The History of the Planar Elastica: Insights into Mechanics and Scientific Method

NASA Astrophysics Data System (ADS)

Goss, Victor Geoffrey Alan

2009-08-01

Euler’s formula for the buckling of an elastic column is widely used in engineering design. However, only a handful of engineers will be familiar with Euler’s classic paper De Curvis Elasticis in which the formula is derived. In addition to the Euler Buckling Formula, De Curvis Elasticis classifies all the bent configurations of elastic rod—a landmark in the development of a rational theory of continuum mechanics. As a historical case study, Euler’s work on elastic rods offers an insight into some important concepts which underlie mechanics. It sheds light on the search for unifying principles of mechanics and the role of analysis. The connection between results obtained from theory and those obtained from experiments on rods, highlights two different approaches to scientific discovery, which can be traced back to Bacon, Descartes and Galileo. The bent rod also has an analogy in dynamics, with a pendulum, which highlights the crucial distinctions between initial value and boundary value problems and between linear and nonlinear differential equations. In addition to benefiting from the overview which a historical study provides, the particular problem of the elastica offers students of science and engineering a clear elucidation of the connection between mathematics and real-world engineering, issues which still have relevance today.

Microtubules soften due to cross-sectional flattening

DOE PAGES

Memet, Edvin; Hilitsk, Feodor; Morris, Margaret A.; ...

2018-06-01

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasing deformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effectmore » in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.« less

Microtubules soften due to cross-sectional flattening

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

Memet, Edvin; Hilitsk, Feodor; Morris, Margaret A.

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasing deformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effectmore » in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.« less

Shear buckling analysis of a hat-stiffened panel

NASA Technical Reports Server (NTRS)

Ko, William L.; Jackson, Raymond H.

1994-01-01

A buckling analysis was performed on a hat-stiffened panel subjected to shear loading. Both local buckling and global buckling were analyzed. The global shear buckling load was found to be several times higher than the local shear buckling load. The classical shear buckling theory for a flat plate was found to be useful in predicting the local shear buckling load of the hat-stiffened panel, and the predicted local shear buckling loads thus obtained compare favorably with the results of finite element analysis.

Buckling of C60 whiskers

NASA Astrophysics Data System (ADS)

Asaka, Koji; Kato, Ryoei; Miyazawa, Kun'ichi; Kizuka, Tokushi

2006-08-01

The authors demonstrated the mechanics of materials for crystalline whiskers composed of C60 molecules; compressive deformation of the whiskers was observed by in situ transmission electron microscopy with simultaneous force measurement by means of an optical cantilever method, as used in atomic force microscopy. In response to compression along the long axis, the whiskers bent first elastically, then buckled. A whisker with 160nm diameter fractured brittlely at a strain of 0.08. According to Euler's formula, Young's modulus of the whisker was estimated to be 32-54GPa, which is 160%-650% of that of C60 bulk crystals.

Calculation of Centrally Loaded Thin-Walled Columns Above the Buckling Limit

NASA Technical Reports Server (NTRS)

Reinitzhuber, F.

1945-01-01

When thin-walled columns formed from flanged sheet, such as used in airplane construction, are subjected to axial load, their behavior at failure varies according to the slenderness ratio. On long columns the axis deflects laterally while the cross section form is maintained; buckling results. The respective breaking load in the elastic range is computed by Euler's formula and for the plastic range by the Engesser- Karman formula. Its magnitude is essentially dependent upon the length. On intermediate length columns, especially where open sections are concerned, the cross section is distorted while the cross section form is preserved; twisting failure results. The buckling load in twisting is calculated according to Wagner and Kappus. On short columns the straight walls of low-bending resistance that form the column are deflected at the same time that the cross section form changes - buckling occurs without immediate failure. Then the buckling load of the total section computable from the buckling loads of the section walls is not the ultimate load; quite often, especially on thin-walled sections, it lies considerably higher and is secured by tests. Both loads, the buckling and the ultimate load are only in a small measure dependent upon length. The present report is an attempt to theoretically investigate the behavior of such short, thin-walled columns above the buckling load with the conventional calculating methods.

The dynamic instability in the hook/flagellum system that triggers bacterial flicks

NASA Astrophysics Data System (ADS)

Jabbarzadeh, Mehdi; Fu, Henry

2017-11-01

Dynamical bending, buckling, and polymorphic transformations of the flagellum are known to affect bacterial motility, but run-reverse-flick motility of monotrichous bacteria also involves the even more flexible hook, which connects the flagellum to the cell body. Here, we identify the dynamic buckling mechanism that produces flicks in Vibrio alginolyticus. Estimates of forces and torques on the hook from experimental observations suggest that flicks are triggered at stresses below the hook's static Euler buckling criterion. Using an accurate linearization of the Kirchoff rod model for the hook in a model of a swimming bacterium with rigid flagellum, we show that as hook stiffness decreases there is a transition from on-axis flagellar rotation with small hook deflections to flagellar precession with large deflections. When flagellum flexibility is incorporated, the precession is disrupted by significant flagellar bending - i.e., incipient flicks. The predicted onset of dynamic instabilities corresponds well with experimentally observed flick events.

Study on axial strength of a channel-shaped pultruded GFRP member

NASA Astrophysics Data System (ADS)

Matsumoto, Yukihiro; Satake, Chito; Nisida, Kenji

2017-10-01

Fiber reinforced polymers (FRP) are widely used in vehicle and aerospace applications because of their lightweight and high-strength characteristics. Additionally, FRPs are increasingly applied to building structures. However, the elastic modulus of glass fiber reinforced polymers (GFRPs) is lower than that of steel. Hence, the evaluating the buckling strength of GFRP members for design purpose is necessary. The buckling strength is determined by Euler buckling mode as well as local buckling. In this study investigated the compressive strength of GFRP members subjected to axial compression through experiments and theoretical calculations. The adopted GFRP member was a channel-shaped GFRP, which was molded via pultrusion, at various lengths. Although, the mechanical properties as longitudinal elastic modulus and fiber volume fraction and strength of GFRP members subjected, to axial can be easily evaluated, evaluating transverse elastic modulus and shear modulus in typical material tests is difficult in standard section. Therefore the composite law was used in this study. As a result, we confirmed that the axial strength of a GFRP member could be calculated by a theoretical evaluation method utilizing longitudinal elastic modulus and fiber volume fraction.

Snap-buckling in asymmetrically constrained elastic strips

NASA Astrophysics Data System (ADS)

Sano, Tomohiko G.; Wada, Hirofumi

2018-01-01

When a flat elastic strip is compressed along its axis, it is bent in one of two possible directions via spontaneous symmetry breaking, forming a cylindrical arc. This is a phenomenon well known as Euler buckling. When this cylindrical section is pushed in the other direction, the bending direction can suddenly reverse. This instability is called "snap-through buckling" and is one of the elementary shape transitions in a prestressed thin structure. Combining experiments and theory, we study snap-buckling of an elastic strip with one end hinged and the other end clamped. These asymmetric boundary constraints break the intrinsic symmetry of the strip, generating mechanical behaviors, including largely hysteretic but reproducible force responses and switchlike discontinuous shape changes. We establish the set of exact analytical solutions to fully explain all our major experimental and numerical findings. Asymmetric boundary conditions arise naturally in diverse situations when a thin object is in contact with a solid surface at one end. The introduction of asymmetry through boundary conditions yields new insight into complex and programmable functionalities in material and industrial design.

Buckling of Low Arches or Curved Beams of Small Curvature

NASA Technical Reports Server (NTRS)

Fung, Y C; Kaplan, A

1952-01-01

A general solution, based on the classical buckling criterion, is given for the problem of buckling of low arches under a lateral loading acting toward the center of curvature. For a sinusoidal arch under sinusoidal loading, the critical load can be expressed exactly as a simple function of the beam dimension parameters. For other arch shapes and load distributions, approximate values of the critical load can be obtained by summing a few terms of a rapidly converging Fourier series. The effects of initial end thrust and axial and lateral elastic support are discussed. The buckling load based on energy criterion of Karman and Tsien is also calculated. Results for both the classical and the energy criteria are compared with experimental results.

A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

NASA Astrophysics Data System (ADS)

Kuehn, Christian

2013-06-01

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast-subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension-two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.

A new solution of measuring thermal response of prestressed concrete bridge girders for structural health monitoring

NASA Astrophysics Data System (ADS)

Jiao, Pengcheng; Borchani, Wassim; Hasni, Hassene; Lajnef, Nizar

2017-08-01

This study develops a novel buckling-based mechanism to measure the thermal response of prestressed concrete bridge girders under continuous temperature changes for structural health monitoring. The measuring device consists of a bilaterally constrained beam and a piezoelectric polyvinylidene fluoride transducer that is attached to the beam. Under thermally induced displacement, the slender beam is buckled. The post-buckling events are deployed to convert the low-rate and low-frequency excitations into localized high-rate motions and, therefore, the attached piezoelectric transducer is triggered to generate electrical signals. Attaching the measuring device to concrete bridge girders, the electrical signals are used to detect the thermal response of concrete bridges. Finite element simulations are conducted to obtain the displacement of prestressed concrete girders under thermal loads. Using the thermal-induced displacement as input, experiments are carried out on a 3D printed measuring device to investigate the buckling response and corresponding electrical signals. A theoretical model is developed based on the nonlinear Euler-Bernoulli beam theory and large deformation assumptions to predict the buckling mode transitions of the beam. Based on the presented theoretical model, the geometry properties of the measuring device can be designed such that its buckling response is effectively controlled. Consequently, the thermally induced displacement can be designed as limit states to detect excessive thermal loads on concrete bridge girders. The proposed solution sufficiently measures the thermal response of concrete bridges.

A Nonlinear Theory of Bending and Buckling of Thin Elastic Shallow Spherical Shells

NASA Technical Reports Server (NTRS)

Kaplan, A; Fung, Y C

1954-01-01

The problem of the finite displacement and buckling, of a shallow spherical dome is investigated both theoretically and experimentally. Experimental results seem to indicate that the classical criterion of buckling is applicable to very shallow spherical domes for which the theoretical calculation was made. A transition to energy criterion for higher domes is also indicated.

Filament instability under constant loads

NASA Astrophysics Data System (ADS)

Monastra, A. G.; Carusela, M. F.; D’Angelo, M. V.; Bruno, L.

2018-04-01

Buckling of semi-flexible filaments appears in different systems and scales. Some examples are: fibers in geophysical applications, microtubules in the cytoplasm of eukaryotic cells and deformation of polymers freely suspended in a flow. In these examples, instabilities arise when a system’s parameter exceeds a critical value, being the Euler force the most known. However, the complete time evolution and wavelength of buckling processes are not fully understood. In this work we solve analytically the time evolution of a filament under a constant compressive force in the small amplitude approximation. This gives an insight into the variable force scenario in terms of normal modes. The evolution is highly sensitive to the initial configuration and to the magnitude of the compressive load. This model can be a suitable approach to many different real situations.

Micron-scale pattern formation in prestressed polygonal films

NASA Astrophysics Data System (ADS)

Annabattula, R. K.; Onck, P. R.

2011-02-01

In this paper we explore the spontaneous formation of micropatterns in thin prestressed polygonal films using finite element simulations. We study films with different size, thickness, and shape, including square, rectangular, pentagonal, and hexagonal films. Patterns form when the films release the internal eigenstrain by buckling-up, after which the films bond-back to the substrate. After an initial symmetric evolution of the buckling profile, the symmetry of the deflection pattern breaks when the wavelength of wriggles near the film edges decreases. During bond back the deflection morphology converges to a fourfold, fivefold, and sixfold ridging pattern for the square, pentagonal and hexagonal films, respectively, showing a close resemblance with experimental film systems of similar size and shape. Rectangular films of large length to width ratio go through a transition in buckling shapes from the initial Euler mode, through the varicose mode into the antisymmetric telephone-cord mode. For all the film shapes, the ratio of the film height to the effective film width scales with the square root of eigenstrain and is independent of thickness. The bond-back mechanism determines the final wrinkle morphology and is governed by the eigenstrain value at the end of the buckling-up stage and the dimensionless parameter (Γ /EWeq)(Weq/t)3, relating the interface energy to the strain energy in the film.

A Revelation: Quantum-Statistics and Classical-Statistics are Analytic-Geometry Conic-Sections and Numbers/Functions: Euler, Riemann, Bernoulli Generating-Functions: Conics to Numbers/Functions Deep Subtle Connections

NASA Astrophysics Data System (ADS)

Descartes, R.; Rota, G.-C.; Euler, L.; Bernoulli, J. D.; Siegel, Edward Carl-Ludwig

2011-03-01

Quantum-statistics Dichotomy: Fermi-Dirac(FDQS) Versus Bose-Einstein(BEQS), respectively with contact-repulsion/non-condensation(FDCR) versus attraction/ condensationBEC are manifestly-demonstrated by Taylor-expansion ONLY of their denominator exponential, identified BOTH as Descartes analytic-geometry conic-sections, FDQS as Elllipse (homotopy to rectangle FDQS distribution-function), VIA Maxwell-Boltzmann classical-statistics(MBCS) to Parabola MORPHISM, VS. BEQS to Hyperbola, Archimedes' HYPERBOLICITY INEVITABILITY, and as well generating-functions[Abramowitz-Stegun, Handbook Math.-Functions--p. 804!!!], respectively of Euler-numbers/functions, (via Riemann zeta-function(domination of quantum-statistics: [Pathria, Statistical-Mechanics; Huang, Statistical-Mechanics]) VS. Bernoulli-numbers/ functions. Much can be learned about statistical-physics from Euler-numbers/functions via Riemann zeta-function(s) VS. Bernoulli-numbers/functions [Conway-Guy, Book of Numbers] and about Euler-numbers/functions, via Riemann zeta-function(s) MORPHISM, VS. Bernoulli-numbers/ functions, visa versa!!! Ex.: Riemann-hypothesis PHYSICS proof PARTLY as BEQS BEC/BEA!!!

The Scaling Group of the 1-D Invisicid Euler Equations

NASA Astrophysics Data System (ADS)

Schmidt, Emma; Ramsey, Scott; Boyd, Zachary; Baty, Roy

2017-11-01

The one dimensional (1-D) compressible Euler equations in non-ideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1-D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials.

Sequential buckling of an elastic wall

NASA Astrophysics Data System (ADS)

Bico, Jose; Bense, Hadrien; Keiser, Ludovic; Roman, Benoit; Melo, Francisco; Abkarian, Manouk

A beam under quasistatic compression classically buckles beyond a critical threshold. In the case of a free beam, the lowest buckling mode is selected. We investigate the case of a long ``wall'' grounded of a compliant base and compressed in the axial compression. In the case of a wall of slender rectangular cross section, the selected buckling mode adopts a nearly fixed wavelength proportional to the height of the wall. Higher compressive loads only increase the amplitude of the buckle. However if the cross section has a sharp shape (such as an Eiffel tower profile), we observe successive buckling modes of increasing wavelength. We interpret this unusual evolution in terms of scaling arguments. At small scales, this variable periodicity might be used to develop tunable optical devices. We thank ECOS C12E07, CNRS-CONICYT, and Fondecyt Grant No. N1130922 for partially funding this work.

Euler buckling-induced folding and rotation of red blood cells in an optical trap

NASA Astrophysics Data System (ADS)

Ghosh, A.; Sinha, Supurna; Dharmadhikari, J. A.; Roy, S.; Dharmadhikari, A. K.; Samuel, J.; Sharma, S.; Mathur, D.

2006-03-01

We investigate the physics of an optically driven micromotor of biological origin. When a single, live red blood cell (RBC) is placed in an optical trap, the normal biconcave disc shape of the cell is observed to fold into a rod-like shape. If the trapping laser beam is circularly polarized, the folded RBC rotates. A model based on geometric considerations, using the concept of buckling instabilities, captures the folding phenomenon; the rotation of the cell is rationalized using the Poincaré sphere. Our model predicts that (i) at a critical power of the trapping laser beam the RBC shape undergoes large fluctuations, and (ii) the torque that is generated is proportional to the power of the laser beam. These predictions are verified experimentally. We suggest a possible mechanism for the emergence of birefringent properties in the RBC in the folded state.

Failure Processes in Embedded Monolayer Graphene under Axial Compression

PubMed Central

Androulidakis, Charalampos; Koukaras, Emmanuel N.; Frank, Otakar; Tsoukleri, Georgia; Sfyris, Dimitris; Parthenios, John; Pugno, Nicola; Papagelis, Konstantinos; Novoselov, Kostya S.; Galiotis, Costas

2014-01-01

Exfoliated monolayer graphene flakes were embedded in a polymer matrix and loaded under axial compression. By monitoring the shifts of the 2D Raman phonons of rectangular flakes of various sizes under load, the critical strain to failure was determined. Prior to loading care was taken for the examined area of the flake to be free of residual stresses. The critical strain values for first failure were found to be independent of flake size at a mean value of –0.60% corresponding to a yield stress up to -6 GPa. By combining Euler mechanics with a Winkler approach, we show that unlike buckling in air, the presence of the polymer constraint results in graphene buckling at a fixed value of strain with an estimated wrinkle wavelength of the order of 1–2 nm. These results were compared with DFT computations performed on analogue coronene/PMMA oligomers and a reasonable agreement was obtained. PMID:24920340

Giant and Tunable Anisotropy of Nanoscale Friction in Graphene

NASA Astrophysics Data System (ADS)

Capaz, Rodrigo; Menezes, Marcos; Almeida, Clara; de Cicco, Marcelo; Achete, Carlos; Fragneaud, Benjamin; Cançado, Luiz Gustavo; Paupitz, Ricardo; Galvão, Douglas; Prioli, Rodrigo

The nanoscale friction between an atomic force microscopy tip and graphene is investigated using friction force microscopy (FFM). During the tip movement, friction forces are observed to increase and then saturate in a highly anisotropic manner. As a result, the friction coefficient of graphene is highly dependent on the scanning direction: Under some conditions, the energy dissipated along the armchair direction can be 80% higher than along the zigzag direction. In comparison, for highly-oriented pyrolitic graphite (HOPG), the friction anisotropy between armchair and zigzag directions is only 15%. This giant friction anisotropy in graphene results from anisotropies in the amplitudes of flexural deformations of the graphene sheet driven by the tip movement, not present in HOPG. The effect can be seen as a novel manifestation of the classical phenomenon of Euler buckling at the nanoscale, which provides the non-linear ingredients that amplify friction anisotropy. Simulations based on a novel version of the 2D Tomlinson model (modified to include the effects of flexural deformations), as well as fully atomistic molecular dynamics simulations and first-principles density-functional theory (DFT) calculations, are able to reproduce and explain the experimental observations.

Giant and Tunable Anisotropy of Nanoscale Friction in Graphene

NASA Astrophysics Data System (ADS)

Almeida, Clara M.; Prioli, Rodrigo; Fragneaud, Benjamin; Cançado, Luiz Gustavo; Paupitz, Ricardo; Galvão, Douglas S.; de Cicco, Marcelo; Menezes, Marcos G.; Achete, Carlos A.; Capaz, Rodrigo B.

2016-08-01

The nanoscale friction between an atomic force microscopy tip and graphene is investigated using friction force microscopy (FFM). During the tip movement, friction forces are observed to increase and then saturate in a highly anisotropic manner. As a result, the friction forces in graphene are highly dependent on the scanning direction: under some conditions, the energy dissipated along the armchair direction can be 80% higher than along the zigzag direction. In comparison, for highly-oriented pyrolitic graphite (HOPG), the friction anisotropy between armchair and zigzag directions is only 15%. This giant friction anisotropy in graphene results from anisotropies in the amplitudes of flexural deformations of the graphene sheet driven by the tip movement, not present in HOPG. The effect can be seen as a novel manifestation of the classical phenomenon of Euler buckling at the nanoscale, which provides the non-linear ingredients that amplify friction anisotropy. Simulations based on a novel version of the 2D Tomlinson model (modified to include the effects of flexural deformations), as well as fully atomistic molecular dynamics simulations and first-principles density-functional theory (DFT) calculations, are able to reproduce and explain the experimental observations.

Postbuckling response of long thick plates loaded in compression including higher order transverse shearing effects

NASA Technical Reports Server (NTRS)

Stein, Manuel; Sydow, P. Daniel; Librescu, Liviu

1990-01-01

Buckling and postbuckling results are presented for compression-loaded simply-supported aluminum plates and composite plates with a symmetric lay-up of thin + or - 45 deg plies composed of many layers. Buckling results for aluminum plates of finite length are given for various length-to-width ratios. Asymptotes to the curves based on buckling results give N(sub xcr) for plates of infinite length. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: Classical von Karman theory using the Kirchoff assumptions, first-order shear deformation theory, higher-order shear deformation theory, and 3-D flexibility theory. Present results indicate that the 3-D flexibility theory gives the lowest buckling loads. The higher-order shear deformation theory has fewer unknowns than the 3-D flexibility theory but does not take into account through-the-thickness effects. The figures presented show that small differences occur in the average longitudinal direct stress resultants from the four theories that are functions of applied end-shortening displacement.

Analogies of the classical Euler top with a rotor to spin squeezing and quantum phase transitions in a generalized Lipkin-Meshkov-Glick model.

PubMed

Opatrný, Tomáš; Richterek, Lukáš; Opatrný, Martin

2018-01-31

We show that the classical model of Euler top (freely rotating, generally asymmetric rigid body), possibly supplemented with a rotor, corresponds to a generalized Lipkin-Meshkov-Glick (LMG) model describing phenomena of various branches of quantum physics. Classical effects such as free precession of a symmetric top, Feynman's wobbling plate, tennis-racket instability and the Dzhanibekov effect, attitude control of satellites by momentum wheels, or twisting somersault dynamics, have their counterparts in quantum effects that include spin squeezing by one-axis twisting and two-axis countertwisting, transitions between the Josephson and Rabi regimes of a Bose-Einstein condensate in a double-well potential, and other quantum critical phenomena. The parallels enable us to expand the range of explored quantum phase transitions in the generalized LMG model, as well as to present a classical analogy of the recently proposed LMG Floquet time crystal.

Structural design criteria for filament-wound composite shells

NASA Technical Reports Server (NTRS)

Hahn, H. T.; Jensen, D. W.; Claus, S. J.; Pai, S. P.; Hipp, P. A.

1994-01-01

Advanced composite cylinders, manufactured by filament winding, provide a cost effective solution to many present structural applications; however, the compressive performance of filament-wound cylinders is lower than comparable shells fabricated from unidirectional tape. The objective of this study was to determine the cause of this reduction in thin filament-wound cylinders by relating the manufacturing procedures to the quality of the cylinder and to its compressive performance. The experiments on cylinder buckling were complemented by eigenvalue buckling analysis using a detailed geometric model in a finite element analysis. The applicability of classical buckling analyses was also investigated as a design tool.

Effects of thermal noise on the transitional dynamics of an inextensible elastic filament in stagnation flow.

PubMed

Deng, Mingge; Grinberg, Leopold; Caswell, Bruce; Karniadakis, George Em

2015-06-28

We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a dissipative particle dynamics (DPD) method. Unlike previous works, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance.

Lagrangians and Euler morphisms from connections on the frame bundle

NASA Astrophysics Data System (ADS)

Kurek, J.; Mikulski, W. M.

