiamatsia Tafeuvoukeng, Irene

A literature survey on plate and beam theories show how the advent of the finite element method and the variational method circa 1940 have been a great stimulant for the research in this field. The initial thin plate formulation has been incrementally expanded to treat the isotropic thick plate, the anisotropic single layer, and then laminated plates. It appears however that current formulations still fall into one of two categories: (1) The formulation is tailored for a specific laminate and/or loading case; (2) or the formulation is too complicated to be of practical relevance. In this work a new unifying approach to laminated plate formulation is presented. All laminated plates, including sandwich panels, subjected to any surface load and with any boundary conditions are treated within a single model. In addition, the fundamental behavior of the plate as a two-dimensional structural element is explained. The novel idea is the introduction of fundamental state solutions, which are analytical far field stress and strain solutions of the laminated plate subjected to a set of hierarchical primary loads, the fundamental loads. These loads are carefully selected to form a basis of the load space, and corresponding solutions are superposed to obtain extremely accurate predictions of the three dimensional solution. six,y,z =aklx,y sikl z where i = 1,..., 6; 1=1,...,l max is a substate of the kth fundamental state k=1,2,3,... Typically, a fundamental state solution is expressed as a through-thickness function (z), while the amplitudes of each fundamental load are found from two dimensional finite element solution as a function of in-plane coordinates (x,y). Three major contributions are produced in this work: (1) A complete calibration of the plate as a two-dimensional structure is performed with pure bending and constant shear fundamental states. (2) There are four independent ways to apply a constant shear resultant on a plate, as opposed to one for a beam. This makes it impossible to define a unique 2 x 2 transverse shear stiffness matrix. Therefore the traditional problem of the shear correction factor loses all relevance. It is however shown that an explicit transverse constitutive relation can be obtained for isotropic-layered laminates or single-layers. (3) Higher accuracy, three-dimensional solutions are obtained using a two-dimensional finite element model with a complexity level (degrees of freedom) similar to the Reissner-Mindlin plate. The proof of concept is realized using Pagano solution for rectangular plates under sinusoidal load, for a sandwich panel. Additional comparisons are also performed for four and six-layer symmetric and antisymmetric laminates, between the new plate theory results and full three-dimensional finite element solutions.

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

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

Installation Assessment of Frankford Arsenal.

DTIC Science & Technology

1977-10-01

sulfate , sulfuric acid , ac ’solution 40 Hot water bath 41 Nickel plate Nickel sulfate and chloride sulfuric acid , acid ...solution 42 Chromium Copper plate Copper sulfate and sulfuric acid , acid solution 11-14 TABLE 11-2 (continued) Tank No. Plating Process Use Contents...46 Water rinse Water 47 Water rinse Water 48 Water rinse Water 49 Acid Chromic acid , acetic acid , nickel sulfate and sulfuric

Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

NASA Astrophysics Data System (ADS)

Lefèvre, Victor; Lopez-Pamies, Oscar

2017-02-01

This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi-)conducting/high-permittivity particles to dielectric elastomers does not lead to the extreme electrostriction enhancements observed in experiments. It is posited that such extreme enhancements are the manifestation of interphasial phenomena.

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.

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

NASA Technical Reports Server (NTRS)

Stein, M.; Stein, P. A.

1978-01-01

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

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.

[Hydrogen peroxide, chloramine T and chlorhexidrine in the disinfection of acrylic resin].

PubMed

Czerwińska, W; Kedzia, A; Kałowski, M

1978-01-01

The effectiveness of 3% h drogen peroxide, 5% chloramine T and 0,5% chlorhexidine gluconate solutions in disinfection of acrylic resine plates massively infected with oral flora was analysed. The acrylic resine plates used for investigations, were infected in vitro with mixed salivary flora characterized by small numbers of yeast-like fungi (1st group), or great number of these microorganisms (2nd group). Infected plates were exposed to solutions of analysed disinfectants during various time periods. After rinsing or inactivation of disinfectant residues, acrylic plates were put into bacteriological medium and incubated during 7 days period in 37 degrees C. The results of this study indicated the effectiveness of acrylic plates disinfection to be dependent on used disinfectant, time of exposition, and microorganisms present on the surface of acrylic resine. The solutions of disinfectants were less active in the cases of plates infected with material containing great numbers of yeast-like microorganisms. Among analysed disinfectants 0,5% solution of chlorhexidine was characterized by most effective and rapid activity, whereas 3% solution of hydrogen peroxide was found to be the least effective.

Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

NASA Astrophysics Data System (ADS)

Geng, Jun; Shen, Zhongwei; Song, Liang

2017-06-01

This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L 2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).

Tissue Elasticity Regulated Tumor Gene Expression: Implication for Diagnostic Biomarkers of Primitive Neuroectodermal Tumor

PubMed Central

Vu, Long T.; Keschrumrus, Vic; Zhang, Xi; Zhong, Jiang F.; Su, Qingning; Kabeer, Mustafa H.; Loudon, William G.; Li, Shengwen Calvin

2015-01-01

Background The tumor microenvironment consists of both physical and chemical factors. Tissue elasticity is one physical factor contributing to the microenvironment of tumor cells. To test the importance of tissue elasticity in cell culture, primitive neuroectodermal tumor (PNET) stem cells were cultured on soft polyacrylamide (PAA) hydrogel plates that mimics the elasticity of brain tissue compared with PNET on standard polystyrene (PS) plates. We report the molecular profiles of PNET grown on either PAA or PS. Methodology/Principal Findings A whole-genome microarray profile of transcriptional expression between the two culture conditions was performed as a way to probe effects of substrate on cell behavior in culture. The results showed more genes downregulated on PAA compared to PS. This led us to propose microRNA (miRNA) silencing as a potential mechanism for downregulation. Bioinformatic analysis predicted a greater number of miRNA binding sites from the 3' UTR of downregulated genes and identified as specific miRNA binding sites that were enriched when cells were grown on PAA—this supports the hypothesis that tissue elasticity plays a role in influencing miRNA expression. Thus, Dicer was examined to determine if miRNA processing was affected by tissue elasticity. Dicer genes were downregulated on PAA and had multiple predicted miRNA binding sites in its 3' UTR that matched the miRNA binding sites found enriched on PAA. Many differentially regulated genes were found to be present on PS but downregulated on PAA were mapped onto intron sequences. This suggests expression of alternative polyadenylation sites within intron regions that provide alternative 3' UTRs and alternative miRNA binding sites. This results in tissue specific transcriptional downregulation of mRNA in humans by miRNA. We propose a mechanism, driven by the physical characteristics of the microenvironment by which downregulation of genes occur. We found that tissue elasticity-mediated cytokines (TGFβ2 and TNFα) signaling affect expression of ECM proteins. Conclusions Our results suggest that tissue elasticity plays important roles in miRNA expression, which, in turn, regulate tumor growth or tumorigenicity. PMID:25774514

Calculation of open and closed system elastic coefficients for multicomponent solids

NASA Astrophysics Data System (ADS)

Mishin, Y.