2011-07-01

We classify all natural operators transforming torsion free classical linear connections ∇ on m-dimensional manifolds M into r-th order Lagrangians λ(∇) and Euler morphisms E(∇) on the linear frame bundle P1M. We also briefly write how this classification result can be generalized on higher order frame bundles PkM instead of P1M.

Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing

NASA Astrophysics Data System (ADS)

Baumgarten, Lorenz; Kierfeld, Jan

2018-05-01

We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Above a critical uniform pressure, an elastic capsule becomes mechanically unstable and spontaneously buckles into a shape with an axisymmetric dimple. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Košmrlj and Nelson, Phys. Rev. X 7, 011002 (2017), 10.1103/PhysRevX.7.011002]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations, the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Remarkably, both parameter renormalization and thermal activation lead to the same parameter dependence of the critical buckling pressure on temperature, capsule radius and thickness, and Young's modulus. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy barrier in thermal activation to obtain our final result for the temperature-dependent critical pressure, which is significantly below the results if only parameter renormalization or only thermal activation is considered.

The Sizing and Optimization Language (SOL): A computer language to improve the user/optimizer interface

NASA Technical Reports Server (NTRS)

Lucas, S. H.; Scotti, S. J.

1989-01-01

The nonlinear mathematical programming method (formal optimization) has had many applications in engineering design. A figure illustrates the use of optimization techniques in the design process. The design process begins with the design problem, such as the classic example of the two-bar truss designed for minimum weight as seen in the leftmost part of the figure. If formal optimization is to be applied, the design problem must be recast in the form of an optimization problem consisting of an objective function, design variables, and constraint function relations. The middle part of the figure shows the two-bar truss design posed as an optimization problem. The total truss weight is the objective function, the tube diameter and truss height are design variables, with stress and Euler buckling considered as constraint function relations. Lastly, the designer develops or obtains analysis software containing a mathematical model of the object being optimized, and then interfaces the analysis routine with existing optimization software such as CONMIN, ADS, or NPSOL. This final state of software development can be both tedious and error-prone. The Sizing and Optimization Language (SOL), a special-purpose computer language whose goal is to make the software implementation phase of optimum design easier and less error-prone, is presented.

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.

On the Local Type I Conditions for the 3D Euler Equations

NASA Astrophysics Data System (ADS)

Chae, Dongho; Wolf, Jörg

2018-05-01

We prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution {v\\in L^∞ (-1,0; L^2 ( B(x_0,r)))\\cap L^∞_{loc} (-1,0; W^{1, ∞} (B(x_0, r)))} of the 3D Euler equations, where {B(x_0,r)} is the ball with radius r and the center at x 0, if the limiting values of certain scale invariant quantities for a solution v(·, t) as {t\\to 0} are small enough, then { \

Axion as a cold dark matter candidate: analysis to third order perturbation for classical axion

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

Noh, Hyerim; Hwang, Jai-chan; Park, Chan-Gyung, E-mail: hr@kasi.re.kr, E-mail: jchan@knu.ac.kr, E-mail: park.chan.gyung@gmail.com

2015-12-01

We investigate aspects of axion as a coherently oscillating massive classical scalar field by analyzing third order perturbations in Einstein's gravity in the axion-comoving gauge. The axion fluid has its characteristic pressure term leading to an axion Jeans scale which is cosmologically negligible for a canonical axion mass. Our classically derived axion pressure term in Einstein's gravity is identical to the one derived in the non-relativistic quantum mechanical context in the literature. We present the general relativistic continuity and Euler equations for an axion fluid valid up to third order perturbation. Equations for axion are exactly the same as thatmore » of a zero-pressure fluid in Einstein's gravity except for an axion pressure term in the Euler equation. Our analysis includes the cosmological constant.« less

Buckling analysis for axially compressed flat plates, structural sections, and stiffened plates reinforced with laminated composites

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Soong, T.; Miller, R. E., Jr.

1971-01-01

A classical buckling analysis is developed for stiffened, flat plates composed of a series of linked plate and beam elements. Plates are idealized as multilayered orthotropic elements. Structural beads and lips are idealized as beams. The loaded edges of the stiffened plate are simply-supported and the conditions at the unloaded edges can be prescribed arbitrarily. The plate and beam elements are matched along their common junctions for displacement continuity and force equilibrium in an exact manner. Offsets between elements are considered in the analysis. Buckling under uniaxial compressive load for plates, sections, and stiffened plates is investigated. Buckling loads are the lowest of all possible general and local failure modes, and the mode shape is used to determine whether buckling is a local or general instability. Numerical correlations with existing analysis and test data for plates, sections, and stiffened plates including boron-reinforced structures are discussed. In general correlations are reasonably good.

Buckling analysis for structural sections and stiffened plates reinforced with laminated composites.

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Soong, T.-C.; Miller, R. E., Jr.

1972-01-01

A classical buckling analysis is developed for stiffened, flat plates composed of a series of linked flat plate and beam elements. Plates are idealized as multilayered orthotropic elements; structural beads and lips are idealized as beams. The loaded edges of the stiffened plate are simply supported and the conditions at the unloaded edges can be prescribed arbitrarily. The plate and beam elements are matched along their common junctions for displacement continuity and force equilibrium in an exact manner. Offsets between elements are considered in the analysis. Buckling under uniaxial compressive load for plates, sections and stiffened plates is investigated. Buckling loads are found as the lowest of all possible general and local failure modes and the mode shape is used to determine whether buckling is a local or general instability. Numerical correlations with existing analysis and test data for plates, sections and stiffened plates including boron-reinforced structures are discussed. In general, correlations are reasonably good.

Generic buckling curves for specially orthotropic rectangular plates

NASA Technical Reports Server (NTRS)

Brunnelle, E. J.; Oyibo, G. A.

1983-01-01

Using a double affine transformation, the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion. These dual representations are characterized by a single material constant, called the generalized rigidity ratio, whose range is predicted to be the closed interval from 0 to 1 (if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect); when natural boundary conditions are considered a generalized Poisson's ratio is introduced. Thus the buckling results are valid for any specially orthotropic material; hence the curves presented in the text are generic rather than specific. The solution trends are twofold; the buckling coefficients decrease with decreasing generalized rigidity ratio and, when applicable, they decrease with increasing generalized Poisson's ratio. Since the isotropic plate is one limiting case of the above analysis, it is also true that isotropic buckling coefficients decrease with increasing Poission's ratio.

Lateral Torsional Buckling of Anisotropic Laminated Composite Beams Subjected to Various Loading and Boundary Conditions

NASA Astrophysics Data System (ADS)

Ahmadi, Habiburrahman

Thin-walled structures are major components in many engineering applications. When a thin-walled slender beam is subjected to lateral loads, causing moments, the beam may buckle by a combined lateral bending and twisting of cross-section, which is called lateral-torsional buckling. A generalized analytical approach for lateral-torsional buckling of anisotropic laminated, thin-walled, rectangular cross-section composite beams under various loading conditions (namely, pure bending and concentrated load) and boundary conditions (namely, simply supported and cantilever) was developed using the classical laminated plate theory (CLPT), with all considered assumptions, as a basis for the constitutive equations. Buckling of such type of members has not been addressed in the literature. Closed form buckling expressions were derived in terms of the lateral, torsional and coupling stiffness coefficients of the overall composite. These coefficients were obtained through dimensional reduction by static condensation of the 6x6 constitutive matrix mapped into an effective 2x2 coupled weak axis bending-twisting relationship. The stability of the beam under different geometric and material parameters, like length/height ratio, ply thickness, and ply orientation, was investigated. The analytical formulas were verified against finite element buckling solutions using ABAQUS for different lamination orientations showing excellent accuracy.

Comprehensive nonlocal analysis of piezoelectric nanobeams with surface effects in bending, buckling and vibrations under magneto-electro-thermo-mechanical loading

NASA Astrophysics Data System (ADS)

Ebrahimi-Nejad, Salman; Boreiry, Mahya

2018-03-01

The bending, buckling and vibrational behavior of size-dependent piezoelectric nanobeams under thermo-magneto-mechano-electrical environment are investigated by performing a parametric study, in the presence of surface effects. The Gurtin-Murdoch surface elasticity and Eringen’s nonlocal elasticity theories are applied in the framework of Euler–Bernoulli beam theory to obtain a new non-classical size-dependent beam model for dynamic and static analyses of piezoelectric nanobeams. In order to satisfy the surface equilibrium equations, cubic variation of stress with beam thickness is assumed for the bulk stress component which is neglected in classical beam models. Results are obtained for clamped - simply-supported (C-S) and simply-supported - simply-supported (S-S) boundary conditions using a proposed analytical solution method. Numerical examples are presented to demonstrate the effects of length, surface effects, nonlocal parameter and environmental changes (temperature, magnetic field and external voltage) on deflection, critical buckling load and natural frequency for each boundary condition. Results of this study can serve as benchmarks for the design and analysis of nanostructures of magneto-electro-thermo-elastic materials.

Recent advances in nonlinear passive vibration isolators

NASA Astrophysics Data System (ADS)

Ibrahim, R. A.

2008-07-01

The theory of nonlinear vibration isolation has witnessed significant developments due to pressing demands for the protection of structural installations, nuclear reactors, mechanical components, and sensitive instruments from earthquake ground motion, shocks, and impact loads. In view of these demands, engineers and physicists have developed different types of nonlinear vibration isolators. This article presents a comprehensive assessment of recent developments of nonlinear isolators in the absence of active control means. It does not deal with other means of linear or nonlinear vibration absorbers. It begins with the basic concept and features of nonlinear isolators and inherent nonlinear phenomena. Specific types of nonlinear isolators are then discussed, including ultra-low-frequency isolators. For vertical vibration isolation, the treatment of the Euler spring isolator is based on the post-buckling dynamic characteristics of the column elastica and axial stiffness. Exact and approximate analyses of axial stiffness of the post-buckled Euler beam are outlined. Different techniques of reducing the resonant frequency of the isolator are described. Another group is based on the Gospodnetic-Frisch-Fay beam, which is free to slide on two supports. The restoring force of this beam resembles to a great extent the restoring roll moment of biased ships. The base isolation of buildings, bridges, and liquid storage tanks subjected to earthquake ground motion is then described. Base isolation utilizes friction elements, laminated-rubber bearings, and the friction pendulum. Nonlinear viscoelastic and composite material springs, and smart material elements are described in terms of material mechanical characteristics and the dependence of their transmissibility on temperature and excitation amplitude. The article is closed by conclusions, which highlight resolved and unresolved problems and recommendations for future research directions.

Spherical shells buckling to the sound of music

NASA Astrophysics Data System (ADS)

Lee, Anna; Marthelot, Joel; Reis, Pedro

We study how the critical buckling load of spherical elastic shells can be modified by a fluctuating external pressure field. In our experiments, we employ thin elastomeric shells of nearly uniform thickness fabricated by the coating of a hemispherical mold with a polymer solution, which upon curing yields elastic structures. A shell is submerged in a water bath and loaded quasi-statically until buckling occurs by reducing its inner volume with a syringe pump. Simultaneously, a plunger connected to an electromagnetic shaker is placed above the shell and driven sinusoidally to create a fluctuating external pressure field that can excite dynamic vibration modes of the shell. These dynamic modes induce effective compressive stresses, in addition to those from the inner pressure loading, which can modify the critical conditions for the onset of buckling. We systematically quantify how the frequency and amplitude of the external driving affects the buckling strength of our shells. In specific regions of the parameter space, we find that pressure fluctuations can result in large reductions of the critical buckling pressure. This is analogous to the classic knock-down effect in shells due to intrinsic geometric imperfections, albeit now in a way that can be controlled externally.

Voidage correction algorithm for unresolved Euler-Lagrange simulations

NASA Astrophysics Data System (ADS)

Askarishahi, Maryam; Salehi, Mohammad-Sadegh; Radl, Stefan

2018-04-01

The effect of grid coarsening on the predicted total drag force and heat exchange rate in dense gas-particle flows is investigated using Euler-Lagrange (EL) approach. We demonstrate that grid coarsening may reduce the predicted total drag force and exchange rate. Surprisingly, exchange coefficients predicted by the EL approach deviate more significantly from the exact value compared to results of Euler-Euler (EE)-based calculations. The voidage gradient is identified as the root cause of this peculiar behavior. Consequently, we propose a correction algorithm based on a sigmoidal function to predict the voidage experienced by individual particles. Our correction algorithm can significantly improve the prediction of exchange coefficients in EL models, which is tested for simulations involving Euler grid cell sizes between 2d_p and 12d_p . It is most relevant in simulations of dense polydisperse particle suspensions featuring steep voidage profiles. For these suspensions, classical approaches may result in an error of the total exchange rate of up to 30%.

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

PubMed

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Failure of flight feathers under uniaxial compression.

PubMed

Schelestow, Kristina; Troncoso, Omar P; Torres, Fernando G

2017-09-01

Flight feathers are light weight engineering structures. They have a central shaft divided in two parts: the calamus and the rachis. The rachis is a thinly walled conical shell filled with foam, while the calamus is a hollow tube-like structure. Due to the fact that bending loads are produced during birds' flight, the resistance to bending of feathers has been reported in different studies. However, the analysis of bent feathers has shown that compression could induce failure by buckling. Here, we have studied the compression of feathers in order to assess the failure mechanisms involved. Axial compression tests were carried out on the rachis and the calamus of dove and pelican feathers. The failure mechanisms and folding structures that resulted from the compression tests were observed from images obtained by scanning electron microscopy (SEM). The rachis and calamus fail due to structural instability. In the case of the calamus, this instability leads to a progressive folding process. In contrast, the rachis undergoes a typical Euler column-type buckling failure. The study of failed specimens showed that delamination buckling, cell collapse and cell densification are the primary failure mechanisms of the rachis structure. The role of the foam is also discussed with regard to the mechanical response of the samples and the energy dissipated during the compression tests. Critical stress values were calculated using delamination buckling models and were found to be in very good agreement with the experimental values measured. Failure analysis and mechanical testing have confirmed that flight feathers are complex thin walled structures with mechanical adaptations that allow them to fulfil their functions. Copyright © 2017 Elsevier B.V. All rights reserved.

Effects of Thermal Noise on the Transitional Dynamics of an Inextensible Elastic Filament in Stagnation Flow

PubMed Central

Deng, Mingge; Grinberg, Leopold; Caswell, Bruce

2015-01-01

We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a Dissipative Particle Dynamics (DPD) method. Unlike previous works1, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance. PMID:26023834

Thin film flow along a periodically-stretched elastic beam

NASA Astrophysics Data System (ADS)

Boamah Mensah, Chris; Chini, Greg; Jensen, Oliver

2017-11-01

Motivated by an application to pulmonary alveolar micro-mechanics, a system of partial differential equations is derived that governs the motion of a thin liquid film lining both sides of an inertia-less elastic substrate. The evolution of the film mass distribution is described by invoking the usual lubrication approximation while the displacement of the substrate is determined by employing a kinematically nonlinear Euler-Bernoulli beam formulation. In the parameter regime of interest, the axial strain can be readily shown to be a linear function of arc-length specified completely by the motion of ends of the substrate. In contrast, the normal force balance on the beam yields an equation for the substrate curvature that is fully coupled to the time-dependent lubrication equation. Linear analyses of both a stationary and periodically-stretched flat substrate confirm the potential for buckling instabilities and reveal an upper bound on the dimensionless axial stiffness for which the coupled thin-film/inertial-less-beam model is well-posed. Numerical simulations of the coupled system are used to explore the nonlinear development of the buckling instabilities.

An approximation method for configuration optimization of trusses

NASA Technical Reports Server (NTRS)

Hansen, Scott R.; Vanderplaats, Garret N.

1988-01-01

Two- and three-dimensional elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints. Constraints on member stresses and Euler buckling are imposed and multiple static loading conditions are considered. The method presented here utilizes an approximate structural analysis based on first order Taylor series expansions of the member forces. A numerical optimizer minimizes the weight of the truss using information from the approximate structural analysis. Comparisons with results from other methods are made. It is shown that the method of forming an approximate structural analysis based on linearized member forces leads to a highly efficient method of truss configuration optimization.

Buckling of pressure-loaded, long, shear deformable, cylindrical laminated shells

NASA Astrophysics Data System (ADS)

Anastasiadis, John S.; Simitses, George J.

A higher-order shell theory was developed (kinematic relations, constitutive relations, equilibrium equations and boundary conditions), which includes initial geometric imperfections and transverse shear effects for a laminated cylindrical shell under the action of pressure, axial compression and in-plane shear. Through the perturbation technique, buckling equations are derived for the corresponding 'perfect geometry' symmetric laminated configuration. Critical pressures are computed for very long cylinders for several stacking sequences, several radius-to-total-thickness ratios, three lamina materials (boron/epoxy, graphite/epoxy, and Kevlar/epoxy), and three shell theories: classical, first-order shear deformable and higher- (third-)order shear deformable. The results provide valuable information concerning the applicability (accurate prediction of buckling pressures) of the various shell theories.

How tall can gelatin towers be? An introduction to elasticity and buckling

NASA Astrophysics Data System (ADS)

Taberlet, Nicolas; Ferrand, Jérémy; Camus, Élise; Lachaud, Léa; Plihon, Nicolas

2017-12-01

The stability of elastic towers is studied through simple hands-on experiments. Using gelatin-based stackable bricks, one can investigate the maximum height a simple structure can reach before collapsing. We show through experiments and by using the classical linear elastic theory that the main limitation to the height of such towers is the buckling of the elastic structures under their own weight. Moreover, the design and architecture of the towers can be optimized to greatly improve their resistance to self-buckling. To this aim, the maximum height of hollow and tapered towers is investigated. The experimental and theoretical developments presented in this paper can help students grasp the fundamental concepts in elasticity and mechanical stability.

Kinks and antikinks of buckled graphene: A testing ground for the φ4 field model

NASA Astrophysics Data System (ADS)

Yamaletdinov, R. D.; Slipko, V. A.; Pershin, Y. V.

2017-09-01

Kinks and antikinks of the classical φ4 field model are topological solutions connecting its two distinct ground states. Here we establish an analogy between the excitations of a long graphene nanoribbon buckled in the transverse direction and φ4 model results. Using molecular dynamics simulations, we investigated the dynamics of a buckled graphene nanoribbon with a single kink and with a kink-antikink pair. Several features of the φ4 model have been observed including the kink-antikink capture at low energies, kink-antikink reflection at high energies, and a bounce resonance. Our results pave the way towards the experimental observation of a rich variety of φ4 model predictions based on graphene.

The general solution to the classical problem of finite Euler Bernoulli beam

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Amba-Rao, C. L.

1977-01-01

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

BUCKO- A BUCKLING ANALYSIS FOR RECTANGULAR PLATES WITH CENTRALLY LOCATED CUTOUTS

NASA Technical Reports Server (NTRS)

Nemeth, M. P.

1994-01-01

BUCKO is a computer program developed to predict the buckling load of a rectangular compression-loaded orthotropic plate with a centrally located cutout. The plate is assumed to be a balanced, symmetric laminate of uniform thickness. The cutout shape can be elliptical, circular, rectangular, or square. The BUCKO package includes sample data that demonstrates the essence of the program and its ease of usage. BUCKO uses an approximate one-dimensional formulation of the classical two-dimensional buckling problem following the Kantorovich method. The boundary conditions are considered to be simply supported unloaded edges and either clamped or simply supported loaded edges. The plate is loaded in uniaxial compression by either uniformly displacing or uniformly stressing two opposite edges of the plate. The BUCKO analysis consists of two parts: calculation of the inplane stress distribution prior to buckling, and calculation of the plate axial load and displacement at buckling. User input includes plate planform and cutout geometry, plate membrane and bending stiffnesses, finite difference parameters, boundary condition data, and loading data. Results generated by BUCKO are the prebuckling strain energy, inplane stress resultants, buckling mode shape, critical end shortening, and average axial and transverse strains at buckling. BUCKO is written in FORTRAN V for batch execution and has been implemented on a CDC CYBER 170 series computer operating under NOS with a central memory requirement of approximately 343K of 60 bit words. This program was developed in 1984 and was last updated in 1990.

Periodic buckling of constrained cylindrical elastic shells

NASA Astrophysics Data System (ADS)

Marthelot, Joel; Brun, Pierre-Thomas; Lopez Jimenez, Francisco; Reis, Pedro M.

We revisit the classic problem of buckling of a thin cylindrical elastic shell loaded either by pneumatic depressurization or axial compression. The control of the resulting dimpled pattern is achieved by using a concentric inner rigid mandrel that constrains and stabilizes the post-buckling response. Under axial compression, a regular lattice of diamond-like dimples appears sequentially on the surface of the shell to form a robust spatially extended periodic pattern. Under pressure loading, a periodic array of ridges facets the surface of the elastic cylindrical shell. The sharpness of these ridges can be readily varied and controlled through a single scalar parameter, the applied pressure. A combination of experiments, simulations and scaling analyses is used to rationalize the combined role of geometry and mechanics in the nucleation and evolution of the diamond-like dimples and ridges networks.

Buckling Analysis for Stiffened Anisotropic Circular Cylinders Based on Sanders Nonlinear Shell Theory

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2014-01-01

Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.

From wrinkling to global buckling of a ring on a curved substrate

NASA Astrophysics Data System (ADS)

Lagrange, R.; López Jiménez, F.; Terwagne, D.; Brojan, M.; Reis, P. M.

2016-04-01

We present a combined analytical approach and numerical study on the stability of a ring bound to an annular elastic substrate, which contains a circular cavity. The system is loaded by depressurizing the inner cavity. The ring is modeled as an Euler-Bernoulli beam and its equilibrium equations are derived from the mechanical energy which takes into account both stretching and bending contributions. The curvature of the substrate is considered explicitly to model the work done by its reaction force on the ring. We distinguish two different instabilities: periodic wrinkling of the ring or global buckling of the structure. Our model provides an expression for the critical pressure, as well as a phase diagram that rationalizes the transition between instability modes. Towards assessing the role of curvature, we compare our results for the critical stress and the wrinkling wavelength to their planar counterparts. We show that the critical stress is insensitive to the curvature of the substrate, while the wavelength is only affected due to the permissible discrete values of the azimuthal wavenumber imposed by the geometry of the problem. Throughout, we contrast our analytical predictions against finite element simulations.

Non-dispersive conservative regularisation of nonlinear shallow water (and isentropic Euler equations)

NASA Astrophysics Data System (ADS)

Clamond, Didier; Dutykh, Denys

2018-02-01

A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and posses a variational structure; thus, the mass, the momentum and the energy are conserved. Hence, for instance, regularised hydraulic jumps are smooth and non-oscillatory. Another particularly interesting feature of this regularisation is that smoothed 'shocks' propagates at exactly the same speed as the original discontinuous ones. The performance of the new model is illustrated numerically on some dam-break test cases, which are classical in the hyperbolic realm.

Model-size reduction for the buckling and vibration analyses of anisotropic panels

NASA Technical Reports Server (NTRS)

Noor, A. K.; Whitworth, S. L.

1986-01-01

A computational procedure is presented for reducing the size of the model used in the buckling and vibration analyses of symmetric anisotropic panels to that of the corresponding orthotropic model. The key elements of the procedure are the application of an operator splitting technique through the decomposition of the material stiffness matrix of the panel into the sum of orthotropic and nonorthotropic (anisotropic) parts and the use of a reduction method through successive application of the finite element method and the classical Rayleigh-Ritz technique. The effectiveness of the procedure is demonstrated by numerical examples.

Cell prestress. II. Contribution of microtubules

NASA Technical Reports Server (NTRS)

Stamenovic, Dimitrije; Mijailovich, Srboljub M.; Tolic-Norrelykke, Iva Marija; Chen, Jianxin; Wang, Ning; Ingber, D. E. (Principal Investigator)

2002-01-01

The tensegrity model hypothesizes that cytoskeleton-based microtubules (MTs) carry compression as they balance a portion of cell contractile stress. To test this hypothesis, we used traction force microscopy to measure traction at the interface of adhering human airway smooth muscle cells and a flexible polyacrylamide gel substrate. The prediction is that if MTs balance a portion of contractile stress, then, upon their disruption, the portion of stress balanced by MTs would shift to the substrate, thereby causing an increase in traction. Measurements were done first in maximally activated cells (10 microM histamine) and then again after MTs had been disrupted (1 microM colchicine). We found that after disruption of MTs, traction increased on average by approximately 13%. Because in activated cells colchicine induced neither an increase in intracellular Ca(2+) nor an increase in myosin light chain phosphorylation as shown previously, we concluded that the observed increase in traction was a result of load shift from MTs to the substrate. In addition, energy stored in the flexible substrate was calculated as work done by traction on the deformation of the substrate. This result was then utilized in an energetic analysis. We assumed that cytoskeleton-based MTs are slender elastic rods supported laterally by intermediate filaments and that MTs buckle as the cell contracts. Using the post-buckling equilibrium theory of Euler struts, we found that energy stored during buckling of MTs was quantitatively consistent with the measured increase in substrate energy after disruption of MTs. This is further evidence supporting the idea that MTs are intracellular compression-bearing elements.

Simulating Thin Sheets: Buckling, Wrinkling, Folding and Growth

NASA Astrophysics Data System (ADS)

Vetter, Roman; Stoop, Norbert; Wittel, Falk K.; Herrmann, Hans J.

2014-03-01

Numerical simulations of thin sheets undergoing large deformations are computationally challenging. Depending on the scenario, they may spontaneously buckle, wrinkle, fold, or crumple. Nature's thin tissues often experience significant anisotropic growth, which can act as the driving force for such instabilities. We use a recently developed finite element model to simulate the rich variety of nonlinear responses of Kirchhoff-Love sheets. The model uses subdivision surface shape functions in order to guarantee convergence of the method, and to allow a finite element description of anisotropically growing sheets in the classical Rayleigh-Ritz formalism. We illustrate the great potential in this approach by simulating the inflation of airbags, the buckling of a stretched cylinder, as well as the formation and scaling of wrinkles at free boundaries of growing sheets. Finally, we compare the folding of spatially confined sheets subject to growth and shrinking confinement to find that the two processes are equivalent.

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.

A new local thickening reverse spiral origami thin-wall construction for improving of energy absorption

NASA Astrophysics Data System (ADS)

Kong, C. H.; Zhao, X. L.; Hagiwara, I. R.

2018-02-01

As an effective and representative origami structure, reverse spiral origami structure can be capable to effectively take up energy in a crash test. The origami structure has origami creases thus this can guide the deformation of structure and avoid of Euler buckling. Even so the origami creases also weaken the support force and this may cut the absorption of crash energy. In order to increase the supporting capacity of the reverse spiral origami structure, we projected a new local thickening reverse spiral origami thin-wall construction. The reverse spiral origami thin-wall structure with thickening areas distributed along the longitudinal origami crease has a higher energy absorption capacity than the ordinary reverse spiral origami thin-wall structure.

Experimental Nonlinear Dynamics and Snap-Through of Post-Buckled Thin Laminated Composite Plates

NASA Astrophysics Data System (ADS)

Kim, Han-Gyu

Modern aerospace systems are increasingly being designed with composite panels and plates to achieve light weight and high specific strength and stiffness. For constrained panels, thermally-induced axial loading may cause buckling of the structure, which can lead to nonlinear and potentially chaotic behavior. When post-buckled composite plates experience snap-through, they are subjected to large-amplitude deformations and in-plane compressive loading. These phenomena pose a potential threat to the structural integrity of composite structures. In this work, the nonlinear dynamic behavior of post-buckled composite plates was investigated experimentally and computationally. For the experimental work, an electrodynamic shaker was used to apply harmonic loads and the dynamic response of plate specimens was measured using a single-point displacement-sensing laser, a double-point laser vibrometer (velocity-sensing), and a set of digital image correlation cameras. Both chaotic and periodic steady-state snap-through behaviors were investigated. The experimental data were used to characterize snap-through behaviors of the post-buckled specimens and their boundaries in the harmonic forcing parameter space. The nonlinear behavior of post-buckled plates was modeled using the classical laminated plate theory (CLPT) and the von Karman strain-displacement relations. The static equilibrium paths of the post-buckled plates were analyzed using an arc-length method with a branch-switching technique. For the dynamic analysis, the nonlinear equations of motion were derived based on CLPT and the nonlinear finite element model of the equations was constructed using the Hermite cubic interpolation functions for both conforming and nonconforming elements. The numerical analyses were conducted using the model and were compared with the experimental data.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

From the elastica compass to the elastica catapult: an essay on the mechanics of soft robot arm.

PubMed

Armanini, C; Dal Corso, F; Misseroni, D; Bigoni, D

2017-02-01

An elastic rod is clamped at one end and has a dead load attached to the other (free) end. The rod is then slowly rotated using the clamp. When the load is smaller than the buckling value, the rod describes a continuous set of quasi-static forms and its end traces a (smooth, convex and simple) closed curve, which would be a circle if the rod were rigid. The closed curve is analytically determined through the integration of the Euler's elastica, so that for sufficiently small loads the mechanical system behaves as an 'elastica compass'. For loads higher than that of buckling, the elastica reaches a configuration from which a snap-back instability occurs, realizing a sort of 'elastica catapult'. The whole quasi-static evolution leading to the critical configuration for snapping is calculated through the elastica and the subsequent dynamic motion simulated using two numerical procedures, one ad hoc developed and another based on a finite-element scheme. The theoretical results are then validated on a specially designed and built apparatus. An obvious application of the present model would be in the development of soft robotic limbs, but the results are also of interest for the optimization analysis in pole vaulting.

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

NASA Astrophysics Data System (ADS)

Antoine, Xavier; Levitt, Antoine; Tang, Qinglin

2017-08-01

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

A hybrid approach for nonlinear computational aeroacoustics predictions

NASA Astrophysics Data System (ADS)

Sassanis, Vasileios; Sescu, Adrian; Collins, Eric M.; Harris, Robert E.; Luke, Edward A.

2017-01-01

In many aeroacoustics applications involving nonlinear waves and obstructions in the far-field, approaches based on the classical acoustic analogy theory or the linearised Euler equations are unable to fully characterise the acoustic field. Therefore, computational aeroacoustics hybrid methods that incorporate nonlinear wave propagation have to be constructed. In this study, a hybrid approach coupling Navier-Stokes equations in the acoustic source region with nonlinear Euler equations in the acoustic propagation region is introduced and tested. The full Navier-Stokes equations are solved in the source region to identify the acoustic sources. The flow variables of interest are then transferred from the source region to the acoustic propagation region, where the full nonlinear Euler equations with source terms are solved. The transition between the two regions is made through a buffer zone where the flow variables are penalised via a source term added to the Euler equations. Tests were conducted on simple acoustic and vorticity disturbances, two-dimensional jets (Mach 0.9 and 2), and a three-dimensional jet (Mach 1.5), impinging on a wall. The method is proven to be effective and accurate in predicting sound pressure levels associated with the propagation of linear and nonlinear waves in the near- and far-field regions.

Computational modelling of the flow of viscous fluids in carbon nanotubes

NASA Astrophysics Data System (ADS)

Khosravian, N.; Rafii-Tabar, H.

2007-11-01

Carbon nanotubes will have extensive application in all areas of nano-technology, and in particular in the field of nano-fluidics, wherein they can be used for molecular separation, nano-scale filtering and as nano-pipes for conveying fluids. In the field of nano-medicine, nanotubes can be functionalized with various types of receptors to act as bio-sensors for the detection and elimination of cancer cells, or be used as bypasses and even neural connections. Modelling fluid flow inside nanotubes is a very challenging problem, since there is a complex interplay between the motion of the fluid and the stability of the walls. A critical issue in the design of nano-fluidic devices is the induced vibration of the walls, due to the fluid flow, which can promote structural instability. It has been established that the resonant frequencies depend on the flow velocity. We have studied, for the first time, the flow of viscous fluids through multi-walled carbon nanotubes, using the Euler-Bernoulli classical beam theory to model the nanotube as a continuum structure. Our aim has been to compute the effect of the fluid flow on the structural stability of the nanotubes, without having to consider the details of the fluid-walls interaction. The variations of the resonant frequencies with the flow velocity are obtained for both unembedded nanotubes, and when they are embedded in an elastic medium. It is found that a nanotube conveying a viscous fluid is more stable against vibration-induced buckling than a nanotube conveying a non-viscous fluid, and that the aspect ratio plays the same role in both cases.

Carbon Nanotubules: Building Blocks for Nanometer-Scale Engineering

NASA Technical Reports Server (NTRS)

Sinnott, Susan B.

1997-01-01

Proximal probe technology has provided researchers with new ways to investigate and manipulate matter on the nanometer scale. We have studied, through molecular dynamics simulations, using a many-body empirical potential, the indentation of a hydrogen-terminated, diamond (111 ) surface, with a proximal probe tip that consists of an open, hydrogen-terminated, (10,10) carbon nanotubule. The simulations showed that upon indenting 1.8 A, the tubule deforms but returns to its original shape upon retraction. The Young's modulus of the tubule was determined using the predicted Euler buckling force and was found to be comparable to measured and calculated values. In a second series of simulations, an open (10, 10) nanotubule was heated to 4500 K and allowed to close. We find that at this temperature the resulting cap contains numerous imperfections, including some not mentioned previously in the literature.

Structural stiffness, strength and dynamic characteristics of large tetrahedral space truss structures

NASA Technical Reports Server (NTRS)

Mikulas, M. M., Jr.; Bush, H. G.; Card, M. F.

1977-01-01

Physical characteristics of large skeletal frameworks for space applications are investigated by analyzing one concept: the tetrahedral truss, which is idealized as a sandwich plate with isotropic faces. Appropriate analytical relations are presented in terms of the truss column element properties which for calculations were taken as slender graphite/epoxy tubes. Column loads, resulting from gravity gradient control and orbital transfer, are found to be small for the class structure investigated. Fundamental frequencies of large truss structures are shown to be an order of magnitude lower than large earth based structures. Permissible loads are shown to result in small lateral deflections of the truss due to low-strain at Euler buckling of the slender graphite/epoxy truss column elements. Lateral thermal deflections are found to be a fraction of the truss depth using graphite/epoxy columns.

Complete mechanical behavior analysis of FG Nano Beam under non-uniform loading using non-local theory

NASA Astrophysics Data System (ADS)

Ghaffari, I.; Parhizkar Yaghoobi, M.; Ghannad, M.

2018-01-01

The purpose of this study is to offer a complete solution to analyze the mechanical behavior (bending, buckling and vibration) of Nano-beam under non-uniform loading. Furthermore, the effects of size (nonlocal parameters), non-homogeneity constants, and different boundary conditions are investigated by using this method. The exact solution presented here reduces costs incurred by experiments. In this research, the displacement field obeys the kinematics of the Euler-Bernoulli beam theory and non-local elasticity theory has been used. The governing equations and general boundary conditions are derived for a beam by using energy method. The presented solution enables us to analyze any kind of loading profile and boundary conditions with no limitations. Furthermore, this solution, unlike previous studies, is not a series-solution; hence, there is no limitation prior to existing with the series-solution, nor does it need to check convergence. Based on the developed analytical solution, the influence of size, non-homogeneity and non-uniform loads on bending, buckling and vibration behaviors is discussed. Also, the obtained result is highly accurate and in good agreement with previous research. In theoretical method, the allowable range for non-local parameters can be determined so as to make a major contribution to the reduction of the cost of experiments determining the value of non-local parameters.

Finite element structural redesign by large admissible perturbations

NASA Technical Reports Server (NTRS)

Bernitsas, Michael M.; Beyko, E.; Rim, C. W.; Alzahabi, B.

1991-01-01

In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.

Extension of lattice Boltzmann flux solver for simulation of compressible multi-component flows

NASA Astrophysics Data System (ADS)

Yang, Li-Ming; Shu, Chang; Yang, Wen-Ming; Wang, Yan

2018-05-01

The lattice Boltzmann flux solver (LBFS), which was presented by Shu and his coworkers for solving compressible fluid flow problems, is extended to simulate compressible multi-component flows in this work. To solve the two-phase gas-liquid problems, the model equations with stiffened gas equation of state are adopted. In this model, two additional non-conservative equations are introduced to represent the material interfaces, apart from the classical Euler equations. We first convert the interface equations into the full conservative form by applying the mass equation. After that, we calculate the numerical fluxes of the classical Euler equations by the existing LBFS and the numerical fluxes of the interface equations by the passive scalar approach. Once all the numerical fluxes at the cell interface are obtained, the conservative variables at cell centers can be updated by marching the equations in time and the material interfaces can be identified via the distributions of the additional variables. The numerical accuracy and stability of present scheme are validated by its application to several compressible multi-component fluid flow problems.

Comparison Between Polynomial, Euler Beta-Function and Expo-Rational B-Spline Bases

NASA Astrophysics Data System (ADS)

Kristoffersen, Arnt R.; Dechevsky, Lubomir T.; Laksa˚, Arne; Bang, Børre

2011-12-01

Euler Beta-function B-splines (BFBS) are the practically most important instance of generalized expo-rational B-splines (GERBS) which are not true expo-rational B-splines (ERBS). BFBS do not enjoy the full range of the superproperties of ERBS but, while ERBS are special functions computable by a very rapidly converging yet approximate numerical quadrature algorithms, BFBS are explicitly computable piecewise polynomial (for integer multiplicities), similar to classical Schoenberg B-splines. In the present communication we define, compute and visualize for the first time all possible BFBS of degree up to 3 which provide Hermite interpolation in three consecutive knots of multiplicity up to 3, i.e., the function is being interpolated together with its derivatives of order up to 2. We compare the BFBS obtained for different degrees and multiplicities among themselves and versus the classical Schoenberg polynomial B-splines and the true ERBS for the considered knots. The results of the graphical comparison are discussed from analytical point of view. For the numerical computation and visualization of the new B-splines we have used Maple 12.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David M.; Anderson, Melvin S.

1998-01-01

The analytical formulation of curved-plate non-linear equilibrium equations that include transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Using several simplifying assumptions, linearized, stability equations are derived that describe the response of the plate just after bifurcation buckling occurs. These equations are then modified to allow the plate reference surface to be located a distance z(c), from the centroid surface which is convenient for modeling stiffened-plate assemblies. The implementation of the new theory into the VICONOPT buckling and vibration analysis and optimum design program code is described. Either classical plate theory (CPT) or first-order shear-deformation plate theory (SDPT) may be selected in VICONOPT. Comparisons of numerical results for several example problems with different loading states are made. Results from the new curved-plate analysis compare well with closed-form solution results and with results from known example problems in the literature. Finally, a design-optimization study of two different cylindrical shells subject to uniform axial compression is presented.

Coherent states for the quantum complete rigid rotor

NASA Astrophysics Data System (ADS)

Fontanari, Daniele; Sadovskií, Dmitrií A.

2018-07-01

Motivated by the possibility to describe orientations of quantum triaxial rigid rotors, such as molecules, with respect to both internal (body-fixed) and external (laboratory) frames, we go through the theory of coherent states and design the appropriate family of coherent states on T∗ SO(3) , the classical phase space of the freely rotating rigid body (the Euler top). We pay particular attention to the resolution of identity property in order to establish the explicit relation between the parameters of the coherent states and classical phase-space variables, actions and angles.

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.

Simple Test Functions in Meshless Local Petrov-Galerkin Methods

NASA Technical Reports Server (NTRS)

Raju, Ivatury S.

2016-01-01

Two meshless local Petrov-Galerkin (MLPG) methods based on two different trial functions but that use a simple linear test function were developed for beam and column problems. These methods used generalized moving least squares (GMLS) and radial basis (RB) interpolation functions as trial functions. These two methods were tested on various patch test problems. Both methods passed the patch tests successfully. Then the methods were applied to various beam vibration problems and problems involving Euler and Beck's columns. Both methods yielded accurate solutions for all problems studied. The simple linear test function offers considerable savings in computing efforts as the domain integrals involved in the weak form are avoided. The two methods based on this simple linear test function method produced accurate results for frequencies and buckling loads. Of the two methods studied, the method with radial basis trial functions is very attractive as the method is simple, accurate, and robust.

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

NASA Astrophysics Data System (ADS)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

Soliton Gases and Generalized Hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien

2018-01-01

We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.

Adapting the Euler-Lagrange equation to study one-dimensional motions under the action of a constant force

NASA Astrophysics Data System (ADS)

Dias, Clenilda F.; Araújo, Maria A. S.; Carvalho-Santos, Vagson L.

2018-01-01

The Euler-Lagrange equations (ELE) are very important in the theoretical description of several physical systems. In this work we have used a simplified form of ELE to study one-dimensional motions under the action of a constant force. From the use of the definition of partial derivative, we have proposed two operators, here called mean delta operators, which may be used to solve the ELE in a simplest way. We have applied this simplification to solve three simple mechanical problems in which the particle is under the action of the gravitational field: a free fall body, the Atwood’s machine and the inclined plan. The proposed simplification can be used to introduce the lagrangian formalism in teaching classical mechanics in introductory physics courses.

Was the Milky Way Bulge Formed from the Buckling Disk Instability, Hierarchical Collapse, Accretion of Clumps, or All of the Above?

NASA Astrophysics Data System (ADS)

Nataf, David M.

2017-09-01

The assembly of the Milky Way bulge is an old topic in astronomy, one now in a period of renewed and rapid development. That is due to tremendous advances in observations of bulge stars, motivating observations of both local and high-redshift galaxies, and increasingly sophisticated simulations. The dominant scenario for bulge formation is that of the Milky Way as a nearly pure disk galaxy, with the inner disk having formed a bar and buckled. This can potentially explain virtually all bulge stars with [Fe/H] ≳ -1.0, which comprise 95% of the stellar population. The evidence is the incredible success in N-body models of this type in making non-trivial, non-generic predictions, such as the rotation curve and velocity dispersion measured from radial velocities, and the spatial morphologies of the peanut/X-shape and the long bar. The classical bulge scenario, whereby the bulge formed from early dissipative collapse and mergers, remains viable for stars with [Fe/H] ≲ -1.0 and potentially a minority of the other stars. A classical bulge is expected from Λ-CDM cosmological simulations, can accentuate the properties of an existing bar in a hybrid system, and is most consistent with the bulge abundance trends such as [Mg/Fe], which are elevated relative to both the thin and thick disks. Finally, the clumpy-galaxy scenario is considered, as it is the correct description of most Milky Way precursors given observations of high-redshift galaxies. Simulations predict that these star-forming clumps will sometimes migrate to the centres of galaxies where they may form a bulge, and galaxies often include a bulge clump as well. They will possibly form a bar with properties consistent with those of the Milky Way, such as the exponential profile and metallicity gradient. Given the relative successes of these scenarios, the Milky Way bulge is plausibly of composite origin, with a classical bulge and/or inner halo numerically dominant for stars with [Fe/H] ≲ -1.0, a buckling thick disk for stars with - 1.0 ≲ [Fe/H

Size-dependent axial instability of microtubules surrounded by cytoplasm of a living cell based on nonlocal strain gradient elasticity theory.

PubMed

Sahmani, S; Aghdam, M M

2017-06-07

Microtubules including tubulin heterodimers arranging in a parallel shape of cylindrical hollow plays an important role in the mechanical stiffness of a living cell. In the present study, the nonlocal strain gradient theory of elasticity including simultaneously the both nonlocality and strain gradient size dependency is put to use within the framework of a refined orthotropic shell theory with hyperbolic distribution of shear deformation to analyze the size-dependent buckling and postbuckling characteristics of microtubules embedded in cytoplasm under axial compressive load. The non-classical governing differential equations are deduced via boundary layer theory of shell buckling incorporating the nonlinear prebuckling deformation and microtubule-cytoplasm interaction in the living cell environment. Finally, with the aid of a two-stepped perturbation solution methodology, the explicit analytical expressions for nonlocal strain gradient stability paths of axially loaded microtubules are achieved. It is illustrated that by taking the nonlocal size effect into consideration, the critical buckling load of microtubule and its maximum deflection associated with the minimum postbuckling load decreases, while the strain gradient size dependency causes to increase them. Copyright © 2017 Elsevier Ltd. All rights reserved.

A simplified lumped model for the optimization of post-buckled beam architecture wideband generator

NASA Astrophysics Data System (ADS)

Liu, Weiqun; Formosa, Fabien; Badel, Adrien; Hu, Guangdi

2017-11-01

Buckled beams structures are a classical kind of bistable energy harvesters which attract more and more interests because of their capability to scavenge energy over a large frequency band in comparison with linear generator. The usual modeling approach uses the Galerkin mode discretization method with relatively high complexity, while the simplification with a single-mode solution lacks accuracy. It stems on the optimization of the energy potential features to finally define the physical and geometrical parameters. Therefore, in this paper, a simple lumped model is proposed with explicit relationship between the potential shape and parameters to allow efficient design of bistable beams based generator. The accuracy of the approximation model is studied with the effectiveness of application analyzed. Moreover, an important fact, that the bending stiffness has little influence on the potential shape with low buckling level and the sectional area determined, is found. This feature extends the applicable range of the model by utilizing the design of high moment of inertia. Numerical investigations demonstrate that the proposed model is a simple and reliable tool for design. An optimization example of using the proposed model is demonstrated with satisfactory performance.

Spin dynamics in the stripe-ordered buckled honeycomb lattice antiferromagnet Ba 2 NiTeO 6

DOE PAGES

Asai, Shinichiro; Soda, Minoru; Kasatani, Kazuhiro; ...

2017-09-01

We carried out inelastic neutron scattering experiments on a buckled honeycomb lattice antiferromagnet Ba 2NiTeO 6 exhibiting a stripe structure at a low temperature. Magnetic excitations are observed in the energy range of ℏω≲10 meV having an anisotropy gap of 2 meV at 2 K. We perform spin-wave calculations to identify the spin model. The obtained microscopic parameters are consistent with the location of the stripe structure in the classical phase diagram. Furthermore, the Weiss temperature independently estimated from a bulk magnetic susceptibility is consistent with the microscopic parameters. The results reveal that a competition between the nearest-neighbor and next-nearest-neighbormore » interactions that together with a relatively large single-ion magnetic anisotropy stabilize the stripe magnetic structure.« less

On the stability of a rod adhering to a rigid surface: Shear-induced stable adhesion and the instability of peeling

NASA Astrophysics Data System (ADS)

Majidi, Carmel; O'Reilly, Oliver M.; Williams, John A.