2015-06-01

Thermodynamic equilibrium in multicomponent solids subject to mechanical stresses is a complex nonlinear problem whose exact solution requires extensive computations. A few decades ago, Larché and Cahn proposed a linearized solution of the mechanochemical equilibrium problem by introducing the concept of open system elastic coefficients [Acta Metall. 21, 1051 (1973), 10.1016/0001-6160(73)90021-7]. Using the Ni-Al solid solution as a model system, we demonstrate that open system elastic coefficients can be readily computed by semigrand canonical Monte Carlo simulations in conjunction with the shape fluctuation approach. Such coefficients can be derived from a single simulation run, together with other thermodynamic properties needed for prediction of compositional fields in solid solutions containing defects. The proposed calculation approach enables streamlined solutions of mechanochemical equilibrium problems in complex alloys. Second order corrections to the linear theory are extended to multicomponent systems.

METHOD OF APPLYING COPPER COATINGS TO URANIUM

DOEpatents

Gray, A.G.

1959-07-14

A method is presented for protecting metallic uranium, which comprises anodic etching of the uranium in an aqueous phosphoric acid solution containing chloride ions, cleaning the etched uranium in aqueous nitric acid solution, promptly electro-plating the cleaned uranium in a copper electro-plating bath, and then electro-plating thereupon lead, tin, zinc, cadmium, chromium or nickel from an aqueous electro-plating bath.

Forearc deformation and great subduction earthquakes: implications for cascadia offshore earthquake potential.

PubMed

McCaffrey, R; Goldfinger, C

1995-02-10

The maximum size of thrust earthquakes at the world's subduction zones appears to be limited by anelastic deformation of the overriding plate. Anelastic strain in weak forearcs and roughness of the plate interface produced by faults cutting the forearc may limit the size of thrust earthquakes by inhibiting the buildup of elastic strain energy or slip propagation or both. Recently discovered active strike-slip faults in the submarine forearc of the Cascadia subduction zone show that the upper plate there deforms rapidly in response to arc-parallel shear. Thus, Cascadia, as a result of its weak, deforming upper plate, may be the type of subduction zone at which great (moment magnitude approximately 9) thrust earthquakes do not occur.

Simulation Study on the Deflection Response of the 921A Steel thin plate under Explosive Impact Load

NASA Astrophysics Data System (ADS)

Zhang, Yu-Xiang; Chen, Fang; Han, Yan

2018-03-01

The Ship cabin would be subject to high-intensity shock wave load when it is attacked by anti-ship weapons, causing its side board damaged. The time course of the deflection of the thin plate made of 921A steel in different initial conditions under the impact load is researched by theoretical analysis and numerical simulation. According to the theory of elastic-plastic deformation of the thin plate, the dynamic response equation of the thin plate under the explosion impact load is established with the method of energy, and the theoretical calculation value is compared with the result from the simulation method. It proved that the theoretical calculation method has better reliability and accuracy in different boundary size.

Analysis of energy dissipation and deposition in elastic bodies impacting at hypervelocities

NASA Technical Reports Server (NTRS)

Medina, David F.; Allahdadi, Firooz A.

1992-01-01

A series of impact problems were analyzed using the Eulerian hydrocode CTH. The objective was to quantify the amount of energy dissipated locally by a projectile-infinite plate impact. A series of six impact problems were formulated such that the mass and speed of each projectile were varied in order to allow for increasing speed with constant kinetic energy. The properties and dimensions of the plate were the same for each projectile impact. The resulting response of the plate was analyzed for global Kinetic Energy, global momentum, and local maximum shear stress. The percentage of energy dissipated by the various hypervelocity impact phenomena appears as a relative change of shear stress at a point away from the impact in the plate.

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.

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.

Exact-solution for cone-plate viscometry

NASA Astrophysics Data System (ADS)

Giacomin, A. J.; Gilbert, P. H.

2017-11-01

The viscosity of a Newtonian fluid is often measured by confining the fluid to the gap between a rotating cone that is perpendicular to a fixed disk. We call this experiment cone-plate viscometry. When the cone angle approaches π/2 , the viscometer gap is called narrow. The shear stress in the fluid, throughout a narrow gap, hardly departs from the shear stress exerted on the plate, and we thus call cone-plate flow nearly homogeneous. In this paper, we derive an exact solution for this slight heterogeneity, and from this, we derive the correction factors for the shear rate on the cone and plate, for the torque, and thus, for the measured Newtonian viscosity. These factors thus allow the cone-plate viscometer to be used more accurately, and with cone-angles well below π/2 . We find cone-plate flow field heterogeneity to be far slighter than previously thought. We next use our exact solution for the velocity to arrive at the exact solution for the temperature rise, due to viscous dissipation, in cone-plate flow subject to isothermal boundaries. Since Newtonian viscosity is a strong function of temperature, we expect our new exact solution for the temperature rise be useful to those measuring Newtonian viscosity, and especially so, to those using wide gaps. We include two worked examples to teach practitioners how to use our main results.

Extended analytical solutions for effective elastic moduli of cracked porous media

NASA Astrophysics Data System (ADS)

Nguyen, Sy-Tuan; To, Quy Dong; Vu, Minh Ngoc

2017-05-01

Extended solutions are derived, on the basis of the micromechanical methods, for the effective elastic moduli of porous media containing stiff pores and both open and closed cracks. Analytical formulas of the overall bulk and shear moduli are obtained as functions of the elastic moduli of the solid skeleton, porosity and the densities of open and closed cracks families. We show that the obtained results are extensions of the classical widely used Walsh's (JGR, 1965) and Budiansky-O‧Connell's (JGR, 1974) solutions. Parametric sensitivity analysis clarifies the impact of the model parameters on the effective elastic properties. An inverse analysis, using sonic and density data, is considered to quantify the density of both open and closed cracks. It is observed that the density of closed cracks depends strongly on stress condition while the dependence of open cracks on the confining stress is negligible.

Bending elasticity of lipid membranes in presence of beta 2 glycoprotein I in the surrounding solution

NASA Astrophysics Data System (ADS)

Pavlič, J. I.; Genova, J.; Zheliaskova, A.; Iglič, A.; Mitov, M. D.

2010-11-01

Thermally induced shape fluctuations of giant quasi-spherical lipid vesicles are used to study the bending elasticity modulus kc of a phospholipid (PHLP) membranes in presence of beta 2 glycoprotein I (β2-GPI) in the aqueous solution which surrounds the vesicle's membrane. The bending elastic modulus kc of PHLP - protein membrane was obtained for different mass concentrations of β2-GPI for pure neutral SOPC membranes and for mixed SOPC: Cardiolipin negatively charged membranes. The experimental results for the bending elastic modulus kc of the PHLP membranes does not show dependence on the concentration of β2-GPI in the range from 5.5 to 55 μg/ml, when β2-GPI is present in the aqueous solution surrounding the vesicle's membrane. Obtained results are in good agreement with predictions, based on different experiments, explaining the mechanism of binding of β2-GPI to neutral membranes.

Source sparsity control of sound field reproduction using the elastic-net and the lasso minimizers.

PubMed

Gauthier, P-A; Lecomte, P; Berry, A

2017-04-01

Sound field reproduction is aimed at the reconstruction of a sound pressure field in an extended area using dense loudspeaker arrays. In some circumstances, sound field reproduction is targeted at the reproduction of a sound field captured using microphone arrays. Although methods and algorithms already exist to convert microphone array recordings to loudspeaker array signals, one remaining research question is how to control the spatial sparsity in the resulting loudspeaker array signals and what would be the resulting practical advantages. Sparsity is an interesting feature for spatial audio since it can drastically reduce the number of concurrently active reproduction sources and, therefore, increase the spatial contrast of the solution at the expense of a difference between the target and reproduced sound fields. In this paper, the application of the elastic-net cost function to sound field reproduction is compared to the lasso cost function. It is shown that the elastic-net can induce solution sparsity and overcomes limitations of the lasso: The elastic-net solves the non-uniqueness of the lasso solution, induces source clustering in the sparse solution, and provides a smoother solution within the activated source clusters.

Stress intensity factors of eccentric cracks in bi-materials plate under mode I loading

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

Ismail, A. E.

2015-05-15

Bi-material plates were generally used to joint electronic devices or mechanical components requiring dissimilar materials to be attached. During services, mechanical failure can be occurred due to the formation of cracks at the interfacial joint or away from the centre. Generally, linear elastic fracture mechanics approach is used to characterize these cracks based on stress intensity factors (SIF). Based on the literature survey, the SIFs for the central cracks were easily available. However, the SIFs for eccentric cracks were difficult to obtain. Therefore, this paper presented the SIFs for eccentric cracks subjected to mode I tension loading. Three important parametersmore » were used such as relative crack depth, a/L, relative offset distance, b/L and elastic mismatch, E{sub 1}/E{sub 2} or α. It was found that such parameters significantly affected the characteristic of SIFs and it was depend on the location of cracks.« less

Gradient-index phononic crystal lens-based enhancement of elastic wave energy harvesting

NASA Astrophysics Data System (ADS)

Tol, S.; Degertekin, F. L.; Erturk, A.

2016-08-01

We explore the enhancement of structure-borne elastic wave energy harvesting, both numerically and experimentally, by exploiting a Gradient-Index Phononic Crystal Lens (GRIN-PCL) structure. The proposed GRIN-PCL is formed by an array of blind holes with different diameters on an aluminum plate, where the blind hole distribution is tailored to obtain a hyperbolic secant gradient profile of refractive index guided by finite-element simulations of the lowest asymmetric mode Lamb wave band diagrams. Under plane wave excitation from a line source, experimentally measured wave field validates the numerical simulation of wave focusing within the GRIN-PCL domain. A piezoelectric energy harvester disk located at the first focus of the GRIN-PCL yields an order of magnitude larger power output as compared to the baseline case of energy harvesting without the GRIN-PCL on the uniform plate counterpart.

Buckling Behavior of Long Anisotropic Plates Subjected to Elastically Restrained Thermal Expansion and Contraction

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2004-01-01

An approach for synthesizing buckling results for thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and elastically restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexural anisotropic plates that are subjected to combined mechanical loads. In addition, stiffness-weighted laminate thermal-expansion parameters and compliance coefficients are derived that are used to determine critical temperatures in terms of physically intuitive mechanical-buckling coefficients. Many results are presented for some common laminates that are intended to facilitate a structural designer s transition to the use of the generic buckling design curves. Several curves that illustrate the fundamental parameters used in the analysis are presented, for nine contemporary material systems, that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of the generic design curves.

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.

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.

Application of low-order potential solutions to higher-order vertical traction boundary problems in an elastic half-space

PubMed Central

Taylor, Adam G.

2018-01-01

New solutions of potential functions for the bilinear vertical traction boundary condition are derived and presented. The discretization and interpolation of higher-order tractions and the superposition of the bilinear solutions provide a method of forming approximate and continuous solutions for the equilibrium state of a homogeneous and isotropic elastic half-space subjected to arbitrary normal surface tractions. Past experimental measurements of contact pressure distributions in granular media are reviewed in conjunction with the application of the proposed solution method to analysis of elastic settlement in shallow foundations. A numerical example is presented for an empirical ‘saddle-shaped’ traction distribution at the contact interface between a rigid square footing and a supporting soil medium. Non-dimensional soil resistance is computed as the reciprocal of normalized surface displacements under this empirical traction boundary condition, and the resulting internal stresses are compared to classical solutions to uniform traction boundary conditions. PMID:29892456

Sound absorption by clamped poroelastic plates.