2012-05-01

Using variational methods, we establish conditions for the nonlinear stability of adhesive states between an elastica and a rigid halfspace. The treatment produces coupled criteria for adhesion and buckling instabilities by exploiting classical techniques from Legendre and Jacobi. Three examples that arise in a broad range of engineered systems, from microelectronics to biologically inspired fiber array adhesion, are used to illuminate the stability criteria. The first example illustrates buckling instabilities in adhered rods, while the second shows the instability of a peeling process and the third illustrates the stability of a shear-induced adhesion. The latter examples can also be used to explain how microfiber array adhesives can be activated by shearing and deactivated by peeling. The nonlinear stability criteria developed in this paper are also compared to other treatments.

Spin dynamics in the stripe-ordered buckled honeycomb lattice antiferromagnet Ba 2 NiTeO 6

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

Asai, Shinichiro; Soda, Minoru; Kasatani, Kazuhiro

We carried out inelastic neutron scattering experiments on a buckled honeycomb lattice antiferromagnet Ba 2NiTeO 6 exhibiting a stripe structure at a low temperature. Magnetic excitations are observed in the energy range of ℏω≲10 meV having an anisotropy gap of 2 meV at 2 K. We perform spin-wave calculations to identify the spin model. The obtained microscopic parameters are consistent with the location of the stripe structure in the classical phase diagram. Furthermore, the Weiss temperature independently estimated from a bulk magnetic susceptibility is consistent with the microscopic parameters. The results reveal that a competition between the nearest-neighbor and next-nearest-neighbormore » interactions that together with a relatively large single-ion magnetic anisotropy stabilize the stripe magnetic structure.« less

Compressive buckling of a rectangular nanoplate

NASA Astrophysics Data System (ADS)

Bochkarev, A. O.

2018-05-01

This paper considers the constitutive relations of the nanoplate theory with surface stresses taken into account according to the original or complete Gurtin-Murdoch (GM) model and according to the simplified strain-consistent GM model (which does not include any non-strain terms in the surface stress-strain relation). It is shown that the potential energy of a deformed nanoplate according to both GM models preserves the classical structure using the redefined elastic moduli (effective tangential and flexural elastic properties, which contain the characteristics of bulk phase and a surface). This allows to apply the known solutions and methods from macroplates to nanoplates. As example, it is shown that the critical load of the compressive buckling of a nanoplate according to the complete and strain-consistent GM models has the difference between two solutions no more than 1.5%.

Statistical Extremes of Turbulence and a Cascade Generalisation of Euler's Gyroscope Equation

NASA Astrophysics Data System (ADS)

Tchiguirinskaia, Ioulia; Scherzer, Daniel

2016-04-01

Turbulence refers to a rather well defined hydrodynamical phenomenon uncovered by Reynolds. Nowadays, the word turbulence is used to designate the loss of order in many different geophysical fields and the related fundamental extreme variability of environmental data over a wide range of scales. Classical statistical techniques for estimating the extremes, being largely limited to statistical distributions, do not take into account the mechanisms generating such extreme variability. An alternative approaches to nonlinear variability are based on a fundamental property of the non-linear equations: scale invariance, which means that these equations are formally invariant under given scale transforms. Its specific framework is that of multifractals. In this framework extreme variability builds up scale by scale leading to non-classical statistics. Although multifractals are increasingly understood as a basic framework for handling such variability, there is still a gap between their potential and their actual use. In this presentation we discuss how to dealt with highly theoretical problems of mathematical physics together with a wide range of geophysical applications. We use Euler's gyroscope equation as a basic element in constructing a complex deterministic system that preserves not only the scale symmetry of the Navier-Stokes equations, but some more of their symmetries. Euler's equation has been not only the object of many theoretical investigations of the gyroscope device, but also generalised enough to become the basic equation of fluid mechanics. Therefore, there is no surprise that a cascade generalisation of this equation can be used to characterise the intermittency of turbulence, to better understand the links between the multifractal exponents and the structure of a simplified, but not simplistic, version of the Navier-Stokes equations. In a given way, this approach is similar to that of Lorenz, who studied how the flap of a butterfly wing could generate a cyclone with the help of a 3D ordinary differential system. Being well supported by the extensive numerical results, the cascade generalisation of Euler's gyroscope equation opens new horizons for predictability and predictions of processes having long-range dependences.

Micro 3D printing using a digital projector and its application in the study of soft materials mechanics.

PubMed

Lee, Howon; Fang, Nicholas X

2012-11-27

Buckling is a classical topic in mechanics. While buckling has long been studied as one of the major structural failure modes(1), it has recently drawn new attention as a unique mechanism for pattern transformation. Nature is full of such examples where a wealth of exotic patterns are formed through mechanical instability(2-5). Inspired by this elegant mechanism, many studies have demonstrated creation and transformation of patterns using soft materials such as elastomers and hydrogels(6-11). Swelling gels are of particular interest because they can spontaneously trigger mechanical instability to create various patterns without the need of external force(6-10). Recently, we have reported demonstration of full control over buckling pattern of micro-scaled tubular gels using projection micro-stereolithography (PμSL), a three-dimensional (3D) manufacturing technology capable of rapidly converting computer generated 3D models into physical objects at high resolution(12,13). Here we present a simple method to build up a simplified PμSL system using a commercially available digital data projector to study swelling-induced buckling instability for controlled pattern transformation. A simple desktop 3D printer is built using an off-the-shelf digital data projector and simple optical components such as a convex lens and a mirror(14). Cross-sectional images extracted from a 3D solid model is projected on the photosensitive resin surface in sequence, polymerizing liquid resin into a desired 3D solid structure in a layer-by-layer fashion. Even with this simple configuration and easy process, arbitrary 3D objects can be readily fabricated with sub-100 μm resolution. This desktop 3D printer holds potential in the study of soft material mechanics by offering a great opportunity to explore various 3D geometries. We use this system to fabricate tubular shaped hydrogel structure with different dimensions. Fixed on the bottom to the substrate, the tubular gel develops inhomogeneous stress during swelling, which gives rise to buckling instability. Various wavy patterns appear along the circumference of the tube when the gel structures undergo buckling. Experiment shows that circumferential buckling of desired mode can be created in a controlled manner. Pattern transformation of three-dimensionally structured tubular gels has significant implication not only in mechanics and material science, but also in many other emerging fields such as tunable matamaterials.

Blade design and analysis using a modified Euler solver

NASA Technical Reports Server (NTRS)

Leonard, O.; Vandenbraembussche, R. A.

1991-01-01

An iterative method for blade design based on Euler solver and described in an earlier paper is used to design compressor and turbine blades providing shock free transonic flows. The method shows a rapid convergence, and indicates how much the flow is sensitive to small modifications of the blade geometry, that the classical iterative use of analysis methods might not be able to define. The relationship between the required Mach number distribution and the resulting geometry is discussed. Examples show how geometrical constraints imposed upon the blade shape can be respected by using free geometrical parameters or by relaxing the required Mach number distribution. The same code is used both for the design of the required geometry and for the off-design calculations. Examples illustrate the difficulty of designing blade shapes with optimal performance also outside of the design point.

Dynamic Modeling and Simulation of a Rotational Inverted Pendulum

NASA Astrophysics Data System (ADS)

Duart, J. L.; Montero, B.; Ospina, P. A.; González, E.

2017-01-01

This paper presents an alternative way to the dynamic modeling of a rotational inverted pendulum using the classic mechanics known as Euler-Lagrange allows to find motion equations that describe our model. It also has a design of the basic model of the system in SolidWorks software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the theoretical results, It was made a contrast between the solutions obtained by simulation SimMechanics-Matlab and the system of equations Euler-Lagrange, solved through ODE23tb method included in Matlab bookstores for solving equations systems of the type and order obtained. This article comprises a pendulum trajectory analysis by a phase space diagram that allows the identification of stable and unstable regions of the system.

Optimal Shakedown of the Thin-Wall Metal Structures Under Strength and Stiffness Constraints

NASA Astrophysics Data System (ADS)

Alawdin, Piotr; Liepa, Liudas

2017-06-01

Classical optimization problems of metal structures confined mainly with 1st class cross-sections. But in practice it is common to use the cross-sections of higher classes. In this paper, a new mathematical model for described shakedown optimization problem for metal structures, which elements are designed from 1st to 4th class cross-sections, under variable quasi-static loads is presented. The features of limited plastic redistribution of forces in the structure with thin-walled elements there are taken into account. Authors assume the elastic-plastic flexural buckling in one plane without lateral torsional buckling behavior of members. Design formulae for Methods 1 and 2 for members are analyzed. Structures stiffness constrains are also incorporated in order to satisfy the limit serviceability state requirements. With the help of mathematical programming theory and extreme principles the structure optimization algorithm is developed and justified with the numerical experiment for the metal plane frames.

Bending and buckling formulation of graphene sheets based on nonlocal simple first-order shear deformation theory

NASA Astrophysics Data System (ADS)

Golmakani, M. E.; Malikan, M.; Sadraee Far, M. N.; Majidi, H. R.

2018-06-01

This paper presents a formulation based on simple first-order shear deformation theory (S-FSDT) for large deflection and buckling of orthotropic single-layered graphene sheets (SLGSs). The S-FSDT has many advantages compared to the classical plate theory (CPT) and conventional FSDT such as needless of shear correction factor, containing less number of unknowns than the existing FSDT and strong similarities with the CPT. Governing equations and boundary conditions are derived based on Hamilton’s principle using the nonlocal differential constitutive relations of Eringen and von Kármán geometrical model. Numerical results are obtained using differential quadrature (DQ) method and the Newton–Raphson iterative scheme. Finally, some comparison studies are carried out to show the high accuracy and reliability of the present formulations compared to the nonlocal CPT and FSDT for different thicknesses, elastic foundations and nonlocal parameters.

Thermal effect on the dynamic response of axially functionally graded beam subjected to a moving harmonic load

NASA Astrophysics Data System (ADS)

Wang, Yuewu; Wu, Dafang

2016-10-01

Dynamic response of an axially functionally graded (AFG) beam under thermal environment subjected to a moving harmonic load is investigated within the frameworks of classical beam theory (CBT) and Timoshenko beam theory (TBT). The Lagrange method is employed to derive the equations of thermal buckling for AFG beam, and then with the critical buckling temperature as a parameter the Newmark-β method is adopted to evaluate the dynamic response of AFG beam under thermal environments. Admissible functions denoting transverse displacement are expressed in simple algebraic polynomial forms. Temperature-dependency of material constituent is considered. The rule of mixture (Voigt model) and Mori-Tanaka (MT) scheme are used to evaluate the beam's effective material properties. A ceramic-metal AFG beam with immovable boundary condition is considered as numerical illustration to show the thermal effects on the dynamic behaviors of the beam subjected to a moving harmonic load.

Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

NASA Astrophysics Data System (ADS)

Román-Roy, Narciso

2009-11-01

This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

A micromechanical expanding coil mechanism for in vivo magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Ichiki, M.; Syms, R. R. A.; Young, I. R.

2005-04-01

A mechanism for an expanding coil designed for use for in vivo magnetic resonance imaging is demonstrated. The mechanism has a small (1 mm) cross-sectional width, and may therefore be passed through a tubular orifice such as the endoscope channel used for accessing a bile duct. Once in place, the coil may be deformed by controlled in-plane buckling and fixed in this state by a rack-and-tooth latch. The latch may be released to return the mechanism to its original state for withdrawal. A simple analytic model of the device is developed using Euler bending theory. Prototypes are fabricated in bonded silicon-on-insulator material by deep reactive ion etching and undercut. Expansion and latching are demonstrated, and performance characteristics are found to be in good agreement with the theoretical models. A lateral expansion of 1 mm was routinely achieved on either side of a device with an initial width of 1 mm (corresponding to a three-fold expansion) using an axial compression of 400 µm.

Stress and Fracture Analyses Under Elastic-plastic and Creep Conditions: Some Basic Developments and Computational Approaches

NASA Technical Reports Server (NTRS)

Reed, K. W.; Stonesifer, R. B.; Atluri, S. N.

1983-01-01

A new hybrid-stress finite element algorith, suitable for analyses of large quasi-static deformations of inelastic solids, is presented. Principal variables in the formulation are the nominal stress-rate and spin. A such, a consistent reformulation of the constitutive equation is necessary, and is discussed. The finite element equations give rise to an initial value problem. Time integration has been accomplished by Euler and Runge-Kutta schemes and the superior accuracy of the higher order schemes is noted. In the course of integration of stress in time, it has been demonstrated that classical schemes such as Euler's and Runge-Kutta may lead to strong frame-dependence. As a remedy, modified integration schemes are proposed and the potential of the new schemes for suppressing frame dependence of numerically integrated stress is demonstrated. The topic of the development of valid creep fracture criteria is also addressed.

Sensory Topography of Oral Structures.

PubMed

Bearelly, Shethal; Cheung, Steven W

2017-01-01

Sensory function in the oral cavity and oropharynx is integral to effective deglutition and speech production. The main hurdle to evaluation of tactile consequences of upper aerodigestive tract diseases and treatments is access to a reliable clinical tool. We propose a rapid and reliable procedure to determine tactile thresholds using buckling monofilaments to advance care. To develop novel sensory testing monofilaments and map tactile thresholds of oral cavity and oropharyngeal structures. A prospective cross-sectional study of 37 healthy adults (12 men, 25 women), specifically without a medical history of head and neck surgery, radiation, or chemotherapy, was carried out in an academic tertiary medical center to capture normative data on tactile sensory function in oral structures. Cheung-Bearelly monofilaments were constructed by securing nylon monofilament sutures (2-0 through 9-0) in the lumen of 5-French ureteral catheters, exposing 20 mm for tapping action. Buckling force consistency was evaluated for 3 lots of each suture size. Sensory thresholds of 4 oral cavity and 2 oropharyngeal subsites in healthy participants (n = 37) were determined by classical signal detection methodology (d-prime ≥1). In 21 participants, test-retest reliability of sensory thresholds was evaluated. Separately in 16 participants, sensory thresholds determined by a modified staircase method were cross-validated with those obtained by classical signal detection. Buckling forces of successive suture sizes were distinct (P < .001), consistent (Cronbach α, 0.99), and logarithmically related (r = 0.99, P < .001). Test-retest reliability of sensory threshold determination was high (Cronbach α, >0.7). The lower lip, anterior tongue, and buccal mucosa were more sensitive than the soft palate, posterior tongue, and posterior pharyngeal wall (P < .001). Threshold determination by classical signal detection and modified staircase methods were highly correlated (r = 0.93, P < .001). Growth of perceptual intensity was logarithmically proportional to stimulus strength (P < .01). Topography of normal oral cavity and oropharyngeal tactile sensation is organized in accordance to decreasing sensitivity along the anteroposterior trajectory and growth of perceptual intensity at all subsites is log-linear. Cheung-Bearelly monofilaments are accessible, disposable, and consistent esthesiometers. This novel clinical tool is deployable for quantitative sensory function assessment of oral cavity and oropharyngeal structures.

Nonideal Rayleigh–Taylor mixing

PubMed Central

Lim, Hyunkyung; Iwerks, Justin; Glimm, James; Sharp, David H.

2010-01-01

Rayleigh–Taylor mixing is a classical hydrodynamic instability that occurs when a light fluid pushes against a heavy fluid. The two main sources of nonideal behavior in Rayleigh–Taylor (RT) mixing are regularizations (physical and numerical), which produce deviations from a pure Euler equation, scale invariant formulation, and nonideal (i.e., experimental) initial conditions. The Kolmogorov theory of turbulence predicts stirring at all length scales for the Euler fluid equations without regularization. We interpret mathematical theories of existence and nonuniqueness in this context, and we provide numerical evidence for dependence of the RT mixing rate on nonideal regularizations; in other words, indeterminacy when modeled by Euler equations. Operationally, indeterminacy shows up as nonunique solutions for RT mixing, parametrized by Schmidt and Prandtl numbers, in the large Reynolds number (Euler equation) limit. Verification and validation evidence is presented for the large eddy simulation algorithm used here. Mesh convergence depends on breaking the nonuniqueness with explicit use of the laminar Schmidt and Prandtl numbers and their turbulent counterparts, defined in terms of subgrid scale models. The dependence of the mixing rate on the Schmidt and Prandtl numbers and other physical parameters will be illustrated. We demonstrate numerically the influence of initial conditions on the mixing rate. Both the dominant short wavelength initial conditions and long wavelength perturbations are observed to play a role. By examination of two classes of experiments, we observe the absence of a single universal explanation, with long and short wavelength initial conditions, and the various physical and numerical regularizations contributing in different proportions in these two different contexts. PMID:20615983

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

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

Yang, Xiaofeng, E-mail: xfyang@math.sc.edu; Han, Daozhi, E-mail: djhan@iu.edu

2017-02-01

In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposedmore » schemes.« less

Nonlinear panel flutter in a rarefied atmosphere - Aerodynamic shear stress effects

NASA Technical Reports Server (NTRS)

Resende, Hugo B.

1991-01-01

The panel flutter phenomenon is studied assuming free-molecule flow. This kind of analysis is relevant in the case of hypersonic flight vehicles traveling at high altitudes, especially in the leeward portion of the vehicle. In these conditions the aerodynamic shear can be expected to be considerably larger than the pressure at a given point, so that the effects of such a loading are incorporated into the structural model. This is accomplished by introducing distributed longitudinal and bending moment loads. The former can lead to buckling of the panel, with the second mode in the case of a simply-supported panel playing a important role, and becoming the dominant mode in the solution. The presence of equivalent springs in the longitudinal direction at the panel's ends also becomes of relative importance, even for the evaluation of the linear flutter parameter. Finally, the behavior of the system is studied in the presence of applied compressive forces, that is, classical buckling.

The influence of gravity and wind on land plant evolution.

PubMed

Niklas, K J

1998-07-01

Aspects of the engineering theory treating the elastic stability of vertical stems and cantilevered leaves supporting their own weight and additional wind-induced forces (drag) are reviewed in light of biomechanical studies of living and fossil terrestrial plant species. The maximum height to which arborescent species can grow before their stems elastically buckle under their own weight is estimated by means of the Euler-Greenhill formula which states that the critical buckling height scales as the 1/3 power of plant tissue-stiffness normalized with respect to tissue bulk density and as the 2/3 power of stem diameter. Data drawn from living plants indicate that progressively taller plant species employ stiffer and lighter-weight plant tissues as the principal stiffening agent in their vertical stems. The elastic stability of plants subjected to high lateral wind-loadings is governed by the drag torque (the product of the drag force and the height above ground at which this force is applied), which cannot exceed the gravitational bending moment (the product of the weight of aerial organs and the lever arm measured at the base of the plant). Data from living plants indicate that the largest arborescent plant species rely on massive trunks and broad, horizontally expansive root crowns to resist drag torques. The drag on the canopies of these plants is also reduced by highly flexible stems and leaves composed of tissues that twist and bend more easily than tissues used to stiffen older, more proximal stems. A brief review of the fossil record suggests that modifications in stem, leaf, and root morphology and anatomy capable of simultaneously coping with self-weight and wind-induced drag forces evolved by Devonian times, suggesting that natural selection acting on the elastic stability of sporophytes occurred early in the history of terrestrial plants.

Compressive buckling analysis of hat-stiffened panel

NASA Technical Reports Server (NTRS)

Ko, William L.; Jackson, Raymond H.

1991-01-01

Buckling analysis was performed on a hat-stiffened panel subjected to uniaxial compression. Both local buckling and global buckling were analyzed. It was found that the global buckling load was several times higher than the buckling load. The predicted local buckling loads compared favorably with both experimental data and finite-element analysis.

Development of a simulation model for dynamic derailment analysis of high-speed trains

NASA Astrophysics Data System (ADS)

Ling, Liang; Xiao, Xin-Biao; Jin, Xue-Song

2014-12-01

The running safety of high-speed trains has become a major concern of the current railway research with the rapid development of high-speed railways around the world. The basic safety requirement is to prevent the derailment. The root causes of the dynamic derailment of high-speed trains operating in severe environments are not easy to identify using the field tests or laboratory experiments. Numerical simulation using an advanced train-track interaction model is a highly efficient and low-cost approach to investigate the dynamic derailment behavior and mechanism of high-speed trains. This paper presents a three-dimensional dynamic model of a high-speed train coupled with a ballast track for dynamic derailment analysis. The model considers a train composed of multiple vehicles and the nonlinear inter-vehicle connections. The ballast track model consists of rails, fastenings, sleepers, ballasts, and roadbed, which are modeled by Euler beams, nonlinear spring-damper elements, equivalent ballast bodies, and continuous viscoelastic elements, in which the modal superposition method was used to reduce the order of the partial differential equations of Euler beams. The commonly used derailment safety assessment criteria around the world are embedded in the simulation model. The train-track model was then used to investigate the dynamic derailment responses of a high-speed train passing over a buckled track, in which the derailment mechanism and train running posture during the dynamic derailment process were analyzed in detail. The effects of train and track modelling on dynamic derailment analysis were also discussed. The numerical results indicate that the train and track modelling options have a significant effect on the dynamic derailment analysis. The inter-vehicle impacts and the track flexibility and nonlinearity should be considered in the dynamic derailment simulations.

Analysis of shear buckling of cylindrical shells. II - Effects of combined loadings

NASA Astrophysics Data System (ADS)

Kokubo, Kunio; Nagashima, Hideaki; Takayanagi, Masaaki; Madokoro, Manabu; Mochizuki, Akira; Ikeuchi, Hisaaki

1992-03-01

Cylindrical shells subjected to lateral loads buckle in shear or bending buckling modes. The effects of combined loadings are investigated by developing a special-purpose FEM program using the 8-node isoparametric shell element. Three types of loading, lateral and axial loads, and pure bending moments are considered. For short cylindrical shells, shear buckling modes are dominant, but elephant-foot bulges take place with an increase in bending moments. Effects of axial loads on shear buckling and the elephant-foot bulge are investigated. In the case of shear buckling the axial load affects the buckling mode as well as the buckling load. For bending bucklings, the axial loads have a great effect on the buckling load.

Combined Euler column vibration isolation and energy harvesting

NASA Astrophysics Data System (ADS)

Davis, R. B.; McDowell, M. D.

2017-05-01

A new device that combines vibration isolation and energy harvesting is modeled, simulated, and tested. The vibration isolating portion of the device uses post-buckled beams as its spring elements. Piezoelectric film is applied to the beams to harvest energy from their dynamic flexure. The entire device operates passively on applied base excitation and requires no external power or control system. The structural system is modeled using the elastica, and the structural response is applied as forcing on the electric circuit equation to predict the output voltage and the corresponding harvested power. The vibration isolation and energy harvesting performance is simulated across a large parameter space and the modeling approach is validated with experimental results. Experimental transmissibilities of 2% and harvested power levels of 0.36 μW are simultaneously demonstrated. Both theoretical and experimental data suggest that there is not necessarily a trade-off between vibration isolation and harvested power. That is, within the practical operational range of the device, improved vibration isolation will be accompanied by an increase in the harvested power as the forcing frequency is increased.

Thermal Buckling Analysis of Rectangular Panels Subjected to Humped Temperature Profile Heating

NASA Technical Reports Server (NTRS)

Ko, William I.

2004-01-01

This research investigates thermal buckling characteristics of rectangular panels subjected to different types of humped temperature profile heating. Minimum potential energy and finite-element methods are used to calculate the panel buckling temperatures. The two methods give fairly close thermal buckling solutions. 'Buckling temperature magnification factor of the first kind, eta' is established for the fixed panel edges to scale up the buckling solution of uniform temperature loading case to give the buckling solution of the humped temperature profile loading cases. Also, 'buckling temperature magnification factor of the second kind, xi' is established for the free panel edges to scale up the buckling solution of humped temperature profile loading cases with unheated boundary heat sinks to give the buckling solutions when the boundary heat sinks are heated up.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David M.

1999-01-01

The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are derived. These equations are then modified to allow the plate reference surface to be located a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described. The terms of the plate stiffness matrix using both classical plate theory (CPT) and first-order shear-deformation plate theory (SDPT) are presented. The effects of in-plane transverse and in-plane shear loads are included in the in-plane stability equations. Numerical results for several example problems with different loading states are presented. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPT are made. The computational effort required by the new analysis is compared to that of the analysis currently in the VICONOPT program. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.

Lithospheric buckling and far-foreland deformation during the Laramide and Appalachian orogenies

NASA Astrophysics Data System (ADS)

Tikoff, B.; Siddoway, C. S.

2017-12-01

Major intraplate tectonics within North America (Laurentia) occurs during times of major orogenesis along the plate margins. During mountain building, typical structures of the hinterland are an orogenic plateau and fold-and-thrust belts, while in the far foreland (intraplate) areas long-wavelength ( 200 km or longer) folds and fault-reactivation features form. Long-wavelength folds are evident in both the Appalachian and Laramide orogenic forelands, with the stratigraphy recording the timing of the uplift. This contribution examines the model of lithospheric buckling - periodic folding associated with a horizontal endload on the edge of the plate - based on scaled, physical experiments and corroborated by numerical models. The Laramide (75-55 Ma) intraplate orogen in the classical location in Wyoming contains basement-cored arches spaced 200 km apart, for which the mechanism of uplift is questioned. Seismic evidence obtained for the Bighorn uplift, Wyoming, obtained by the EarthScope Bighorn project, shows an upwarp of the Moho beneath, but oblique to the trend of the surface exposure of the basement arch. Both the surface and Moho exhibit approximately the same structural relief. The seismic data exhibit no evidence for a regionally continuous decollement, nor is there evidence of rotation of structural markers within these features, of the type that is observed in the detached fold-and-thrust belt. The intraplate region affected by long-wavelength folding includes western Wyoming, with continuation of some features across the E-W-oriented Cheyenne belt (e.g., Rock Springs-Douglas Creek arch), Colorado Plateau, and High Plains east of the Rocky Mountains, where surface and subsurface structures display a series of anticlinal arches ("plains-type" folds). Appalachian mountain building also caused long-wavelength folding, with a spacing consistent with lithospheric buckling, mostly associated with the Devonian Acadian orogeny. The Laramide arches in the High Plains seem to occur on arches inherited from the Appalachian orogeny, suggesting the permanence of these lithospheric buckles once they have formed.

Critical Buckling Pressure in Mouse Carotid Arteries with Altered Elastic Fibers

PubMed Central

Luetkemeyer, Callan M.; James, Rhys H.; Devarakonda, Siva Teja; Le, Victoria P.; Liu, Qin; Han, Hai-Chao; Wagenseil, Jessica E.

2015-01-01

Arteries can buckle axially under applied critical buckling pressure due to a mechanical instability. Buckling can cause arterial tortuosity leading to flow irregularities and stroke. Genetic mutations in elastic fiber proteins are associated with arterial tortuosity in humans and mice, and may be the result of alterations in critical buckling pressure. Hence, the objective of this study is to investigate how genetic defects in elastic fibers affect buckling pressure. We use mouse models of human disease with reduced amounts of elastin (Eln+/−) and with defects in elastic fiber assembly due to the absence of fibulin-5 (Fbln5−/−). We find that Eln+/− arteries have reduced buckling pressure compared to their wild-type controls. Fbln5−/− arteries have similar buckling pressure to wild-type at low axial stretch, but increased buckling pressure at high stretch. We fit material parameters to mechanical test data for Eln+/−, Fbln5−/− and wild-type arteries using Fung and four-fiber strain energy functions. Fitted parameters are used to predict theoretical buckling pressure based on equilibrium of an inflated, buckled, thick-walled cylinder. In general, the theoretical predictions underestimate the buckling pressure at low axial stretch and overestimate the buckling pressure at high stretch. The theoretical predictions with both models replicate the increased buckling pressure at high stretch for Fbln5−/− arteries, but the four-fiber model predictions best match the experimental trends in buckling pressure changes with axial stretch. This study provides experimental and theoretical methods for further investigating the influence of genetic mutations in elastic fibers on buckling behavior and the development of arterial tortuosity. PMID:25771258

Light-Induced Buckles Localized by Polymeric Inks Printed on Bilayer Films.

PubMed

Park, Sungjune; Nallainathan, Umaash; Mondal, Kunal; Sen, Pratik; Dickey, Michael D

2018-04-16

Buckling instabilities generate microscale features in thin films in a facile manner. Buckles can form, for example, by heating a metal/polymer film stack on a rigid substrate. Thermal expansion differences of the individual layers generate compressive stress that causes the metal to buckle over the entire surface. The ability to dictate and confine the location of buckle formation can enable patterns with more than one length scale, including hierarchical patterns. Here, sacrificial "ink" patterned on top of the film stack localizes the buckles via two mechanisms. First, stiff inks suppress buckles such that only the non-inked regions buckle in response to infrared light. The metal in the non-inked regions absorbs the infrared light and thus gets sufficiently hot to induce buckles. Second, soft inks that absorb light get hot faster than the non-inked regions and promote buckling when exposed to visible light. The exposed metal in the non-inked regions reflects the light and thus never get sufficiently hot to induce buckles. This second method works on glass substrates, but not silicon substrates, due to the superior thermal insulation of glass. The patterned ink can be removed, leaving behind hierarchical patterns consisting of regions of buckles among non-buckled regions. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Study of sleeper’s impact on the deep-water pipeline lateral global buckling

NASA Astrophysics Data System (ADS)

Liu, Wenbin; Li, Bin

2017-08-01

Pipelines are the most important transportation way for offshore oil and gas, and the lateral buckling is the main global buckling form for deep-water pipelines. The sleeper is an economic and efficient device to trigger the lateral buckling in preset location. This paper analyzed the lateral buckling features for on-bottom pipeline and pipeline with sleeper. The stress and strain variation during buckling process is shown to reveal the impact of sleeper on buckling.

Three-dimensional Sponges with Super Mechanical Stability: Harnessing True Elasticity of Individual Carbon Nanotubes in Macroscopic Architectures

PubMed Central

Dai, Zhaohe; Liu, Luqi; Qi, Xiaoying; Kuang, Jun; Wei, Yueguang; Zhu, Hongwei; Zhang, Zhong

2016-01-01

Efficient assembly of carbon nanotube (CNT) based cellular solids with appropriate structure is the key to fully realize the potential of individual nanotubes in macroscopic architecture. In this work, the macroscopic CNT sponge consisting of randomly interconnected individual carbon nanotubes was grown by CVD, exhibiting a combination of super-elasticity, high strength to weight ratio, fatigue resistance, thermo-mechanical stability and electro-mechanical stability. To deeply understand such extraordinary mechanical performance compared to that of conventional cellular materials and other nanostructured cellular architectures, a thorough study on the response of this CNT-based spongy structure to compression is conducted based on classic elastic theory. The strong inter-tube bonding between neighboring nanotubes is examined, believed to play a critical role in the reversible deformation such as bending and buckling without structural collapse under compression. Based on in-situ scanning electron microscopy observation and nanotube deformation analysis, structural evolution (completely elastic bending-buckling transition) of the carbon nanotubes sponges to deformation is proposed to clarify their mechanical properties and nonlinear electromechanical coupling behavior. PMID:26732143

Spontaneous Mechanical Buckling in Two-Dimensional Materials: A Power Source for Ambient Vibration Energy Harvesters

NASA Astrophysics Data System (ADS)

Thibado, Paul; Kumar, Pradeep; Singh, Surendra

Internet-of-Things (IoT) is projected to become a multi-trillion-dollar market, but most applications cannot afford replacing batteries on such a large scale, driving the need for battery alternatives. We recently discovered that freestanding graphene membranes are in perpetual motion when held at room temperature. Surprisingly, the random up-down motion of the membrane does not follow classical Brownian motion, but instead is super-diffusive at short times and sub-diffusive at long times. Furthermore, the velocity probability distribution function is non-Gaussian and follows the heavy-tailed Cauchy-Lorentz distribution, consistent with Lévy flights. Molecular dynamics simulations reveal that mechanical buckling is spontaneously occurring, and that this is the mechanism responsible for the anomalous movement. Bucking in this system occurs when the local material suddenly flips from concave to convex. The higher kinetic energy associated with this motion is derived from the surrounding thermal waste heat, and it may be converted into an electrical current and used as the active component of small power generators known as ambient vibration energy harvesters. thibado@uark.edu.

Local buckling and crippling of composite stiffener sections

NASA Technical Reports Server (NTRS)

Bonanni, David L.; Johnson, Eric R.; Starnes, James H., Jr.

1988-01-01

Local buckling, postbuckling, and crippling (failure) of channel, zee, and I- and J-section stiffeners made of AS4/3502 graphite-epoxy unidirectional tape are studied by experiment and analysis. Thirty-six stiffener specimens were tested statically to failure in axial compression as intermediate length columns. Web width is 1.25 inches for all specimens, and the flange width-to-thickness ratio ranges from 7 to 28 for the specimens tested. The radius of the stiffener corners is either 0.125 or 0.250 inches. A sixteen-ply orthotropic layup, an eight-ply quasi-isotropic layup, and a sixteen-ply quasi-isotropic layup are examined. Geometrically nonlinear analyses of five specimens were performed with the STAGS finite element code. Analytical results are compared to experimental data. Inplane stresses from STAGS are used to conduct a plane stress failure analysis of these specimens. Also, the development of interlaminar stress equations from equilibrium for classical laminated plate theory is presented. An algorithm to compute high order displacement derivatives required by these equations based on the Discrete Fourier Transform (DFT) is discussed.

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.

Functional buckling behavior of silicone rubber shells for biomedical use.

PubMed

van der Houwen, E B; Kuiper, L H; Burgerhof, J G M; van der Laan, B F A M; Verkerke, G J

2013-12-01

The use of soft elastic biomaterials in medical devices enables substantial function integration. The consequent increased simplification in design can improve reliability at a lower cost in comparison to traditional (hard) biomaterials. Functional bi-stable buckling is one of the many new mechanisms made possible by soft materials. The buckling behavior of shells, however, is typically described from a structural failure point of view: the collapse of arches or rupture of steam vessels, for example. There is little or no literature about the functional elastic buckling of small-sized silicone rubber shells, and it is unknown whether or not theory can predict their behavior. Is functional buckling possible within the scale, material and pressure normally associated with physiological applications? An automatic speech valve is used as an example application. Silicone rubber spherical shells (diameter 30mm) with hinged and double-hinged boundaries were subjected to air pressure loading. Twelve different geometrical configurations were tested for buckling and reverse buckling pressures. Data were compared with the theory. Buckling pressure increases linearly with shell thickness and shell height. Reverse buckling shows these same relations, with pressures always below normal buckling pressure. Secondary hinges change normal/reverse buckling pressure ratios and promote symmetrical buckling. All tested configurations buckled within or closely around physiological pressures. Functional bi-stable buckling of silicone rubber shells is possible with adjustable properties in the physiological pressure range. Results can be predicted using the proposed relations and equations. Copyright © 2013 Elsevier Ltd. All rights reserved.

Buckling and Post-Buckling Behaviors of a Variable Stiffness Composite Laminated Wing Box Structure

NASA Astrophysics Data System (ADS)

Wang, Peiyan; Huang, Xinting; Wang, Zhongnan; Geng, Xiaoliang; Wang, Yuansheng

2018-04-01

The buckling and post-buckling behaviors of variable stiffness composite laminates (VSCL) with curvilinear fibers were investigated and compared with constant stiffness composite laminates (CSCL) with straight fibers. A VSCL box structure was evaluated under a pure bending moment. The results of the comparative test showed that the critical buckling load of the VSCL box was approximately 3% higher than that of the CSCL box. However, the post-buckling load-bearing capacity was similar due to the layup angle and the immature status of the material processing technology. The properties of the VSCL and CSCL boxes under a pure bending moment were simulated using the Hashin criterion and cohesive interface elements. The simulation results are consistent with the experimental results in stiffness, critical buckling load and failure modes but not in post-buckling load capacity. The results of the experiment, the simulation and laminated plate theory show that VSCL greatly improves the critical buckling load but has little influence on the post-buckling load-bearing capacity.

Mechanical and thermal buckling analysis of sandwich panels under different edge conditions

NASA Technical Reports Server (NTRS)

Ko, William L.

1993-01-01

By using the Rayleigh-Ritz method of minimizing the total potential energy of a structural system, combined load (mechanical or thermal load) buckling equations are established for orthotropic rectangular sandwich panels supported under four different edge conditions. Two-dimensional buckling interaction curves and three dimensional buckling interaction surfaces are constructed for high-temperature honeycomb-core sandwich panels supported under four different edge conditions. The interaction surfaces provide easy comparison of the panel buckling strengths and the domains of symmetrical and antisymmetrical buckling associated with the different edge conditions. Thermal buckling curves of the sandwich panels also are presented. The thermal buckling conditions for the cases with and without thermal moments were found to be identical for the small deformation theory. In sandwich panels, the effect of transverse shear is quite large, and by neglecting the transverse shear effect, the buckling loads could be overpredicted considerably. Clamping of the edges could greatly increase buckling strength more in compression than in shear.

Computational Nanomechanics of Carbon Nanotubes and Composites

NASA Technical Reports Server (NTRS)

Srivastava, Deepak; Wei, Chenyu; Cho, Kyeongjae; Biegel, Bryan (Technical Monitor)

2002-01-01

Nanomechanics of individual carbon and boron-nitride nanotubes and their application as reinforcing fibers in polymer composites has been reviewed with interplay of theoretical modeling, computer simulations and experimental observations. The emphasis in this work is on elucidating the multi-length scales of the problems involved, and of different simulation techniques that are needed to address specific characteristics of individual nanotubes and nanotube polymer-matrix interfaces. Classical molecular dynamics simulations are shown to be sufficient to describe the generic behavior such as strength and stiffness modulus but are inadequate to describe elastic limit and nature of plastic buckling at large strength. Quantum molecular dynamics simulations are shown to bring out explicit atomic nature dependent behavior of these nanoscale materials objects that are not accessible either via continuum mechanics based descriptions or through classical molecular dynamics based simulations. As examples, we discus local plastic collapse of carbon nanotubes under axial compression and anisotropic plastic buckling of boron-nitride nanotubes. Dependence of the yield strain on the strain rate is addressed through temperature dependent simulations, a transition-state-theory based model of the strain as a function of strain rate and simulation temperature is presented, and in all cases extensive comparisons are made with experimental observations. Mechanical properties of nanotube-polymer composite materials are simulated with diverse nanotube-polymer interface structures (with van der Waals interaction). The atomistic mechanisms of the interface toughening for optimal load transfer through recycling, high-thermal expansion and diffusion coefficient composite formation above glass transition temperature, and enhancement of Young's modulus on addition of nanotubes to polymer are discussed and compared with experimental observations.

Erosion and intrusion of silicone rubber scleral buckle. Presentation and management.

PubMed

Nguyen, Q D; Lashkari, K; Hirose, T; Pruett, R C; McMeel, J W; Schepens, C L

2001-01-01

To describe the clinical presentation and management of erosion and intrusion of silicone rubber implants that are used in scleral buckling procedures for the treatment of retinal detachment. The authors identified four patients from their practices during the last 20 years (1978-1998) who had erosion or intrusion of silicone rubber scleral buckles that were used to manage retinal detachment. Approximately 4400 scleral buckling procedures were performed during this period. A retrospective review of the medical records of all patients was performed. Factors that influenced management decisions concerning the intruding buckle are emphasized. All four patients had myopia. The interval between placement of the scleral buckle and development of intrusion ranged from 1 to 20 years. The buckles were intrascleral in three cases and episcleral in one. Recurrent detachment and vitreous hemorrhage were indications for surgical intervention in three cases. After the surgical removal of buckling elements, visual acuity stabilized in all patients and the retina remained attached in all cases. Erosion and intrusion of scleral buckle are rare complications of scleral buckling procedures. The intruding buckle may be left intact unless there is significant threat to the integrity of ocular structures, recurrent detachment, or hemorrhage. Manipulation of the encircling band or buckle does not necessarily alter the visual acuity or the status of the retina.

Divergences and boundary modes in $$ \\mathcal{N}=8 $$ supergravity

DOE PAGES

Larsen, Finn; Lisbao, Pedro

2016-01-07

We reconsider the one loop divergence ofmore » $$ \\mathcal{N}=8 $$ supergravity in four dimensions. We compute the finite effective potential of $$ \\mathcal{N}=8 $$ anti-deSitter supergravity and interpret it as logarithmic running of the cosmological constant. We show that quantum inequivalence between fields that are classically dual is due to boundary modes in AdS 4. In conclusion, the boundary modes are important in global AdS 4 but not in thermal AdS 4 since these geometries have different Euler characteristic.« less

Mechanical and thermal buckling analysis of rectangular sandwich panels under different edge conditions

NASA Technical Reports Server (NTRS)

Ko, William L.

1994-01-01

The combined load (mechanical or thermal load) buckling equations were established for orthotropic rectangular sandwich panels under four different edge conditions by using the Rayleigh-Ritz method of minimizing the total potential energy of a structural system. Two-dimensional buckling interaction curves and three-dimensional buckling interaction surfaces were constructed for high-temperature honeycomb-core sandwich panels supported under four different edge conditions. The interaction surfaces provide overall comparison of the panel buckling strengths and the domains of symmetrical and antisymmetrical buckling associated with the different edge conditions. In addition, thermal buckling curves of these sandwich panels are presented. The thermal buckling conditions for the cases with and without thermal moments were found to be identical for the small deformation theory.

Free-form reticulated shell structures searched for maximum buckling strength

NASA Astrophysics Data System (ADS)

Takiuchi, Yuji; Kato, Shiro; Nakazawa, Shoji

2017-10-01

In this paper, a scheme of shape optimization is proposed for maximum buckling strength of free-form steel reticulated shells. In order to discuss the effectiveness of objective functions with respect to maximizing buckling strength, several different optimizations are applied to shallow steel single layer reticulated shells targeting rigidly jointed tubular members. The objective functions to be compared are linear buckling load, strain energy, initial yield load, and elasto-plastic buckling strength evaluated based on Modified Dunkerley Formula. With respect to obtained free-forms based on the four optimization schemes, both of their elastic buckling and elasto-plastic buckling behaviour are investigated and compared considering geometrical imperfections. As a result, it is concluded that the first and fourth optimization methods are effective from a viewpoint of buckling strength. And the relation between generalized slenderness ratio and appropriate objective function applied in buckling strength maximization is made clear.

A note on powers in finite fields

NASA Astrophysics Data System (ADS)

Aabrandt, Andreas; Lundsgaard Hansen, Vagn

2016-08-01

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.

Characterizing chaotic melodies in automatic music composition

NASA Astrophysics Data System (ADS)

Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

2010-09-01

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

Numerical research on the lateral global buckling characteristics of a high temperature and pressure pipeline with two initial imperfections

PubMed Central

Liu, Wenbin; Liu, Aimin

2018-01-01

With the exploitation of offshore oil and gas gradually moving to deep water, higher temperature differences and pressure differences are applied to the pipeline system, making the global buckling of the pipeline more serious. For unburied deep-water pipelines, the lateral buckling is the major buckling form. The initial imperfections widely exist in the pipeline system due to manufacture defects or the influence of uneven seabed, and the distribution and geometry features of initial imperfections are random. They can be divided into two kinds based on shape: single-arch imperfections and double-arch imperfections. This paper analyzed the global buckling process of a pipeline with 2 initial imperfections by using a numerical simulation method and revealed how the ratio of the initial imperfection’s space length to the imperfection’s wavelength and the combination of imperfections affects the buckling process. The results show that a pipeline with 2 initial imperfections may suffer the superposition of global buckling. The growth ratios of buckling displacement, axial force and bending moment in the superposition zone are several times larger than no buckling superposition pipeline. The ratio of the initial imperfection’s space length to the imperfection’s wavelength decides whether a pipeline suffers buckling superposition. The potential failure point of pipeline exhibiting buckling superposition is as same as the no buckling superposition pipeline, but the failure risk of pipeline exhibiting buckling superposition is much higher. The shape and direction of two nearby imperfections also affects the failure risk of pipeline exhibiting global buckling superposition. The failure risk of pipeline with two double-arch imperfections is higher than pipeline with two single-arch imperfections. PMID:29554123

Poly-Frobenius-Euler polynomials

NASA Astrophysics Data System (ADS)

Kurt, Burak

2017-07-01

Hamahata [3] defined poly-Euler polynomials and the generalized poly-Euler polynomials. He proved some relations and closed formulas for the poly-Euler polynomials. By this motivation, we define poly-Frobenius-Euler polynomials. We give some relations for this polynomials. Also, we prove the relationships between poly-Frobenius-Euler polynomials and Stirling numbers of the second kind.

Buckling of Carbon Nanotubes: A State of the Art Review

PubMed Central

Shima, Hiroyuki

2011-01-01

The nonlinear mechanical response of carbon nanotubes, referred to as their “buckling" behavior, is a major topic in the nanotube research community. Buckling means a deformation process in which a large strain beyond a threshold causes an abrupt change in the strain energy vs. deformation profile. Thus far, much effort has been devoted to analysis of the buckling of nanotubes under various loading conditions: compression, bending, torsion, and their certain combinations. Such extensive studies have been motivated by (i) the structural resilience of nanotubes against buckling and (ii) the substantial influence of buckling on their physical properties. In this contribution, I review the dramatic progress in nanotube buckling research during the past few years. PMID:28817032

Single-strain-gage force/stiffness buckling prediction techniques on a hat-stiffened panel

NASA Technical Reports Server (NTRS)

Hudson, Larry D.; Thompson, Randolph C.

1991-01-01

Predicting the buckling characteristics of a test panel is necessary to ensure panel integrity during a test program. A single-strain-gage buckling prediction method was developed on a hat-stiffened, monolithic titanium buckling panel. The method is an adaptation of the original force/stiffness method which requires back-to-back gages. The single-gage method was developed because the test panel did not have back-to-back gages. The method was used to predict buckling loads and temperatures under various heating and loading conditions. The results correlated well with a finite element buckling analysis. The single-gage force/stiffness method was a valid real-time and post-test buckling prediction technique.