PubMed

Aygun, H; Attenborough, K

2008-09-01

Measurements and predictions have been made of the absorption coefficient and the surface acoustic impedance of poroelastic plates clamped in a large impedance tube and separated from the rigid termination by an air gap. The measured and predicted absorption coefficient and surface impedance spectra exhibit low frequency peaks. The peak frequencies observed in the absorption coefficient are close to those predicted and measured in the deflection spectra of the clamped poroelastic plates. The influences of the rigidity of the clamping conditions and the width of the air gap have been investigated. Both influences are found to be important. Increasing the rigidity of clamping reduces the low frequency absorption peaks compared with those measured for simply supported plates or plates in an intermediate clamping condition. Results for a closed cell foam plate and for two open cell foam plates made from recycled materials are presented. For identical clamping conditions and width of air gap, the results for the different materials differ as a consequence mainly of their different elasticity, thickness, and cell structure.

The Shock and Vibration Digest. Volume 12, Number 8,

DTIC Science & Technology

1980-08-01

half tme coefficient of 0.315 in the above lamina. Sequential delamination began when a strip equation because two surfaces are formed). of width D in...a striker plate. Each specimen study of the two-dimensional ( plane -strain) response was subjected to two separate impact loadings: an of an elastic...laminated plate; they used a finite ele- in- plane impact and a so-called shear-bending impact. ment/normal mode technique. The physical behavior The

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

On stress field near a stationary crack tip

NASA Technical Reports Server (NTRS)

Nemat-Nasser, S.; Obata, M.

1984-01-01

It is well known that the stress and elastic-plastic deformation fields near a crack tip have important roles in the corresponding fracture process. For elastic-perfectly-plastic solids, different solutions are given in the literature. In this work several of these solutions are examined and compared for Mode I (tension), Mode II (shear), and mixed Modes I and II loading conditions in plane strain. By consideration of the dynamic solution, it is shown that the assumption that the material is yielding all around a crack tip may not be reasonable in all cases. By admitting the existence of some elastic sectors, continuous stress fields are obtained even for mixed Modes I and II.

A double tuned rail damper—increased damping at the two first pinned-pinned frequencies

NASA Astrophysics Data System (ADS)

Maes, J.; Sol, H.

2003-10-01

Railway-induced vibrations are a growing matter of environmental concern. The rapid development of transportation, the increase of vehicle speeds and vehicle weights have resulted in higher vibration levels. In the meantime vibrations that were tolerated in the past are now considered to be a nuisance. Numerous solutions have been proposed to remedy these problems. The majority only acts on a specific part of the dynamic behaviour of the track. This paper presents a possible solution to reduce the noise generated by the 'pinned-pinned' frequencies. Pinned-pinned frequencies correspond with standing waves whose nodes are positioned exactly at the sleeper supports. The two first pinned-pinned frequencies are situated approximately at 950 and 2200 Hz (UIC60-rail and sleeper spacing of 0.60 m). To attenuate these vibrations, the Department of MEMC at the VUB has developed a dynamic vibration absorber called the Double Tuned Rail Damper (DTRD). The DTRD is mounted between two sleepers on the rail and is powered by the motion of the rail. The DTRD consists of two major parts: a steel plate which is connected to the rail with an interface of an elastic layer, and a rubber mass. The two first resonance frequencies of the steel plate coincide with the targeted pinned-pinned frequencies of the rail. The rubber mass acts as a motion controller and energy absorber. Measurements at a test track of the French railway company (SNCF) have shown considerable attenuation of the envisaged pinned-pinned frequencies. The attenuation rate surpasses 5 dB/m at certain frequency bands.

Method for controlling protein crystallization

NASA Technical Reports Server (NTRS)

Noever, David A. (Inventor)

1993-01-01

A method and apparatus for controlling the crystallization of protein by solvent evaporation including placing a drop of protein solution between and in contact with a pair of parallel plates and driving one of the plates toward and away from the other plate in a controlled manner to adjust the spacing between the plates is presented. The drop of solution forms a liquid cylinder having a height dependent upon the plate spacing thereby effecting the surface area available for solvent evaporation. When the spacing is close, evaporation is slow. Evaporation is increased by increasing the spacing between the plates until the breaking point of the liquid cylinder. One plate is mounted upon a fixed post while the other plate is carried by a receptacle movable relative to the post and driven by a belt driven screw drive. The temperature and humidity of the drop of protein solution are controlled by sealing the drop within the receptacle and mounting a heater and dessicant within the receptacle.

Tunable sub-wavelength acoustic energy harvesting with a metamaterial plate

NASA Astrophysics Data System (ADS)

Oudich, Mourad; Li, Yong

2017-08-01

We report theoretically on sub-wavelength acoustic energy harvesting (AEH) using a thin acoustic metamaterial (AM) made of spring-mass resonators attached to the surface of a homogeneous elastic thin plate. Considering an incident acoustic wave hitting the AM plate, tunable and highly efficient AEH is achieved by introducing a sub-wavelength defect inside the AM structure to confine the elastic energy into a spot which is then electromechanically converted into electrical power using a ceramic PZT patch. Several types of sub-wavelength cavities capable of confining acoustic energy at the sonic regime are extensively investigated for the optimization of AEH. Three analytical approaches—band structure, sound transmission loss and electrical-to-mechanical energy conversion—are proposed to fully describe the system interaction with the acoustic wave and quantify the AEH performance. The computed results show that an average power of 18 μW can be harvested using a specific cavity design of only 3 × 3 cm2 size from an incident acoustic wave with a sound pressure level of 100 dB at 520 Hz. Such a system can open up a way through the design of effective tunable sub-wavelength acoustic energy harvesters based on AM applied to scavenge energy from sound.

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.

Friction on a granular-continuum interface: Effects of granular media

NASA Astrophysics Data System (ADS)

Ecke, Robert; Geller, Drew

We consider the frictional interactions of two soft plates with interposed granular material subject to normal and shear forces. The plates are soft photo-elastic material, have length 50 cm, and are separated by a gap of variable width from 0 to 20 granular particle diameters. The granular materials are two-dimensional rods that are bi-dispersed in size to prevent crystallization. Different rod materials with frictional coefficients between 0 . 04 < μ < 0 . 5 are used to explore the effects of inter-granular friction on the effective friction of a granular medium. The gap is varied to test the dependence of the friction coefficient on the thickness of the granular layer. Because the soft plates absorb most of the displacement associated with the compressional normal force, the granular packing fractions are close to a jamming threshold, probably a shear jamming criterion. The overall shear and normal forces are measured using force sensors and the local strain tensor over a central portion of the gap is obtained using relative displacements of fiducial markers on the soft elastic material. These measurements provide a good characterization of the global and local forces giving rise to an effective friction coefficient. Funded by US DOE LDRD Program.

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.

Experimental and numerical investigation on laser-assisted bending of pre-loaded metal plate

NASA Astrophysics Data System (ADS)

Nowak, Zdzisław; Nowak, Marcin; Widłaszewski, Jacek; Kurp, Piotr

2018-01-01

The laser forming technique has an important disadvantage, which is the limitation of plastic deformation generated by a single laser beam pass. To increase the plastic deformation it is possible to apply external forces in the laser forming process. In this paper, we investigate the influence of external pre-loads on the laser bending of steel plate. The pre-loads investigated generate bending towards the laser beam. The thermal, elastic-plastic analysis is performed using the commercial nonlinear finite element analysis package ABAQUS. The focus of the paper is to identify how this pattern of the pre-load influence the final bend angle of the plate.

Dynamic responses of graphite/epoxy laminated beam to impact of elastic spheres

NASA Technical Reports Server (NTRS)

Sun, C. T.; Wang, T.

1982-01-01

Wave propagation in 90/45/90/-45/902s and 0/45/0/-45/02s laminates of a graphite/epoxy composite due to impact of a steel ball was investigated experimentally and also by using a high order beam finite element. Dynamic strain responses at several locations were obtained using strain gages. The finite element program which incorporated statically determined contact laws was employed to calculate the contact force history as well as the target beam dynamic deformation. The comparison of the finite element solutions with the experimental data indicated that the static contact laws for loading and unloading (developed under this grant) are adequate for the dynamic impact analysis. It was found that for the 0/45/0/-45/02s laminate which has a much larger longitudinal bending rigidity, the use of beam finite elements is not suitable and plate finite element should be used instead.

Eigensolution of finite element problems in a completely connected parallel architecture

NASA Technical Reports Server (NTRS)

Akl, F.; Morel, M.

1989-01-01

A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm is successfully implemented on a tightly coupled MIMD parallel processor. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts, and the dimension of the subspace on the performance of the algorithm is investigated. For a 64-element rectangular plate, speed-ups of 1.86, 3.13, 3.18, and 3.61 are achieved on two, four, six, and eight processors, respectively.

Material orientation design of planar structures with prescribed anisotropy classes. Study of rhombic systems

NASA Astrophysics Data System (ADS)

Czubacki, Radosław

2018-01-01

The paper deals with the minimum compliance problem of 2D structures made of a non-homogeneous elastic material. In the first part of the paper a comparison between solutions of Free Material Design (FMD), Cubic Material Design (CMD) and Isotropic Material Design (IMD) is shown for a simply supported plate in a shape of a deep beam, subjected to a concentrated in-plane force at its upper face. The isoperimetric condition fixes the value of the cost of the design expressed as the integral of the trace of the Hooke tensor. In the second part of the paper the material design approaches are extended to rhombic system in 2D. For the rhombic system the material properties of the structures are set, the design variables being the trajectories of anisotropy directions which in 2D are described by one parameter. In the Orthotropic Orientation Design (OOD) no isoperimetric condition is used.

Finite element stress, vibration, and buckling analysis of laminated beams with the use of refined elements

NASA Astrophysics Data System (ADS)

Borovkov, Alexei I.; Avdeev, Ilya V.; Artemyev, A.

1999-05-01

In present work, the stress, vibration and buckling finite element analysis of laminated beams is performed. Review of the equivalent single-layer (ESL) laminate theories is done. Finite element algorithms and procedures integrated into the original FEA program system and based on the classical laminated plate theory (CLPT), first-order shear deformation theory (FSDT), third-order theory of Reddy (TSDT-R) and third- order theory of Kant (TSDT-K) with the use of the Lanczos method for solving of the eigenproblem are developed. Several numerical tests and examples of bending, free vibration and buckling of multilayered and sandwich beams with various material, geometry properties and boundary conditions are solved. New effective higher-order hierarchical element for the accurate calculation of transverse shear stress is proposed. The comparative analysis of results obtained by the considered models and solutions of 2D problems of the heterogeneous anisotropic elasticity is fulfilled.

Indentation property and corrosion resistance of electroless nickel-phosphorus coatings deposited on austenitic high-Mn TWIP steel

NASA Astrophysics Data System (ADS)

Hamada, A. S.; Sahu, P.; Porter, D. A.

2015-11-01

A multilayer coating using electroless nickel-phosphorus (Ni-P) was applied on a twinning-induced plasticity (TWIP) steel containing nominally 25 wt.% Mn and 3 wt.% Al to improve the indentation hardness and corrosion properties. Microindentation tests with two different indenters, namely, a three-sided pyramidal Berkovich indenter and a ball indenter were performed to study the mechanical response, the indentation hardness and elastic modulus of the coatings in conditions: as-plated, and post treated (PT) at 350 °C and 700 °C for 1 h. The deformation morphology underneath the indenters was examined using a scanning laser microscope. The results showed that Ni-P coatings could significantly enhance the surface hardness of the TWIP steel. Significant improvement in the corrosion resistance could be observed in a sulfuric acid solution for the Ni-P coated steel compared to the uncoated substrate TWIP steel.

The use of COD and plastic instability in crack propagation and arrest in shells

NASA Technical Reports Server (NTRS)

Erdogan, F.; Ratwani, M.

1974-01-01

The initiation, growth, and possible arrest of fracture in cylindrical shells containing initial defects are dealt with. For those defects which may be approximated by a part-through semi-elliptic surface crack which is sufficiently shallow so that part of the net ligament in the plane of the crack is still elastic, the existing flat plate solution is modified to take into account the shell curvature effect as well as the effect of the thickness and the small scale plastic deformations. The problem of large defects is then considered under the assumptions that the defect may be approximated by a relatively deep meridional part-through surface crack and the net ligament through the shell wall is fully yielded. The results given are based on an 8th order bending theory of shallow shells using a conventional plastic strip model to account for the plastic deformations around the crack border.