Buckling analysis of planar compression micro-springs

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

Zhang, Jing; Sui, Li; Shi, Gengchen

2015-04-15

Large compression deformation causes micro-springs buckling and loss of load capacity. We analyzed the impact of structural parameters and boundary conditions for planar micro-springs, and obtained the change rules for the two factors that affect buckling. A formula for critical buckling deformation of micro-springs under compressive load was derived based on elastic thin plate theory. Results from this formula were compared with finite element analysis results but these did not always correlate. Therefore, finite element analysis is necessary for micro-spring buckling analysis. We studied the variation of micro-spring critical buckling deformation caused by four structural parameters using ANSYS software undermore » two constraint conditions. The simulation results show that when an x-direction constraint is added, the critical buckling deformation increases by 32.3-297.9%. The critical buckling deformation decreases with increase in micro-spring arc radius or section width and increases with increase in micro-spring thickness or straight beam width. We conducted experiments to confirm the simulation results, and the experimental and simulation trends were found to agree. Buckling analysis of the micro-spring establishes a theoretical foundation for optimizing micro-spring structural parameters and constraint conditions to maximize the critical buckling load.« less

Understanding the nanoscale local buckling behavior of vertically aligned MWCNT arrays with van der Waals interactions

NASA Astrophysics Data System (ADS)

Li, Yupeng; Kim, Hyung-Ick; Wei, Bingqing; Kang, Junmo; Choi, Jae-Boong; Nam, Jae-Do; Suhr, Jonghwan

2015-08-01

The local buckling behavior of vertically aligned carbon nanotubes (VACNTs) has been investigated and interpreted in the view of a collective nanotube response by taking van der Waals interactions into account. To the best of our knowledge, this is the first report on the case of collective VACNT behavior regarding van der Waals force among nanotubes as a lateral support effect during the buckling process. The local buckling propagation and development of VACNTs were experimentally observed and theoretically analyzed by employing finite element modeling with lateral support from van der Waals interactions among nanotubes. Both experimental and theoretical analyses show that VACNTs buckled in the bottom region with many short waves and almost identical wavelengths, indicating a high mode buckling. Furthermore, the propagation and development mechanism of buckling waves follow the wave damping effect.The local buckling behavior of vertically aligned carbon nanotubes (VACNTs) has been investigated and interpreted in the view of a collective nanotube response by taking van der Waals interactions into account. To the best of our knowledge, this is the first report on the case of collective VACNT behavior regarding van der Waals force among nanotubes as a lateral support effect during the buckling process. The local buckling propagation and development of VACNTs were experimentally observed and theoretically analyzed by employing finite element modeling with lateral support from van der Waals interactions among nanotubes. Both experimental and theoretical analyses show that VACNTs buckled in the bottom region with many short waves and almost identical wavelengths, indicating a high mode buckling. Furthermore, the propagation and development mechanism of buckling waves follow the wave damping effect. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr03581c

Phenomenology and control of buckling dynamics in multicomponent colloidal droplets

NASA Astrophysics Data System (ADS)

Pathak, Binita; Basu, Saptarshi

2015-06-01

Self-assembly of nano sized particles during natural drying causes agglomeration and shell formation at the surface of micron sized droplets. The shell undergoes sol-gel transition leading to buckling at the weakest point on the surface and produces different types of structures. Manipulation of the buckling rate with inclusion of surfactant (sodium dodecyl sulphate, SDS) and salt (anilinium hydrochloride, AHC) to the nano-sized particle dispersion (nanosilica) is reported here in an acoustically levitated single droplet. Buckling in levitated droplets is a cumulative, complicated function of acoustic streaming, chemistry, agglomeration rate, porosity, radius of curvature, and elastic energy of shell. We put forward our hypothesis on how buckling occurs and can be suppressed during natural drying of the droplets. Global precipitation of aggregates due to slow drying of surfactant-added droplets (no added salts) enhances the rigidity of the shell formed and hence reduces the buckling probability of the shell. On the contrary, adsorption of SDS aggregates on salt ions facilitates the buckling phenomenon with an addition of minute concentration of the aniline salt to the dispersion. Variation in the concentration of the added particles (SDS/AHC) also leads to starkly different morphologies and transient behaviour of buckling (buckling modes like paraboloid, ellipsoid, and buckling rates). Tuning of the buckling rate causes a transition in the final morphology from ring and bowl shapes to cocoon type of structure.

In vitro culture increases mechanical stability of human tissue engineered cartilage constructs by prevention of microscale scaffold buckling.

PubMed

Middendorf, Jill M; Shortkroff, Sonya; Dugopolski, Caroline; Kennedy, Stephen; Siemiatkoski, Joseph; Bartell, Lena R; Cohen, Itai; Bonassar, Lawrence J

2017-11-07

Many studies have measured the global compressive properties of tissue engineered (TE) cartilage grown on porous scaffolds. Such scaffolds are known to exhibit strain softening due to local buckling under loading. As matrix is deposited onto these scaffolds, the global compressive properties increase. However the relationship between the amount and distribution of matrix in the scaffold and local buckling is unknown. To address this knowledge gap, we studied how local strain and construct buckling in human TE constructs changes over culture times and GAG content. Confocal elastography techniques and digital image correlation (DIC) were used to measure and record buckling modes and local strains. Receiver operating characteristic (ROC) curves were used to quantify construct buckling. The results from the ROC analysis were placed into Kaplan-Meier survival function curves to establish the probability that any point in a construct buckled. These analysis techniques revealed the presence of buckling at early time points, but bending at later time points. An inverse correlation was observed between the probability of buckling and the total GAG content of each construct. This data suggests that increased GAG content prevents the onset of construct buckling and improves the microscale compressive tissue properties. This increase in GAG deposition leads to enhanced global compressive properties by prevention of microscale buckling. Copyright © 2017 Elsevier Ltd. All rights reserved.

The Buckling of Curved Tension-field Girders

NASA Technical Reports Server (NTRS)

Limpert, G

1938-01-01

The present paper reports on experiments made to determine the buckling load under shear of circular curved tension-field webs. The buckling load of the webs may be expressed with reference to the buckling load of the stiffeners. It is found that within the explored range the buckling load is approximately twice as great as that of the identically stiffened flat wall of equal web depth.

Failure mechanism of the polymer infiltration of carbon nanotube forests

NASA Astrophysics Data System (ADS)

Buchheim, Jakob; Park, Hyung Gyu

2016-11-01

Polymer melt infiltration is one of the feasible methods for manufacturing filter membranes out of carbon nanotubes (CNTs) on large scales. Practically, however, its process suffers from low yields, and the mechanism behind this failure is rather poorly understood. Here, we investigate a failure mechanism of polymer melt infiltration of vertical aligned (VA-) CNTs. In penetrating the VA-CNT interstices, polymer melts exert a capillarity-induced attractive force laterally on CNTs at the moving meniscus, leading to locally agglomerated macroscale bunches. Such a large configurational change can deform and distort individual CNTs so much as to cause buckling or breakdown of the alignment. In view of membrane manufacturing, this irreversible distortion of nanotubes is detrimental, as it could block the transport path of the membranes. The failure mechanism of the polymer melt infiltration is largely attributed to steric hindrance and an energy penalty of confined polymer chains. Euler beam theory and scaling analysis affirm that CNTs with low aspect ratio, thick walls and sparse distribution can maintain their vertical alignment. Our results can enrich a mechanistic understanding of the polymer melt infiltration process and offer guidelines to the facile large-scale manufacturing of the CNT-polymer filter membranes.

A discrete element model for the investigation of the geometrically nonlinear behaviour of solids

NASA Astrophysics Data System (ADS)

Ockelmann, Felix; Dinkler, Dieter

2018-07-01

A three-dimensional discrete element model for elastic solids with large deformations is presented. Therefore, an discontinuum approach is made for solids. The properties of elastic material are transferred analytically into the parameters of a discrete element model. A new and improved octahedron gap-filled face-centred cubic close packing of spheres is split into unit cells, to determine the parameters of the discrete element model. The symmetrical unit cells allow a model with equal shear components in each contact plane and fully isotropic behaviour for Poisson's ratio above 0. To validate and show the broad field of applications of the new model, the pin-pin Euler elastica is presented and investigated. The thin and sensitive structure tends to undergo large deformations and rotations with a highly geometrically nonlinear behaviour. This behaviour of the elastica can be modelled and is compared to reference solutions. Afterwards, an improved more realistic simulation of the elastica is presented which softens secondary buckling phenomena. The model is capable of simulating solids with small strains but large deformations and a strongly geometrically nonlinear behaviour, taking the shear stiffness of the material into account correctly.

Non-isothermal buckling behavior of viscoplastic shell structures

NASA Technical Reports Server (NTRS)

Riff, Richard; Simitses, G. J.

1988-01-01

Described are the mathematical model and solution methodologies for analyzing the structural response of thin, metallic elasto-viscoplastic shell structures under large thermomechanical loads and their non-isothermal buckling behavior. Among the system responses associated with these loads and conditions are snap-through, buckling, thermal buckling, and creep buckling. This geometric and material nonlinearities (of high order) can be anticipated and are considered in the model and the numerical treatment.

Mechanical model for filament buckling and growth by phase ordering.

PubMed

Rey, Alejandro D; Abukhdeir, Nasser M

2008-02-05

A mechanical model of open filament shape and growth driven by phase ordering is formulated. For a given phase-ordering driving force, the model output is the filament shape evolution and the filament end-point kinematics. The linearized model for the slope of the filament is the Cahn-Hilliard model of spinodal decomposition, where the buckling corresponds to concentration fluctuations. Two modes are predicted: (i) sequential growth and buckling and (ii) simultaneous buckling and growth. The relation among the maximum buckling rate, filament tension, and matrix viscosity is given. These results contribute to ongoing work in smectic A filament buckling.

Buckling Design and Analysis of a Payload Fairing One-Sixth Cylindrical Arc-Segment Panel

NASA Technical Reports Server (NTRS)

Kosareo, Daniel N.; Oliver, Stanley T.; Bednarcyk, Brett A.

2013-01-01

Design and analysis results are reported for a panel that is a 16th arc-segment of a full 33-ft diameter cylindrical barrel section of a payload fairing structure. Six such panels could be used to construct the fairing barrel, and, as such, compression buckling testing of a 16th arc-segment panel would serve as a validation test of the buckling analyses used to design the fairing panels. In this report, linear and nonlinear buckling analyses have been performed using finite element software for 16th arc-segment panels composed of aluminum honeycomb core with graphiteepoxy composite facesheets and an alternative fiber reinforced foam (FRF) composite sandwich design. The cross sections of both concepts were sized to represent realistic Space Launch Systems (SLS) Payload Fairing panels. Based on shell-based linear buckling analyses, smaller, more manageable buckling test panel dimensions were determined such that the panel would still be expected to buckle with a circumferential (as opposed to column-like) mode with significant separation between the first and second buckling modes. More detailed nonlinear buckling analyses were then conducted for honeycomb panels of various sizes using both Abaqus and ANSYS finite element codes, and for the smaller size panel, a solid-based finite element analysis was conducted. Finally, for the smaller size FRF panel, nonlinear buckling analysis was performed wherein geometric imperfections measured from an actual manufactured FRF were included. It was found that the measured imperfection did not significantly affect the panel's predicted buckling response

Buckling behavior of Rene 41 tubular panels for a hypersonic aircraft wing

NASA Technical Reports Server (NTRS)

Ko, W. L.; Fields, R. A.; Shideler, J. L.

1986-01-01

The buckling characteristics of Rene 41 tubular panels for a hypersonic aircraft wing were investigated. The panels were repeatedly tested for buckling characteristics using a hypersonic wing test structure and a universal tension/compression testing machine. The nondestructive buckling tests were carried out under different combined load conditions and in different temperature environments. The force/stiffness technique was used to determine the buckling loads of the panels. In spite of some data scattering resulting from large extrapolations of the data-fitting curve (because of the termination of applied loads at relatively low percentages of the buckling loads), the overall test data correlate fairly well with theoretically predicted buckling interaction curves. Also, the structural efficiency of the tubular panels was found to be slightly higher than that of beaded panels.

Buckling behavior of Rene 41 tubular panels for a hypersonic aircraft wing

NASA Technical Reports Server (NTRS)

Ko, W. L.; Shideler, J. L.; Fields, R. A.

1986-01-01

The buckling characteristics of Rene 41 tubular panels for a hypersonic aircraft wing were investigated. The panels were repeatedly tested for buckling characteristics using a hypersonic wing test structure and a universal tension/compression testing machine. The nondestructive buckling tests were carried out under different combined load conditions and in different temperature environments. The force/stiffness technique was used to determine the buckling loads of the panel. In spite of some data scattering, resulting from large extrapolations of the data fitting curve (because of the termination of applied loads at relatively low percentages of the buckling loads), the overall test data correlate fairly well with theoretically predicted buckling interaction curves. Also, the structural efficiency of the tubular panels was found to be slightly higher than that of beaded panels.

The stochastic energy-Casimir method

NASA Astrophysics Data System (ADS)

Arnaudon, Alexis; Ganaba, Nader; Holm, Darryl D.

2018-04-01

In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems. xml:lang="fr"

Quantum calculus of classical vortex images, integrable models and quantum states

NASA Astrophysics Data System (ADS)

Pashaev, Oktay K.

2016-10-01

From two circle theorem described in terms of q-periodic functions, in the limit q→1 we have derived the strip theorem and the stream function for N vortex problem. For regular N-vortex polygon we find compact expression for the velocity of uniform rotation and show that it represents a nonlinear oscillator. We describe q-dispersive extensions of the linear and nonlinear Schrodinger equations, as well as the q-semiclassical expansions in terms of Bernoulli and Euler polynomials. Different kind of q-analytic functions are introduced, including the pq-analytic and the golden analytic functions.

Dark energy simulacrum in nonlinear electrodynamics

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

Labun, Lance; Rafelski, Johann

2010-03-15

Quasiconstant external fields in nonlinear electromagnetism generate a global contribution proportional to g{sup {mu}{nu}}in the energy-momentum tensor, thus a simulacrum of dark energy. To provide a thorough understanding of the origin and strength of its effects, we undertake a complete theoretical and numerical study of the energy-momentum tensor T{sup {mu}{nu}}for nonlinear electromagnetism. The Euler-Heisenberg nonlinearity due to quantum fluctuations of spinor and scalar matter fields is considered and contrasted with the properties of classical nonlinear Born-Infeld electromagnetism. We address modifications of charged particle kinematics by strong background fields.

The Effects of Boundary Conditions and Friction on the Helical Buckling of Coiled Tubing in an Inclined Wellbore

PubMed Central

Ai, Zhijiu; Sun, Xu; Fu, Biwei

2016-01-01

Analytical buckling models are important for down-hole operations to ensure the structural integrity of the drill string. A literature survey shows that most published analytical buckling models do not address the effects of inclination angle, boundary conditions or friction. The objective of this paper is to study the effects of boundary conditions, friction and angular inclination on the helical buckling of coiled tubing in an inclined wellbore. In this paper, a new theoretical model is established to describe the buckling behavior of coiled tubing. The buckling equations are derived by applying the principles of virtual work and minimum potential energy. The proper solution for the post-buckling configuration is determined based on geometric and natural boundary conditions. The effects of angular inclination and boundary conditions on the helical buckling of coiled tubing are considered. Many significant conclusions are obtained from this study. When the dimensionless length of the coiled tubing is greater than 40, the effects of the boundary conditions can be ignored. The critical load required for helical buckling increases as the angle of inclination and the friction coefficient increase. The post-buckling behavior of coiled tubing in different configurations and for different axial loads is determined using the proposed analytical method. Practical examples are provided that illustrate the influence of the angular inclination on the axial force. The rate of change of the axial force decreases with increasing angular inclination. Moreover, the total axial friction also decreases with an increasing inclination angle. These results will help researchers to better understand helical buckling in coiled tubing. Using this knowledge, measures can be taken to prevent buckling in coiled tubing during down-hole operations. PMID:27649535

The Effects of Boundary Conditions and Friction on the Helical Buckling of Coiled Tubing in an Inclined Wellbore.

PubMed

Gong, Yinchun; Ai, Zhijiu; Sun, Xu; Fu, Biwei

2016-01-01

Analytical buckling models are important for down-hole operations to ensure the structural integrity of the drill string. A literature survey shows that most published analytical buckling models do not address the effects of inclination angle, boundary conditions or friction. The objective of this paper is to study the effects of boundary conditions, friction and angular inclination on the helical buckling of coiled tubing in an inclined wellbore. In this paper, a new theoretical model is established to describe the buckling behavior of coiled tubing. The buckling equations are derived by applying the principles of virtual work and minimum potential energy. The proper solution for the post-buckling configuration is determined based on geometric and natural boundary conditions. The effects of angular inclination and boundary conditions on the helical buckling of coiled tubing are considered. Many significant conclusions are obtained from this study. When the dimensionless length of the coiled tubing is greater than 40, the effects of the boundary conditions can be ignored. The critical load required for helical buckling increases as the angle of inclination and the friction coefficient increase. The post-buckling behavior of coiled tubing in different configurations and for different axial loads is determined using the proposed analytical method. Practical examples are provided that illustrate the influence of the angular inclination on the axial force. The rate of change of the axial force decreases with increasing angular inclination. Moreover, the total axial friction also decreases with an increasing inclination angle. These results will help researchers to better understand helical buckling in coiled tubing. Using this knowledge, measures can be taken to prevent buckling in coiled tubing during down-hole operations.

A rare case of scleral buckle infection with Curvularia species.

PubMed

Singh, Shalini; Shrivastav, Ankita; Agarwal, Manisha; Gandhi, Arpan; Mayor, Rahul; Paul, Lagan

2018-02-09

Scleral buckling is an established modality of treating retinal detachment. Being an external implant the buckle may be prone to infections. We report such a case with a delayed presentation and a rare etiology. A 45 year old male presented with redness, foreign body sensation and discharge for one month in his right eye. The patient had undergone a retinal detachment surgery elsewhere 14 years back without any visual gain. Right eye demonstrated no perception of light and the best corrected visual acuity in the left eye was 6/6, N6. On downgaze an exposed and anteriorly displaced scleral buckle was identified with black deposits and mucopurulent material overlying the buckle. Scleral buckle removal was done. On microbiological examination Curvularia species was identified. Successful treatment with antifungals was done. Scleral buckle infection with dematiaceous fungi is a rare occurrence. To the best of our knowledge this is the first case report describing a buckle infection caused by the curvularia species.

Buckling Response of a Large-Scale, Seamless, Orthogrid-Stiffened Metallic Cylinder

NASA Technical Reports Server (NTRS)

Rudd, Michelle Tillotson; Hilburger, Mark W.; Lovejoy, Andrew E.; Lindell, Michael C.; Gardner, Nathaniel W.; Schultz, Marc R.

2018-01-01

Results from the buckling test of a compression-loaded 8-ft-diameter seamless (i.e., without manufacturing joints), orthogrid-stiffened metallic cylinder are presented. This test was used to assess the buckling response and imperfection sensitivity characteristics of a seamless cylinder. In addition, the test article and test served as a technology demonstration to show the application of the flow forming manufacturing process to build more efficient buckling-critical structures by eliminating the welded joints that are traditionally used in the manufacturing of large metallic barrels. Pretest predictions of the cylinder buckling response were obtained using a finite-element model that included measured geometric imperfections. The buckling load predicted using this model was 697,000 lb, and the test article buckled at 743,000 lb (6% higher). After the test, the model was revised to account for measured variations in skin and stiffener geometry, nonuniform loading, and material properties. The revised model predicted a buckling load of 754,000 lb, which is within 1.5% of the tested buckling load. In addition, it was determined that the load carrying capability of the seamless cylinder is approximately 28% greater than a corresponding cylinder with welded joints.

FE Analysis of Buckling Behavior Caused by Welding in Thin Plates of High Tensile Strength Steel

NASA Astrophysics Data System (ADS)

Wang, Jiangchao; Rashed, Sherif; Murakawa, Hidekazu

2014-12-01

The target of this study was to investigate buckling behavior during the entire welding process which consists of the heating and the cooling processes. For thin plate structures made of high tensile strength steel, not only residual buckling during or after cooling down but also transient buckling during heating may occur. The thermal elastic plastic FE analysis to investigate welding-induced buckling during the entire welding process is presented. Because of the high yield stress of high tensile strength steel, larger longitudinal compressive thermal stress is produced near the welding line compared with that in the case of carbon steel. Therefore, the plate may buckle due to thermal expansion, before the material nears yielding. During cooling down, the longitudinal compressive thermal stress close to the welding line disappears, and longitudinal tensile residual stress is produced due to contraction. Meanwhile, longitudinal compressive residual stress occurs far from the welding line to balance the tensile stress close to the welding line. This distribution of longitudinal residual stress would change the deformed dish shape of transient buckling into a saddle buckling type when the stress exceeds the critical buckling condition.

Energy Absorption of Expansion Tube Considering Local Buckling Characteristics

NASA Astrophysics Data System (ADS)

Ahn, Kwang-Hyun; Kim, Jin-Sung; Huh, Hoon

This paper deals with the crash energy absorption and the local buckling characteristics of the expansion tube during the tube expanding processes. In order to improve energy absorption capacity of expansion tubes, local buckling characteristics of an expansion tube must be considered. The local buckling load and the absorbed energy during the expanding process were calculated for various types of tubes and punch shapes with finite element analysis. The energy absorption capacity of the expansion tube is influenced by the tube and the punch shape. The material properties of tubes are also important parameter for energy absorption. During the expanding process, local buckling occurs in some cases, which causes significant decreasing the absorbed energy of the expansion tube. Therefore, it is important to predict the local buckling load accurately to improve the energy absorption capacity of the expansion tube. Local buckling takes place relatively easily at the large punch angle and expansion ratio. Local buckling load is also influenced by both the tube radius and the thickness. In prediction of the local buckling load, modified Plantema equation was used for strain hardening and strain rate hardening. The modified Plantema equation shows a good agreement with the numerical result.

Analyses of Buckling and Stable Tearing in Thin-Sheet Materials

NASA Technical Reports Server (NTRS)

Seshadri, B. R.; Newman, J. C., Jr.

1998-01-01

This paper was to verify the STAGS (general shell, geometric and material nonlinear) code and the critical crack tip opening angle (CTOA) fracture criterion for predicting stable tearing in cracked panels that fail with severe out of plane buckling. Materials considered ranged from brittle to ductile behavior. Test data used in this study are reported elsewhere. The STAGS code was used to model stable tearing using a critical CTOA value that was determined from a cracked panel that was 'restrained' from buckling. ne analysis methodology was then used to predict the influence of buckling on stable tearing and failure loads. Parameters like crack length to specimen width ratio, crack configuration, thickness, and material tensile properties had a significant influence on the buckling behavior of cracked thin sheet materials. Experimental and predicted results showed a varied buckling response for different crack length to sheet thickness ratios because different buckling modes were activated. Effects of material tensile properties and fracture toughness on buckling response were presented. The STAGS code and the CTOA fracture criterion were able to predict the influence of buckling on stable tearing behavior and failure loads on a variety of materials and crack configurations.

Probabilistic Dynamic Buckling of Smart Composite Shells

NASA Technical Reports Server (NTRS)

Abumeri, Galib H.; Chamis, Christos C.

2003-01-01

A computational simulation method is presented to evaluate the deterministic and nondeterministic dynamic buckling of smart composite shells. The combined use of composite mechanics, finite element computer codes, and probabilistic analysis enable the effective assessment of the dynamic buckling load of smart composite shells. A universal plot is generated to estimate the dynamic buckling load of composite shells at various load rates and probabilities. The shell structure is also evaluated with smart fibers embedded in the plies right below the outer plies. The results show that, on the average, the use of smart fibers improved the shell buckling resistance by about 10 percent at different probabilities and delayed the buckling occurrence time. The probabilistic sensitivities results indicate that uncertainties in the fiber volume ratio and ply thickness have major effects on the buckling load while uncertainties in the electric field strength and smart material volume fraction have moderate effects. For the specific shell considered in this evaluation, the use of smart composite material is not recommended because the shell buckling resistance can be improved by simply re-arranging the orientation of the outer plies, as shown in the dynamic buckling analysis results presented in this report.