Exact solutions for laminated composite cylindrical shells in cylindrical bending

NASA Technical Reports Server (NTRS)

Yuan, F. G.

1992-01-01

Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

Recovery process for electroless plating baths

DOEpatents

Anderson, Roger W.; Neff, Wayne A.

1992-01-01

A process for removing, from spent electroless metal plating bath solutions, accumulated byproducts and counter-ions that have deleterious effects on plating. The solution, or a portion thereof, is passed through a selected cation exchange resin bed in hydrogen form, the resin selected from strong acid cation exchangers and combinations of intermediate acid cation exchangers with strong acid cation exchangers. Sodium and nickel ions are sorbed in the selected cation exchanger, with little removal of other constituents. The remaining solution is subjected to sulfate removal through precipitation of calcium sulfate hemihydrate using, sequentially, CaO and then CaCO.sub.3. Phosphite removal from the solution is accomplished by the addition of MgO to form magnesium phosphite trihydrate. The washed precipitates of these steps can be safely discarded in nontoxic land fills, or used in various chemical industries. Finally, any remaining solution can be concentrated, adjusted for pH, and be ready for reuse. The plating metal can be removed from the exchanger with sulfuric acid or with the filtrate from the magnesium phosphite precipitation forming a sulfate of the plating metal for reuse. The process is illustrated as applied to processing electroless nickel plating baths.

Recovery process for electroless plating baths

DOEpatents

Anderson, R.W.; Neff, W.A.

1992-05-12

A process is described for removing, from spent electroless metal plating bath solutions, accumulated byproducts and counter-ions that have deleterious effects on plating. The solution, or a portion thereof, is passed through a selected cation exchange resin bed in hydrogen form, the resin selected from strong acid cation exchangers and combinations of intermediate acid cation exchangers with strong acid cation exchangers. Sodium and nickel ions are sorbed in the selected cation exchanger, with little removal of other constituents. The remaining solution is subjected to sulfate removal through precipitation of calcium sulfate hemihydrate using, sequentially, CaO and then CaCO[sub 3]. Phosphite removal from the solution is accomplished by the addition of MgO to form magnesium phosphite trihydrate. The washed precipitates of these steps can be safely discarded in nontoxic land fills, or used in various chemical industries. Finally, any remaining solution can be concentrated, adjusted for pH, and be ready for reuse. The plating metal can be removed from the exchanger with sulfuric acid or with the filtrate from the magnesium phosphite precipitation forming a sulfate of the plating metal for reuse. The process is illustrated as applied to processing electroless nickel plating baths. 18 figs.

Elastic Properties of Chimpanzee Craniofacial Cortical Bone

PubMed Central

Gharpure, Poorva; Kontogiorgos, Elias D.; Opperman, Lynne A.; Ross, Callum F.; Strait, David S.; Smith, Amanda; Pryor, Leslie C.; Wang, Qian; Dechow, Paul C.

2017-01-01

Relatively few assessments of cranial biomechanics formally take into account variation in the material properties of cranial cortical bone. Our aim was to characterize the elastic properties of chimpanzee craniofacial cortical bone and compare these to the elastic properties of dentate human craniofacial cortical bone. From seven cranial regions, 27 cylindrical samples were harvested from each of five chimpanzee crania. Assuming orthotropy, axes of maximum stiffness in the plane of the cortical plate were derived using modified equations of Hooke’s law in a Mathcad program. Consistent orientations among individuals were observed in the zygomatic arch and alveolus. The density of cortical bone showed significant regional variation (P<0.001). The elastic moduli demonstrated significant differences between sites, and a distinct pattern where E3 >E2 > E1. Shear moduli were significantly different among regions (P<0.001). The pattern by which chimpanzee cranial cortical bone varies in elastic properties resembled that seen in humans, perhaps suggesting that the elastic properties of craniofacial bone in fossil hominins can be estimated with at least some degree of confidence. PMID:27870344

Scaling Symmetries in Elastic-Plastic Dynamic Cavity Expansion Equations Using the Isovector Method

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

Albright, Eric Jason; Ramsey, Scott D.; Schmidt, Joseph H.

Cavity-expansion approximations are widely-used in the study of penetration mechanics and indentation phenomena. We apply the isovector method to a well-established model in the literature for elastic-plastic cavity-expansion to systematically demonstrate the existence of Lie symmetries corresponding to scale-invariant solutions. Here we use the symmetries obtained from the equations of motion to determine compatible auxiliary conditions describing the cavity wall trajectory and the elastic-plastic material interface. The admissible conditions are then compared with specific similarity solutions in the literature.

Scaling Symmetries in Elastic-Plastic Dynamic Cavity Expansion Equations Using the Isovector Method

DOE PAGES

Albright, Eric Jason; Ramsey, Scott D.; Schmidt, Joseph H.; ...

2017-09-16

Cavity-expansion approximations are widely-used in the study of penetration mechanics and indentation phenomena. We apply the isovector method to a well-established model in the literature for elastic-plastic cavity-expansion to systematically demonstrate the existence of Lie symmetries corresponding to scale-invariant solutions. Here we use the symmetries obtained from the equations of motion to determine compatible auxiliary conditions describing the cavity wall trajectory and the elastic-plastic material interface. The admissible conditions are then compared with specific similarity solutions in the literature.

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

Cascading elastic perturbation in Japan due to the 2012 M w 8.6 Indian Ocean earthquake.

PubMed

Delorey, Andrew A; Chao, Kevin; Obara, Kazushige; Johnson, Paul A

2015-10-01

Since the discovery of extensive earthquake triggering occurring in response to the 1992 M w (moment magnitude) 7.3 Landers earthquake, it is now well established that seismic waves from earthquakes can trigger other earthquakes, tremor, slow slip, and pore pressure changes. Our contention is that earthquake triggering is one manifestation of a more widespread elastic disturbance that reveals information about Earth's stress state. Earth's stress state is central to our understanding of both natural and anthropogenic-induced crustal processes. We show that seismic waves from distant earthquakes may perturb stresses and frictional properties on faults and elastic moduli of the crust in cascading fashion. Transient dynamic stresses place crustal material into a metastable state during which the material recovers through a process termed slow dynamics. This observation of widespread, dynamically induced elastic perturbation, including systematic migration of offshore seismicity, strain transients, and velocity transients, presents a new characterization of Earth's elastic system that will advance our understanding of plate tectonics, seismicity, and seismic hazards.

A finite element analysis of viscoelastically damped sandwich plates

NASA Astrophysics Data System (ADS)

Ma, B.-A.; He, J.-F.

1992-01-01

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

Nonlinear resonance of the rotating circular plate under static loads in magnetic field

NASA Astrophysics Data System (ADS)

Hu, Yuda; Wang, Tong

2015-11-01

The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.

Time reversal focusing of elastic waves in plates for an educational demonstration.

PubMed

Heaton, Christopher; Anderson, Brian E; Young, Sarah M

2017-02-01

The purpose of this research is to develop a visual demonstration of time reversal focusing of vibrations in a thin plate. Various plate materials are tested to provide optimal conditions for time reversal focusing. Specifically, the reverberation time in each plate and the vibration coupling efficiency from a shaker to the plate are quantified to illustrate why a given plate provides the best spatially confined focus as well as the highest focal amplitude possible. A single vibration speaker and a scanning laser Doppler vibrometer (SLDV) are used to provide the time reversal focusing. Table salt is sprinkled onto the plate surface to allow visualization of the high amplitude, spatially localized time reversal focus; the salt is thrown upward only at the focal position. Spatial mapping of the vibration focusing on the plate using the SLDV is correlated to the visual salt jumping demonstration. The time reversal focusing is also used to knock over an object when the object is placed at the focal position; some discussion of optimal objects to use for this demonstration are given.

Plating methods, a survey

NASA Technical Reports Server (NTRS)

Berkowitz, J. B.; Emerson, N. H.

1972-01-01

Results are presented of a comprehensive search of the literature available, much of which has been generated by the research centers of NASA and its contractors, on plating and coating methods and techniques. Methods covered included: (1) electroplating from aqueous solutions; (2) electroplating from nonaqueous solutions; (3) electroplating from fused-salt baths; (4) electroforming; (5) electroless plating, immersion plating, and mirroring; (6) electroplating from gaseous plasmas; and (7) anodized films and conversion coatings.

Stability Analysis of an Encapsulated Microbubble against Gas Diffusion

PubMed Central

Katiyar, Amit; Sarkar, Kausik

2009-01-01

Linear stability analysis is performed for a mathematical model of diffusion of gases from an encapsulated microbubble. It is an Epstein-Plesset model modified to account for encapsulation elasticity and finite gas permeability. Although, bubbles, containing gases other than air is considered, the final stable bubble, if any, contains only air, and stability is achieved only when the surrounding medium is saturated or oversaturated with air. In absence of encapsulation elasticity, only a neutral stability is achieved for zero surface tension, the other solution being unstable. For an elastic encapsulation, different equilibrium solutions are obtained depending on the saturation level and whether the surface tension is smaller or higher than the elasticity. For an elastic encapsulation, elasticity can stabilize the bubble. However, imposing a non-negativity condition on the effective surface tension (consisting of reference surface tension and the elastic stress) leads to an equilibrium radius which is only neutrally stable. If the encapsulation can support net compressive stress, it achieves actual stability. The linear stability results are consistent with our recent numerical findings. Physical mechanisms for the stability or instability of various equilibriums are provided. PMID:20005522

On application of the Floquet theory for radially periodic membranes and plates

NASA Astrophysics Data System (ADS)

Hvatov, Alexander; Sorokin, Sergey

2018-02-01

The paper is concerned with the vibro-isolation effects in radially periodic membranes and plates. Alternative formulations of the canonical Floquet theory for analysis of wave propagation in these elastic structures are compared with each other. An extension of this theory beyond the applicability limits of the well-known theory of Bragg fiber is proposed. The similarities and differences in performance of infinite and finite structures periodic in Cartesian and polar coordinates are highlighted and explained.

Linear-Elastic 2D and 3D Finite Element Contact Analysis of a Hole Containing a Circular Insert in a Fatigue Test Coupon

DTIC Science & Technology

2015-07-01

circular hole in an aluminium plate fitted with a titanium fastener that were computed using two-dimensional finite element contact analysis. By...used to validate the contact stress distributions associated with a circular hole in an aluminium plate fitted with a titanium fastener that were...fatigue life and aircraft structural integrity management of RAAF airframes. An aluminium coupon has been previously designed in support of the

Transient response of an active nonlinear sandwich piezolaminated plate

NASA Astrophysics Data System (ADS)

Oveisi, Atta; Nestorović, Tamara

2017-04-01

In this paper, the dynamic modelling and active vibration control of a piezolaminated plate with geometrical nonlinearities are investigated using a semi-analytical approach. For active vibration control purposes, the core orthotropic elastic layer is assumed to be perfectly bonded with two piezo-layers on its top and bottom surfaces which act as sensor and actuator, respectively. In the modelling procedure, the piezo-layers are assumed to be connected via a proportional derivative (PD) feedback control law. Hamilton's principle is employed to acquire the strong form of the dynamic equation in terms of additional higher order strain expressions by means of von Karman strain-displacement correlation. The obtained nonlinear partial differential equation (NPDE) is converted to a system of nonlinear ordinary differential equations (NODEs) by engaging Galerkin method and using the orthogonality of shape functions for the simply supported boundary conditions. Then, the resulting system of NODEs is solved numerically by employing the built-in Mathematica function, "NDSolve". Next, the vibration attenuation performance is evaluated and sensitivity of the closed-loop system is investigated for several control parameters and the external disturbance parameters. The proposed solution in open loop configuration is validated by finite element (FE) package ABAQUS both in the spatial domain and for the time-/frequency-dependent response.

Residual stresses in cross-ply composite tubes

NASA Technical Reports Server (NTRS)

Cohen, D.; Hyer, M. W.

1984-01-01

The residual thermal stresses in 4-layer cross-ply tubes are studied. The tubes considered has a small radius to wall-thickness ratios and so elasticity solutions were used. The residual thermal stress problem was considered to be axisymmetric and three elasticity solutions were derived and the results compared with the results using classical lamination theory. The comparison illustrates the limitations of classical lamination theory. The three elasticity solutions derived were: plane stress, plane strain, and generalized plane strain, the latter being the most realistic. Residual stresses in both the hoop and axial direction is significant. Stacking arrangement effects the residual stress to some extent, as do the material properties of the individual lamina. The benefits of hybrid construction are briefly discussed.