Probabilistic Dynamic Buckling of Smart Composite Shells

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Abumeri, Galib H.

2007-01-01

A computational simulation method is presented to evaluate the deterministic and nondeterministic dynamic buckling of smart composite shells. The combined use of intraply hybrid composite mechanics, finite element computer codes, and probabilistic analysis enable the effective assessment of the dynamic buckling load of smart composite shells. A universal plot is generated to estimate the dynamic buckling load of composite shells at various load rates and probabilities. The shell structure is also evaluated with smart fibers embedded in the plies right next to the outer plies. The results show that, on the average, the use of smart fibers improved the shell buckling resistance by about 10% at different probabilities and delayed the buckling occurrence time. The probabilistic sensitivities results indicate that uncertainties in the fiber volume ratio and ply thickness have major effects on the buckling load while uncertainties in the electric field strength and smart material volume fraction have moderate effects. For the specific shell considered in this evaluation, the use of smart composite material is not recommended because the shell buckling resistance can be improved by simply re-arranging the orientation of the outer plies, as shown in the dynamic buckling analysis results presented in this report.

Thermal and Mechanical Buckling Analysis of Hypersonic Aircraft Hat-Stiffened Panels With Varying Face Sheet Geometry and Fiber Orientation

NASA Technical Reports Server (NTRS)

Ko, William L.

1996-01-01

Mechanical and thermal buckling behavior of monolithic and metal-matrix composite hat-stiffened panels were investigated. The panels have three types of face-sheet geometry: Flat face sheet, microdented face sheet, and microbulged face sheet. The metal-matrix composite panels have three types of face-sheet layups, each of which is combined with various types of hat composite layups. Finite-element method was used in the eigenvalue extractions for both mechanical and thermal buckling. The thermal buckling analysis required both eigenvalue and material property iterations. Graphical methods of the dual iterations are shown. The mechanical and thermal buckling strengths of the hat-stiffened panels with different face-sheet geometry are compared. It was found that by just microdenting or microbulging of the face sheet, the axial, shear, and thermal buckling strengths of both types of hat-stiffened panels could be enhanced considerably. This effect is more conspicuous for the monolithic panels. For the metal-matrix composite panels, the effect of fiber orientations on the panel buckling strengths was investigated in great detail, and various composite layup combinations offering, high panel buckling strengths are presented. The axial buckling strength of the metal-matrix panel was sensitive to the change of hat fiber orientation. However, the lateral, shear, and thermal buckling strengths were insensitive to the change of hat fiber orientation.

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse-Shear Effects

NASA Technical Reports Server (NTRS)

McGowan, David Michael

1997-01-01

The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. The formulation uses the principle of virtual work. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are then derived after the application of several simplifying assumptions. These equations are then modified to allow the reference surface of the plate to be located at a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described as well. The terms of the plate stiffness matrix using both Classical Plate Theory (CPT) and first-order Shear-Deformation Plate Theory (SDPT) are presented. The necessary steps to include the effects of in-plane transverse and in-plane shear loads in the in-plane stability equations are also outlined. Numerical results are presented using the newly implemented capability. Comparisons of results for several example problems with different loading states are made. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPF are also made. Results comparing the computational effort required by the new analysis to that of the analysis currently in the VICONOPT program are presented. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.

Buckling of circular cylindrical shells under dynamically applied axial loads

NASA Technical Reports Server (NTRS)

Tulk, J. D.

1972-01-01

A theoretical and experimental study was made of the buckling characteristics of perfect and imperfect circular cylindrical shells subjected to dynamic axial loading. Experimental data included dynamic buckling loads (124 data points), high speed photographs of buckling mode shapes and observations of the dynamic stability of shells subjected to rapidly applied sub-critical loads. A mathematical model was developed to describe the dynamic behavior of perfect and imperfect shells. This model was based on the Donnell-Von Karman compatibility and equilibrium equations and had a wall deflection function incorporating five separate modes of deflection. Close agreement between theory and experiment was found for both dynamic buckling strength and buckling mode shapes.

Revivals of electron currents and topological-band insulator transitions in 2D gapped Dirac materials

NASA Astrophysics Data System (ADS)

Romera, E.; Bolívar, J. C.; Roldán, J. B.; de los Santos, F.

2016-07-01

We have studied the time evolution of electron wave packets in silicene under perpendicular magnetic and electric fields to characterize topological-band insulator transitions. We have found that at the charge neutrality points, the periodicities exhibited by the wave packet dynamics (classical and revival times) reach maximum values, and that the electron currents reflect the transition from a topological insulator to a band insulator. This provides a signature of topological phase transition in silicene that can be extended to other 2D Dirac materials isostructural to graphene and with a buckled structure and a significant spin-orbit coupling.

Numerical and experimental study on buckling and postbuckling behavior of cracked cylindrical shells

NASA Astrophysics Data System (ADS)

Saemi, J.; Sedighi, M.; Shariati, M.

2015-09-01

The effect of crack on load-bearing capacity and buckling behavior of cylindrical shells is an essential consideration in their design. In this paper, experimental and numerical buckling analysis of steel cylindrical shells of various lengths and diameters with cracks have been studied using the finite element method, and the effect of crack position, crack orientation and the crack length-to-cylindrical shell perimeter ( λ = a/(2 πr)) and shell length-to-diameter ( L/ D) ratios on the buckling and post-buckling behavior of cylindrical shells has been investigated. For several specimens, buckling test was performed using an INSTRON 8802 servo hydraulic machine, and the results of experimental tests were compared to numerical results. A very good correlation was observed between numerical simulation and experimental results. Finally, based on the experimental and numerical results, sensitivity of the buckling load to the shell length, crack length and orientation has also been investigated.

Regularized estimation of Euler pole parameters

NASA Astrophysics Data System (ADS)

Aktuğ, Bahadir; Yildirim, Ömer

2013-07-01

Euler vectors provide a unified framework to quantify the relative or absolute motions of tectonic plates through various geodetic and geophysical observations. With the advent of space geodesy, Euler parameters of several relatively small plates have been determined through the velocities derived from the space geodesy observations. However, the available data are usually insufficient in number and quality to estimate both the Euler vector components and the Euler pole parameters reliably. Since Euler vectors are defined globally in an Earth-centered Cartesian frame, estimation with the limited geographic coverage of the local/regional geodetic networks usually results in highly correlated vector components. In the case of estimating the Euler pole parameters directly, the situation is even worse, and the position of the Euler pole is nearly collinear with the magnitude of the rotation rate. In this study, a new method, which consists of an analytical derivation of the covariance matrix of the Euler vector in an ideal network configuration, is introduced and a regularized estimation method specifically tailored for estimating the Euler vector is presented. The results show that the proposed method outperforms the least squares estimation in terms of the mean squared error.

78 FR 54594 - Airworthiness Directives; Pacific Scientific Aviation Services (Pacific Scientific) Seat...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-05

... Buckle Assemblies AGENCY: Federal Aviation Administration (FAA), DOT. ACTION: Notice of proposed... Scientific seat restraint rotary buckle assemblies (buckle). This proposed AD is prompted by several reports... checking the P/N on the reverse side of the buckle assembly against the P/N listed in Appendix 1 of the SB...

Thermostructural Analysis of Unconventional Wing Structures of a Hyper-X Hypersonic Flight Research Vehicle for the Mach 7 Mission

NASA Technical Reports Server (NTRS)

Ko, William L.; Gong, Leslie

2001-01-01

Heat transfer, thermal stresses, and thermal buckling analyses were performed on the unconventional wing structures of a Hyper-X hypersonic flight research vehicle (designated as X-43) subjected to nominal Mach 7 aerodynamic heating. A wing midspan cross section was selected for the heat transfer and thermal stress analyses. Thermal buckling analysis was performed on three regions of the wing skin (lower or upper); 1) a fore wing panel, 2) an aft wing panel, and 3) a unit panel at the middle of the aft wing panel. A fourth thermal buckling analysis was performed on a midspan wing segment. The unit panel region is identified as the potential thermal buckling initiation zone. Therefore, thermal buckling analysis of the Hyper-X wing panels could be reduced to the thermal buckling analysis of that unit panel. "Buckling temperature magnification factors" were established. Structural temperature-time histories are presented. The results show that the concerns of shear failure at wing and spar welded sites, and of thermal buckling of Hyper-X wing panels, may not arise under Mach 7 conditions.

Local buckling of composite channel columns

NASA Astrophysics Data System (ADS)

Szymczak, Czesław; Kujawa, Marcin

2018-05-01

The investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is taken into account here. The buckling mode of the member flange is defined by rotation angle a flange about the line of its connection with the web. The channel column under investigation is made of unidirectional fibre-reinforced laminate. Two approaches to member orthotropic material modelling are performed: the homogenization with the aid of theory of mixture and periodicity cell or homogenization upon the Voigt-Reuss hypothesis. The fundamental differential equation of local buckling is derived with the aid of the stationary total potential energy principle. The critical buckling stress corresponding to a number of buckling half-waves is assumed to be a minimum eigenvalue of the equation. Some numerical examples dealing with columns are given here. The analytical results are compared with the finite element stability analysis carried out by means of ABAQUS software. The paper is focused on a close analytical solution of the critical buckling stress and the associated buckling mode while the web-flange cooperation is assumed.

Effects of interfacial debonding and fiber breakage on static and dynamic buckling of fibers embedded in matrices

NASA Astrophysics Data System (ADS)

Serttunc, Metin

1992-09-01

Analyses were performed for static and dynamic buckling of a continuous fiber embedded in a matrix in order to determine the effects of interfacial debonding and fiber breakage on the critical buckling load and the domain of instability. A beam on elastic foundation model was used. The study showed that a local interfacial debonding between a fiber and a surrounding matrix resulted in an increase of the wavelength of the buckling mode. An increase of the wave length yielded a decrease of the static buckling load and lowered the dynamic instability domain. In general, the effect of a partial or complete interfacial debonding was more significant on the domain of dynamic instability than on the effects of static buckling load. For dynamic buckling of a fiber, a local debonding of size 10 to 20 percent of the fiber length had the most important influence on the domains of dynamic instability regardless of the location of debonding and the boundary conditions of the fiber. For static buckling, the location of a local debonding was critical to a free-simply supported fiber but not to a fiber with both ends simply supported. Fiber breakage also lowered the critical buckling load significantly.

An analytical study of the effects of transverse shear deformation and anisotropy on buckling loads of laminated cylinders. M.S. Thesis - George Washington Univ.

NASA Technical Reports Server (NTRS)

Jegley, Dawn C.

1987-01-01

Buckling loads of thick-walled orthotropic and anisotropic simply supported circular cylinders are predicted using a higher-order transverse-shear deformation theory. A comparison of buckling loads predicted by the conventional first-order transverse-shear deformation theory and the higher-order theory show that the additional allowance for transverse shear deformation has a negligible effect on the predicted buckling loads of medium-thick metallic isotropic cylinders. However, the higher-order theory predicts buckling loads which are significantly lower than those predicted by the first-order transverse-shear deformation theory for certain short, thick-walled cylinders which have low through-the-thickness shear moduli. A parametric study of the effects of ply orientation on the buckling load of axially compressed cylinders indicates that laminates containing 45 degree plies are most sensitive to transverse-shear deformation effects. Interaction curves for buckling loads of cylinders subjected to axial compressive and external pressure loadings indicate that buckling loads due to external pressure loadings are as sensitive to transverse-shear deformation effects as buckling loads due to axial compressive loadings. The effects of anisotropy are important over a much wider range of cylinder geometries than the effects of transverse shear deformation.

Anomalous Buckling Characteristics of Laminated Metal-Matrix Composite Plates with Central Square Holes

NASA Technical Reports Server (NTRS)

Ko, William L.

1998-01-01

Compressive buckling analysis was performed on metal-matrix composite (MMC) plates with central square holes. The MMC plates have varying aspect ratios and hole sizes and are supported under different boundary conditions. The finite-element structural analysis method was used to study the effects of plate boundary conditions, plate aspect ratio, hole size, and the composite stacking sequence on the compressive buckling strengths of the perforated MMC plates. Studies show that by increasing the hole sizes, compressive buckling strengths of the perforated MMC plates could be considerably increased under certain boundary conditions and aspect ratios ("anomalous" buckling behavior); and that the plate buckling mode could be symmetrical or antisymmetrical, depending on the plate boundary conditions, aspect ratio, and the hole size. For same-sized plates with same-sized holes, the compressive buckling strengths of the perforated MMC plates with [90/0/0/90]2 lamination could be as much as 10 percent higher or lower than those of the [45/- 45/- 45/45]2 laminations, depending on the plate boundary conditions, plate aspect ratios, and the hole size. Clamping the plate edges induces far stronger "anomalous" buckling behavior (enhancing compressive buckling strengths at increasing hole sizes) of the perforated MMC plates than simply supporting the plate edges.

Active stabilization of thin-wall structures under compressive loading

NASA Astrophysics Data System (ADS)

Welham, Jared; Calius, Emilio P.; Chase, J. Geoffrey

2003-08-01

The active suppression of elastic buckling instability has the potential to significantly increase the effective strength of thin-wall structures. Despite all the interest in smart structures, the active suppression of buckling has received comparatively little attention. This paper addresses the effects of embedded actuation on the compression buckling strength of laminated composite plates through analysis and simulation. Numerical models are formulated that include the influence of essential features such as sensor uncertainty and noise, actuator saturation and control architecture on the buckling process. Silicon-based strain sensors and diffuse laser distance sensors are both considered for use in the detection of incipient buckling behavior due to their increased sensitivity. Actuation is provided by paired distributions of piezo-electric material incorporated into both sides of the laminate. Optimal controllers are designed to command the structure to deform in ways that interfere with the development of buckling mode shapes. Commercial software packages are used to solve the resulting non-linear equations, and some of the tradeoffs are enumerated. Overall, the results show that active buckling control can considerably enhance resistance to instability under compressive loads. These buckling load predictions demonstrate the viability of optimal control and piezo-electric actuation for implementing active buckling control. Due to the importance of early detection, the relative effectiveness of active buckling control is shown to be strongly dependent on the performance of the sensing scheme, as well as on the characteristics of the structure.

Knee Instability and Basic and Advanced Function Decline in Knee Osteoarthritis.

PubMed

Sharma, Leena; Chmiel, Joan S; Almagor, Orit; Moisio, Kirsten; Chang, Alison H; Belisle, Laura; Zhang, Yunhui; Hayes, Karen W

2015-08-01

Manifestations of instability in knee osteoarthritis (OA) include low overall knee confidence, low confidence that the knees will not buckle, buckling, and excessive motion during gait. Confidence and buckling may particularly influence activity choices, contributing to events leading to disability. Buckling is more likely to affect advanced than basic functional tasks. In this prospective longitudinal study, we tested the hypothesis that overall knee confidence, buckling confidence, buckling, and frontal plane motion during gait are associated with advanced 2-year function outcomes in persons with knee OA. Persons with knee OA were queried about overall knee confidence (higher score = worse confidence), buckling confidence, and knee buckling, and underwent quantitative gait analysis to quantify varus-valgus excursion and angular velocity. Physical function was assessed using the Late-Life Function and Disability Instrument Basic and Advanced Lower Extremity Domain scores. Logistic regression was used to evaluate the relationship between baseline instability measures and baseline-to-2-year function outcome, adjusting for potential confounders. The sample was comprised of 212 persons (mean age 64.6 years, 76.9% women). Buckling was significantly associated with poor advanced function outcome (adjusted odds ratio [OR] 2.08, 95% confidence interval [95% CI] 1.03-4.20) but not basic function outcome. Overall knee confidence was significantly associated with advanced outcome (adjusted OR 1.65, 95% CI 1.01-2.70), while associations between buckling confidence and both outcomes approached significance. Neither varus-valgus excursion nor angular velocity during gait was associated with either outcome. Knee buckling and low knee confidence were each associated with poor 2-year advanced function outcomes. Current treatment does not address these modifiable factors; interventions to address them may improve outcome in knee OA. © 2015, American College of Rheumatology.

Free Vibration Analysis of DWCNTs Using CDM and Rayleigh-Schmidt Based on Nonlocal Euler-Bernoulli Beam Theory

PubMed Central

2014-01-01

The free vibration response of double-walled carbon nanotubes (DWCNTs) is investigated. The DWCNTs are modelled as two beams, interacting between them through the van der Waals forces, and the nonlocal Euler-Bernoulli beam theory is used. The governing equations of motion are derived using a variational approach and the free frequencies of vibrations are obtained employing two different approaches. In the first method, the two double-walled carbon nanotubes are discretized by means of the so-called “cell discretization method” (CDM) in which each nanotube is reduced to a set of rigid bars linked together by elastic cells. The resulting discrete system takes into account nonlocal effects, constraint elasticities, and the van der Waals forces. The second proposed approach, belonging to the semianalytical methods, is an optimized version of the classical Rayleigh quotient, as proposed originally by Schmidt. The resulting conditions are solved numerically. Numerical examples end the paper, in which the two approaches give lower-upper bounds to the true values, and some comparisons with existing results are offered. Comparisons of the present numerical results with those from the open literature show an excellent agreement. PMID:24715807

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

Theory of buckling and post-buckling behavior of elastic structures

NASA Technical Reports Server (NTRS)

Budiansky, B.

1974-01-01

The present paper provides a unified, general presentation of the basic theory of the buckling and post-buckling behavior of elastic structures in a form suitable for application to a wide variety of special problems. The notation of functional analysis is used for this purpose. Before the general analysis, simple conceptual models are used to elucidate the basic concepts of bifurcation buckling, snap buckling, imperfection sensitivity, load-shortening relations, and stability. The energy approach, the virtual-work approach, and mode interaction are discussed. The derivations and results are applicable to continua and finite-dimensional systems. The virtual-work and energy approaches are given separate treatments, but their equivalence is made explicit. The basic concepts of stability occupy a secondary position in the present approach.

The Carnegie-Irvine Galaxy Survey. V. Statistical Study of Bars and Buckled Bars

NASA Astrophysics Data System (ADS)

Li, Zhao-Yu; Ho, Luis C.; Barth, Aaron J.

2017-08-01

Simulations have shown that bars are subject to a vertical buckling instability that transforms thin bars into boxy or peanut-shaped structures, but the physical conditions necessary for buckling to occur are not fully understood. We use the large sample of local disk galaxies in the Carnegie-Irvine Galaxy Survey to examine the incidence of bars and buckled bars across the Hubble sequence. Depending on the disk inclination angle (I), a buckled bar reveals itself as either a boxy/peanut-shaped bulge (at high I) or as a barlens structure (at low I). We visually identify bars, boxy/peanut-shaped bulges, and barlenses, and examine the dependence of bar and buckled bar fractions on host galaxy properties, including Hubble type, stellar mass, color, and gas mass fraction. We find that the barred and unbarred disks show similar distributions in these physical parameters. The bar fraction is higher (70%-80%) in late-type disks with low stellar mass (M * < 1010.5 M ⊙) and high gas mass ratio. In contrast, the buckled bar fraction increases to 80% toward massive and early-type disks (M * > 1010.5 M ⊙), and decreases with higher gas mass ratio. These results suggest that bars are more difficult to grow in massive disks that are dynamically hotter than low-mass disks. However, once a bar forms, it can easily buckle in the massive disks, where a deeper potential can sustain the vertical resonant orbits. We also find a probable buckling bar candidate (ESO 506-G004) that could provide further clues to understand the timescale of the buckling process.

Artery buckling analysis using a two-layered wall model with collagen dispersion.

PubMed

Mottahedi, Mohammad; Han, Hai-Chao

2016-07-01

Artery buckling has been proposed as a possible cause for artery tortuosity associated with various vascular diseases. Since microstructure of arterial wall changes with aging and diseases, it is essential to establish the relationship between microscopic wall structure and artery buckling behavior. The objective of this study was to developed arterial buckling equations to incorporate the two-layered wall structure with dispersed collagen fiber distribution. Seven porcine carotid arteries were tested for buckling to determine their critical buckling pressures at different axial stretch ratios. The mechanical properties of these intact arteries and their intima-media layer were determined via pressurized inflation test. Collagen alignment was measured from histological sections and modeled by a modified von-Mises distribution. Buckling equations were developed accordingly using microstructure-motivated strain energy function. Our results demonstrated that collagen fibers disperse around two mean orientations symmetrically to the circumferential direction (39.02°±3.04°) in the adventitia layer; while aligning closely in the circumferential direction (2.06°±3.88°) in the media layer. The microstructure based two-layered model with collagen fiber dispersion described the buckling behavior of arteries well with the model predicted critical pressures match well with the experimental measurement. Parametric studies showed that with increasing fiber dispersion parameter, the predicted critical buckling pressure increases. These results validate the microstructure-based model equations for artery buckling and set a base for further studies to predict the stability of arteries due to microstructural changes associated with vascular diseases and aging. Copyright © 2016 Elsevier Ltd. All rights reserved.

Optomechanical design of a buckling cavity in a low-cost high-performance ferruleless field-installable single-mode fiber connector

NASA Astrophysics Data System (ADS)

Ebraert, Evert; Van Erps, Jürgen; Beri, Stefano; Watté, Jan; Thienpont, Hugo

2014-10-01

To boost the deployment of fiber-to-the-home networks in order to meet the ever-increasing demand for bandwidth, there is a strong need for single-mode fiber (SMF) connectors which combine low insertion loss with field installability. Shifting from ferrule-based to ferruleless connectors can reduce average insertion losses appreciably and minimize modal noise interference. We propose a ferruleless connector and adaptor in which physical contact between two inline fibers is ensured by at least one fiber being in a buckled state. To this end, we design a buckling cavity in which the SMF can buckle in a controlled way to ensure good optical performance as well as mechanical stability. This design is based on both mechanical and optical considerations. Finite element analysis suggests that mechanically a minimal buckling cavity length of 17 mm is required, while the height of the cavity should be chosen such that the buckled SMF is not mechanically confined to ensure buckling in a first-order mode. The optical bending loss in the buckled SMF is calculated using a fully vectorial mode solver, showing that a minimal buckling cavity length of 20 mm is necessary to keep the excess optical loss from bending below 0.1 dB. Both our optical and mechanical simulation results are experimentally verified.

3 CFR 8632 - Proclamation 8632 of February 28, 2011. Death of Army Corporal Frank W. Buckles, the Last...

Code of Federal Regulations, 2012 CFR

2012-01-01

... Army Corporal Frank W. Buckles, the Last Surviving American Veteran of World War I 8632 Proclamation... Army Corporal Frank W. Buckles, the Last Surviving American Veteran of World War IBy the President of... W. Buckles, the last surviving American veteran of World War I, and in remembrance of the generation...

Dynamics of a homogeneous ball on a horizontal plane with sliding, spinning, and rolling friction taken into account

NASA Astrophysics Data System (ADS)

Ishkhanyan, M. V.; Karapetyan, A. V.