Gaseous Viscous Peeling of Linearly Elastic Substrates

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2017-11-01

We study pressure-driven propagation of gas into a micron-scale gap between two linearly elastic substrates. Applying the lubrication approximation, the governing nonlinear evolution equation describes the interaction between elasticity and viscosity, as well as weak rarefaction and low-Mach-number compressibility, characteristic to gaseous microflows. Several physical limits allow simplification of the evolution equation and enable solution by self-similarity. During the peeling process the flow-field transitions between the different limits and the respective approximate solutions. The sequence of limits occurring during the propagation dynamics can be related to the thickness of the prewetting layer of the configuration at rest, yielding an approximate description of the entire peeling dynamics. The results are validated by numerical solutions of the evolution equation. Israel Science Foundation 818/13.

Process for metallization of a substrate by curing a catalyst applied thereto

DOEpatents

Chen, Ken S.; Morgan, William P.; Zich, John L.

2002-10-08

An improved additive process for metallization of substrates is described whereby a catalyst solution is applied to a surface of a substrate. Metallic catalytic clusters can be formed in the catalyst solution on the substrate surface by heating the substrate. Electroless plating can then deposit metal onto the portion of the substrate surface coated with catalyst solution. Additional metallization thickness can be obtained by electrolytically plating the substrate surface after the electroless plating step.

On the application of the partition of unity method for nonlocal response of low-dimensional structures

NASA Astrophysics Data System (ADS)

Natarajan, Sundararajan

2014-12-01

The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen's nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

Analysis of surface cracks in finite plates under tension or bending loads

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Raju, I. S.

1979-01-01

Stress-intensity factors calculated with a three-dimensional, finite-element analysis for shallow and deep semielliptical surface cracks in finite elastic isotropic plates subjected to tension or bending loads are presented. A wide range of configuration parameters was investigated. The ratio of crack depth to plate thickness ranged from 0.2 to 0.8 and the ratio of crack depth to crack length ranged from 0.2 to 2.0. The effects of plate width on stress-intensity variations along the crack front was also investigated. A wide-range equation for stress-intensity factors along the crack front as a function of crack depth, crack length, plate thickness, and plate width was developed for tension and bending loads. The equation was used to predict patterns of surface-crack growth under tension or bending fatigue loads. A modified form of the equation was also used to correlate surface-crack fracture data for a brittle epoxy material within + or - 10 percent for a wide range of crack shapes and crack sizes.

Buckling transition and boundary layer in non-Euclidean plates.

PubMed

Efrati, Efi; Sharon, Eran; Kupferman, Raz

2009-07-01

Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled equilibrium configurations at a critical value of the plate thickness. Depending on the reference metric, the buckling transition may be either continuous or discontinuous. In the infinitely thin plate limit, under the assumption that a limiting configuration exists, we show that the limit is a configuration that minimizes the bending content, among all configurations with zero stretching content (isometric immersions of the midsurface). For small but finite plate thickness, we show the formation of a boundary layer, whose size scales with the square root of the plate thickness and whose shape is determined by a balance between stretching and bending energies.

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.

Fluid-structure interaction in Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Kempf, Martin Horst Willi

1998-10-01

The linear stability of a viscous fluid between two concentric, rotating cylinders is considered. The inner cylinder is a rigid boundary and the outer cylinder has an elastic layer exposed to the fluid. The subject is motivated by flow between two adjoining rollers in a printing press. The governing equations of the fluid layer are the incompressible Navier-Stokes equations, and the governing equations of the elastic layer are Navier's equations. A narrow gap, neutral stability, and axisymmetric disturbances are assumed. The solution involves a novel technique for treating two layer stability problems, where an exact solution in the elastic layer is used to isolate the problem in the fluid layer. The results show that the presence of the elastic layer has only a slight effect on the critical Taylor numbers for the elastic parameters of modern printing presses. However, there are parameter values where the critical Taylor number is dramatically different than the classical Taylor-Couette problem.

Elasticity of fractal materials using the continuum model with non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Comparison between the basic least squares and the Bayesian approach for elastic constants identification

NASA Astrophysics Data System (ADS)

Gogu, C.; Haftka, R.; LeRiche, R.; Molimard, J.; Vautrin, A.; Sankar, B.

2008-11-01

The basic formulation of the least squares method, based on the L2 norm of the misfit, is still widely used today for identifying elastic material properties from experimental data. An alternative statistical approach is the Bayesian method. We seek here situations with significant difference between the material properties found by the two methods. For a simple three bar truss example we illustrate three such situations in which the Bayesian approach leads to more accurate results: different magnitude of the measurements, different uncertainty in the measurements and correlation among measurements. When all three effects add up, the Bayesian approach can have a large advantage. We then compared the two methods for identification of elastic constants from plate vibration natural frequencies.

Homogenization theory for designing graded viscoelastic sonic crystals

NASA Astrophysics Data System (ADS)

Qu, Zhao-Liang; Ren, Chun-Yu; Pei, Yong-Mao; Fang, Dai-Ning

2015-02-01

In this paper, we propose a homogenization theory for designing graded viscoelastic sonic crystals (VSCs) which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material. We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC. The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement. According to the relation of the effective loss factor to the filling fraction, a graded VSC plate is easily and quickly designed. Then, the graded VSC may have potential applications in the vibration absorption and noise reduction fields. Project supported by the National Basic Research Program of China (Grant No. 2011CB610301).

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.

Measurement of leaky Lamb wave dispersion curves with application on coating characterization

NASA Astrophysics Data System (ADS)

Lee, Yung-Chun; Cheng, Sheng Wen

2001-04-01

This paper describes a new measurement system for measuring dispersion curves of leaky Lamb waves. The measurement system is based on a focusing PVDF transducer, the defocusing measurement, the V(f,z) waveform processing method, and an image displaying technique. The measurement system is applied for the determination of thin-film elastic properties, namely Young's modulus and shear modulus, by the inversion of dispersion curves measured from a thin-film/plate configuration. Elastic constants of electro-deposited nickel layers are determined with this method.

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.