2010-04-01

We analyze the dynamics of a homogeneous ball on a horizontal plane with friction of all kinds, namely, sliding, spinning, and rolling friction, taken into account. The qualitative-analytic study of the ball dynamics is supplemented with numerical experiments. The problem on the motion of a homogeneous ball on a horizontal plane with friction was apparently first studied in 1758 by I. Euler (Leonard Euler's son) with sliding friction taken into account in the framework of the Coulomb model. I. Euler showed that the ball sliding ceases in finite time, after which the ball uniformly rolls along a fixed straight line and uniformly spins about the vertical. This result has long become classical and is described in many textbooks on theoretical mechanics. In 1998, V. F. Zhuravlev considered the problem of motion of a homogeneous ball on a horizontal plane with sliding and spinning friction taken into account in the framework of the Contensou-Zhuravlev model [1, 2] and showed that the ball sliding and spinning cease simultaneously, after which the ball uniformly rolls along a fixed straight line. The Contensou-Zhuravlev theory was further developed in [3-7]. In the present paper, we consider themotion of a homogeneous ball on a horizontal plane with friction of all kinds taken into account in the framework of the model proposed in [8]. We show that, in one and the same time, both the sliding velocity and the angular velocity of the ball become zero. Our studies are based on the results obtained in [2], the properties of the friction model proposed in [8], and the method for qualitative analysis of dynamics of dissipative systems [9, 10]. The qualitative-analytic study is supplemented with numerical experiments.

Summary of Research Report

NASA Technical Reports Server (NTRS)

Elishakoff, Isaac

1998-01-01

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

The inward bulge type buckling of monocoque cylinders I : calculation of the effect upon the buckling stress of a compressive force, a nonlinear direct stress distribution, and a shear force

NASA Technical Reports Server (NTRS)

Hoff, N J; Klein, Bertram

1944-01-01

In the present part I of a series of reports on the inward bulge type buckling of monocoque cylinders the buckling load in combined bending and compression is first derived. Next the reduction in the buckling load because of a nonlinear direct stress distribution is determined. In experiments nonlinearity may result from an inadequate stiffness of the end attachments in actual airplanes from the existence of concentrated loads or cut-outs. The effect of a shearing force upon the critical load is investigated through an analysis of the results of tests carried out at GALCIT with 55 reinforced monocoque cylinders. Finally, a simple criterion of general instability is presented in the form of a buckling inequality which should be helpful to the designer of a monocoque in determining the sizes of the rings required for excluding the possibility of inward bulge type buckling.

Buckling of Cracked Laminated Composite Cylindrical Shells Subjected to Combined Loading

NASA Astrophysics Data System (ADS)

Allahbakhsh, Hamidreza; Shariati, Mahmoud

2013-10-01

A series of finite element analysis on the cracked composite cylindrical shells under combined loading is carried out to study the effect of loading condition, crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, bending, internal pressure and external pressure are obtained, using the finite element method. Results show that the internal pressure increases the critical buckling load of the CFRP cylindrical shells and bending and external pressure decrease it. Numerical analysis show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell and results show that for lower values of the axial compressive load and higher values of the external pressure, the buckling is usually in the global mode and for higher values of axial compressive load and lower levels of external pressure the buckling mode is mostly in the local mode.

Fracture and buckling of piezoelectric nanowires subject to an electric field

NASA Astrophysics Data System (ADS)

Zhang, Jin; Wang, Chengyuan; Adhikari, Sondipon

2013-11-01

Fracture and buckling are major failure modes of thin and long nanowires (NWs), which could be affected significantly by an electric field when piezoelectricity is involved in the NWs. This paper aims to examine the issue based on the molecular dynamics simulations, where the gallium nitride (GaN) NWs are taken as an example. The results show that the influence of the electric field is strong for the fracture and the critical buckling strains, detectable for the fracture strength but almost negligible for the critical buckling stress. In addition, the reversed effects are achieved for the fracture and the critical buckling strains. Subsequently, the Timoshenko beam model is utilized to account for the effect of the electric field on the axial buckling of the GaN NWs, where nonlocal effect is observed and characterized by the nonlocal coefficient e0a=1.1 nm. The results show that the fracture and buckling of piezoelectric NWs can be controlled by applying an electric field.

Micro-wrinkling and delamination-induced buckling of stretchable electronic structures

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

Oyewole, O. K.; Department of Materials Science and Engineering, Kwara State University, Malete, P.M.B 1530, Ilorin, Kwara State; Yu, D.

This paper presents the results of experimental and theoretical/computational micro-wrinkles and buckling on the surfaces of stretchable poly-dimethylsiloxane (PDMS) coated with nano-scale Gold (Au) layers. The wrinkles and buckles are formed by the unloading of pre-stretched PDMS/Au structure after the evaporation of nano-scale Au layers. They are then characterized using atomic force microscopy and scanning electron microscopy. The critical stresses required for wrinkling and buckling are analyzed using analytical models. The possible interfacial cracking that can occur along with film buckling is also studied using finite element simulations of the interfacial crack growth. The implications of the results are discussedmore » for potential applications of micro-wrinkles and micro-buckles in stretchable electronic structures and biomedical devices.« less

Design of efficient stiffened shells of revolution

NASA Technical Reports Server (NTRS)

Majumder, D. K.; Thornton, W. A.

1976-01-01

A method to produce efficient piecewise uniform stiffened shells of revolution is presented. The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach. A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process. The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function. This allows the general buckling constraint to be included in the design process only when it is violated. The self-adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort. Results for four conical shells and one spherical shell are given.

The Buckling of a Column on Equally Spaced Deflectional and Rotational Springs

DTIC Science & Technology

1948-03-01

PN)~ - fj! 2(~N)2 0 r-,ee 03151 r=1,3,5 00 00 z PNa PM = 1 rN%N l-1,3,5 r=&3,5 . #O $=-. 2 2 p=l,3,5 p2fc2 -(j)’ ( B16 ) . which is the...berxiuse it always gives a higher buckling~load than doe6 eqvation ( B16 ). In order to obtain the buckling criterioxu for the other modes, equations (Bl...equations (B23) for a given q therefore corresponds to a buckling configuration of q buckles. Equation ( Bl6 ), as previously indicated, corresponds to

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.

Study on Buckling of Stiff Thin Films on Soft Substrates as Functional Materials

NASA Astrophysics Data System (ADS)

Ma, Teng

In engineering, buckling is mechanical instability of walls or columns under compression and usually is a problem that engineers try to prevent. In everyday life buckles (wrinkles) on different substrates are ubiquitous -- from human skin to a rotten apple they are a commonly observed phenomenon. It seems that buckles with macroscopic wavelengths are not technologically useful; over the past decade or so, however, thanks to the widespread availability of soft polymers and silicone materials micro-buckles with wavelengths in submicron to micron scale have received increasing attention because it is useful for generating well-ordered periodic microstructures spontaneously without conventional lithographic techniques. This thesis investigates the buckling behavior of thin stiff films on soft polymeric substrates and explores a variety of applications, ranging from optical gratings, optical masks, energy harvest to energy storage. A laser scanning technique is proposed to detect micro-strain induced by thermomechanical loads and a periodic buckling microstructure is employed as a diffraction grating with broad wavelength tunability, which is spontaneously generated from a metallic thin film on polymer substrates. A mechanical strategy is also presented for quantitatively buckling nanoribbons of piezoelectric material on polymer substrates involving the combined use of lithographically patterning surface adhesion sites and transfer printing technique. The precisely engineered buckling configurations provide a route to energy harvesters with extremely high levels of stretchability. This stiff-thin-film/polymer hybrid structure is further employed into electrochemical field to circumvent the electrochemically-driven stress issue in silicon-anode-based lithium ion batteries. It shows that the initial flat silicon-nanoribbon-anode on a polymer substrate tends to buckle to mitigate the lithiation-induced stress so as to avoid the pulverization of silicon anode. Spontaneously generated submicron buckles of film/polymer are also used as an optical mask to produce submicron periodic patterns with large filling ratio in contrast to generating only ˜100 nm edge submicron patterns in conventional near-field soft contact photolithography. This thesis aims to deepen understanding of buckling behavior of thin films on compliant substrates and, in turn, to harness the fundamental properties of such instability for diverse applications.

Research on Annular Frictional Pressure Loss of Hydraulic-Fracturing in Buckling Coiled Tubing

NASA Astrophysics Data System (ADS)

Liu, Bin; Cai, Meng; Li, Junliang; Xu, Yongquan; Wang, Peng

2018-01-01

Compared with conventional hydraulic fracturing, coiled tubing (CT) annular delivery sand fracturing technology is a new method to enhance the recovery ratio of low permeability reservoir. Friction pressure loss through CT has been a concern in fracturing. The small diameter of CT limits the cross-sectional area open to flow, therefore, to meet large discharge capacity, annular delivery sand technology has been gradually developed in oilfield. Friction pressure is useful for determining the required pump horsepower and fracturing construction design programs. Coiled tubing can buckle when the axial compressive load acting on the tubing is greater than critical buckling load, then the geometry shape of annular will change. Annular friction pressure loss elevates dramatically with increasing of discharge capacity, especially eccentricity and CT buckling. Despite the frequency occurrence of CT buckling in oilfield operations, traditionally annular flow frictional pressure loss considered concentric and eccentric annuli, not discussing the effects of for discharge capacity and sand ratio varying degree of CT buckling. The measured data shows that the factors mentioned above cannot be ignored in the prediction of annular pressure loss. It is necessary to carry out analysis of annulus flow pressure drop loss in coiled tubing annular with the methods of theoretical analysis and numerical simulation. Coiled tubing buckling has great influence on pressure loss of fracturing fluid. Therefore, the correlations have been developed for turbulent flow of Newtonian fluids and Two-phase flow (sand-liquid), and that improve the friction pressure loss estimation in coiled tubing operations involving a considerable level of buckling. Quartz sand evidently increases pressure loss in buckling annular, rising as high as 40%-60% more than fresh water. Meanwhile, annulus flow wetted perimeter increases with decreasing helical buckling pitch of coiled tubing, therefore, the annulus flow frictional pressure loss rapidly increases with decreasing helical buckling pitch. The research achievement provides theoretical guidance for coiled tubing annular delivery sand fracturing operation and design.

Modal nudging in nonlinear elasticity: Tailoring the elastic post-buckling behaviour of engineering structures

NASA Astrophysics Data System (ADS)

Cox, B. S.; Groh, R. M. J.; Avitabile, D.; Pirrera, A.

2018-07-01

The buckling and post-buckling behaviour of slender structures is increasingly being harnessed for smart functionalities. Equally, the post-buckling regime of many traditional engineering structures is not being used for design and may therefore harbour latent load-bearing capacity for further structural efficiency. Both applications can benefit from a robust means of modifying and controlling the post-buckling behaviour for a specific purpose. To this end, we introduce a structural design paradigm termed modal nudging, which can be used to tailor the post-buckling response of slender engineering structures without any significant increase in mass. Modal nudging uses deformation modes of stable post-buckled equilibria to perturb the undeformed baseline geometry of the structure imperceptibly, thereby favouring the seeded post-buckling response over potential alternatives. The benefits of this technique are enhanced control over the post-buckling behaviour, such as modal differentiation for smart structures that use snap-buckling for shape adaptation, or alternatively, increased load-carrying capacity, increased compliance or a shift from imperfection sensitivity to imperfection insensitivity. Although these concepts are, in theory, of general applicability, we concentrate here on planar frame structures analysed using the nonlinear finite element method and numerical continuation procedures. Using these computational techniques, we show that planar frame structures may exhibit isolated regions of stable equilibria in otherwise unstable post-buckling regimes, or indeed stable equilibria entirely disconnected from the natural structural response. In both cases, the load-carrying capacity of these isolated stable equilibria is greater than the natural structural response of the frames. Using the concept of modal nudging it is possible to "nudge" the frames onto these equilibrium paths of greater load-carrying capacity. Due to the scale invariance of modal nudging, these findings may impact the design of structures from the micro- to the macro-scale.

The Carnegie-Irvine Galaxy Survey. V. Statistical Study of Bars and Buckled Bars

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

Li, Zhao-Yu; Ho, Luis C.; Barth, Aaron J., E-mail: lizy@shao.ac.cn

Simulations have shown that bars are subject to a vertical buckling instability that transforms thin bars into boxy or peanut-shaped structures, but the physical conditions necessary for buckling to occur are not fully understood. We use the large sample of local disk galaxies in the Carnegie-Irvine Galaxy Survey to examine the incidence of bars and buckled bars across the Hubble sequence. Depending on the disk inclination angle ( i ), a buckled bar reveals itself as either a boxy/peanut-shaped bulge (at high i ) or as a barlens structure (at low i ). We visually identify bars, boxy/peanut-shaped bulges, andmore » barlenses, and examine the dependence of bar and buckled bar fractions on host galaxy properties, including Hubble type, stellar mass, color, and gas mass fraction. We find that the barred and unbarred disks show similar distributions in these physical parameters. The bar fraction is higher (70%–80%) in late-type disks with low stellar mass ( M {sub *} < 10{sup 10.5} M {sub ⊙}) and high gas mass ratio. In contrast, the buckled bar fraction increases to 80% toward massive and early-type disks ( M {sub *} > 10{sup 10.5} M {sub ⊙}), and decreases with higher gas mass ratio. These results suggest that bars are more difficult to grow in massive disks that are dynamically hotter than low-mass disks. However, once a bar forms, it can easily buckle in the massive disks, where a deeper potential can sustain the vertical resonant orbits. We also find a probable buckling bar candidate (ESO 506−G004) that could provide further clues to understand the timescale of the buckling process.« less

Measurements of Young's and shear moduli of rail steel at elevated temperatures.

PubMed

Bao, Yuanye; Zhang, Haifeng; Ahmadi, Mehdi; Karim, Md Afzalul; Felix Wu, H

2014-03-01

The design and modelling of the buckling effect of Continuous Welded Rail (CWR) requires accurate material constants, especially at elevated temperatures. However, such material constants have rarely been found in literature. In this article, the Young's moduli and shear moduli of rail steel at elevated temperatures are determined by a new sonic resonance method developed in our group. A network analyser is used to excite a sample hanged inside a furnace through a simple tweeter type speaker. The vibration signal is picked up by a Polytec OFV-5000 Laser Vibrometer and then transferred back to the network analyser. Resonance frequencies in both the flexural and torsional modes are measured, and the Young's moduli and shear moduli are determined through the measured resonant frequencies. To validate the measured elastic constants, the measurements have been repeated by using the classic sonic resonance method. The comparisons of obtained moduli from the two methods show an excellent consistency of the results. In addition, the material elastic constants measured are validated by an ultrasound test based on a pulse-echo method and compared with previous published results at room temperature. The measured material data provides an invaluable reference for the design of CWR to avoid detrimental buckling failure. Copyright © 2013 Elsevier B.V. All rights reserved.

Thermal buckling behavior of defective CNTs under pre-load: A molecular dynamics study.

PubMed

Mehralian, Fahimeh; Tadi Beni, Yaghoub; Kiani, Yaser

2017-05-01

Current study is concentrated on the extraordinary properties of defective carbon nanotubes (CNTs). The role of vacancy defects in thermal buckling response of precompressed CNTs is explored via molecular dynamics (MD) simulations. Defective CNTs are initially compressed at a certain ratio of their critical buckling strain and then undergo a uniform temperature rise. Comprehensive study is implemented on both armchair and zigzag CNTs with different vacancy defects including monovacancy, symmetric bivacancy and asymmetric bivacancy. The results reveal that defects have a pronounced impact on the buckling behavior of CNTs; interestingly, defective CNTs under compressive pre-load show higher resistance to thermal buckling than pristine ones. In the following, the buckling response of defective CNTs is shown to be dependent on the vacancy defects, location of defects and chirality. Copyright © 2017 Elsevier Inc. All rights reserved.

Effects of transverse shear deformation on buckling of laminated cylinders as a function of thickness and ply orientation

NASA Technical Reports Server (NTRS)

Jegley, Dawn C.

1987-01-01

Buckling loads of thick-walled, orthotropic, simply-supported right circular cylinders are predicted using a new higher-order transverse shear deformation theory. The higher-order theory shows that, by more accurately accounting for transverse shear deformation effects, the predicted buckling load may be reduced by as much as 80 percent compared to predictions based on conventional transverse shear deformation theory. A parametric study of the effect of ply orientation on the buckling load of axially compressed cylinders indicates that laminates containing 0 deg plies are the most sensitive to transverse shear deformation effects. Interaction curves for buckling of cylinders with axial compressive and external pressure loadings indicate that buckling loads due to external pressure loadings are much less sensitive to transverse shear deformation effects than those due to axial compressive loadings.

Buckling and Vibration of Fiber Reinforced Composite Plates With Nanofiber Reinforced Matrices

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Murthy, Pappu L. N.

2011-01-01

Anisotropic composite plates were evaluated with nanofiber reinforced matrices (NFRM). The nanofiber reinforcement volumes ratio in the matrix was 0.01. The plate dimensions were 20 by 10 by 1.0 in. (508 by 254 by 25.4 mm). Seven different loading condition cases were evaluated for buckling: three for uniaxial loading, three for pairs of combined loading, and one with three combined loadings. The anisotropy arose from the unidirectional plates having been at 30 from the structural axis. The anisotropy had a full 6 by 6 rigidities matrix which were satisfied and solved by a Galerkin buckling algorithm. For vibration the same conditions were used with the applied cods about a small fraction of the buckling loads. The buckling and vibration results showed that the NFRM plates buckled at about twice those with conventional matrix.

Helical coil buckling mechanism for a stiff nanowire on an elastomeric substrate

NASA Astrophysics Data System (ADS)

Chen, Youlong; Liu, Yilun; Yan, Yuan; Zhu, Yong; Chen, Xi

2016-10-01

When a stiff nanowire is deposited on a compliant soft substrate, it may buckle into a helical coil form when the system is compressed. Using theoretical and finite element method (FEM) analyses, the detailed three-dimensional coil buckling mechanism for a silicon nanowire (SiNW) on a polydimethylsiloxane (PDMS) substrate is studied. A continuum mechanics approach based on the minimization of the strain energy in the SiNW and elastomeric substrate is developed. Due to the helical buckling, the bending strain in SiNW is significantly reduced and the maximum local strain is almost uniformly distributed along SiNW. Based on the theoretical model, the energy landscape for different buckling modes of SiNW on PDMS substrate is given, which shows that both the in-plane and out-of-plane buckling modes have the local minimum potential energy, whereas the helical buckling model has the global minimum potential energy. Furthermore, the helical buckling spacing and amplitudes are deduced, taking into account the influences of the elastic properties and dimensions of SiNWs. These features are verified by systematic FEM simulations and parallel experiments. As the effective compressive strain in elastomeric substrate increases, the buckling profile evolves from a vertical ellipse to a lateral ellipse, and then approaches to a circle when the effective compressive strain is larger than 30%. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and 3D complex nano-structures.

Development of Euler's ideas at the Moscow State Regional University

NASA Astrophysics Data System (ADS)

Vysikaylo, P. I.; Belyaev, V. V.

2018-03-01

In honor of the 250th anniversary of Euler's discovery of three libration points in Russia in 1767 in the area of two rotating gravitational attractors in 2017 an International Interdisciplinary Conference “Euler Readings MRSU 2017” was held in Moscow Region State University (MRSU). The Conference demonstrated that the Euler's ideas continue to remain relevant at the present time. This paper summarizes the main achievements on the basis of Leonard Euler's ideas presented at the Conference.

Redesigning of a Canard Control Surface of an Advanced Fighter Aircraft: Effect on Buckling and Aerodynamic Behavior

NASA Astrophysics Data System (ADS)

Shrivastava, Sachin; Mohite, P. M.

2015-01-01

A redesign of canard control-surface of an advanced all-metallic fighter aircraft was carried out by using carbon fibre composite (CFC) for ribs and panels. In this study ply-orientations of CFC structure are optimized using a Genetic-Algorithm (GA) with an objective function to have minimum failure index (FI) according to Tsai-Wu failure criterion. The redesigned CFC structure was sufficiently strong to withstand aerodynamic loads from stress and deflection points of view. Now, in the present work CFC canard structure has been studied for its buckling strength in comparison to existing metallic design. In this study, the existing metallic design was found to be weak in buckling. Upon a detailed investigation, it was revealed that there are reported failures in the vicinity of zones where initial buckling modes are excited as predicted by the finite element based buckling analysis. In view of buckling failures, the redesigned CFC structure is sufficiently reinforced with stringers at specific locations. After providing reinforcements against buckling, the twist and the camber variations of the airfoil are checked and compared with existing structure data. Finally, the modal analysis has been carried out to compare the variation in excitation frequency due to material change. The CFC structure thus redesigned is safe from buckling and aerodynamic aspects as well.

Buckling Analysis of a Honeycomb-Core Composite Cylinder with Initial Geometric Imperfections

NASA Technical Reports Server (NTRS)

Cha, Gene; Schultz, Marc R.

2013-01-01

Thin-walled cylindrical shell structures often have buckling as the critical failure mode, and the buckling of such structures can be very sensitive to small geometric imperfections. The buckling analyses of an 8-ft-diameter, 10-ft-long honeycomb-core composite cylinder loaded in pure axial compression is discussed in this document. Two loading configurations are considered configuration 1 uses simple end conditions, and configuration 2 includes additional structure that may more closely approximate experimental loading conditions. Linear eigenvalue buckling analyses and nonlinear analyses with and without initial geometric imperfections were performed on both configurations. The initial imperfections were introduced in the shell by applying a radial load at the midlength of the cylinder to form a single inward dimple. The critical bifurcation buckling loads are predicted to be 924,190 lb and 924,020 lb for configurations 1 and 2, respectively. Nonlinear critical buckling loads of 918,750 lb and 954,900 lb were predicted for geometrically perfect configurations 1 and 2, respectively. Lower-bound critical buckling loads for configurations 1 and 2 with radial perturbations were found to be 33% and 36% lower, respectively, than the unperturbed critical loads. The inclusion of the load introduction cylinders in configuration 2 increased the maximum bending-boundary-layer rotation up to 11%.

Structural Stability of a Stiffened Aluminum Fuselage Panel Subjected to Combined Mechanical and Internal Pressure Loads

NASA Technical Reports Server (NTRS)

Rouse, Marshall; Young, Richard D.; Gehrki, Ralph R.

2003-01-01

Results from an experimental and analytical study of a curved stiffened aluminum panel subjected to combined mechanical and internal pressure loads are presented. The panel loading conditions were simulated using a D-box test fixture. Analytical buckling load results calculated from a finite element analysis are presented and compared to experimental results. Buckling results presented indicate that the buckling load of the fuselage panel is significantly influenced by internal pressure loading. The experimental results suggest that the stress distribution is uniform in the panel prior to buckling. Nonlinear finite element analysis results correlates well with experimental results up to buckling.

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

DOE PAGES

Larios, Adam; Petersen, Mark R.; Titi, Edriss S.; ...

2017-04-29

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formationmore » in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.« less

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

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

Larios, Adam; Petersen, Mark R.; Titi, Edriss S.

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formationmore » in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.« less

A Universal Formula for Extracting the Euler Angles

NASA Technical Reports Server (NTRS)

Shuster, Malcolm D.; Markley, F. Landis

2004-01-01

Recently, the authors completed a study of the Davenport angles, which are a generalization of the Euler angles for which the initial and final Euler axes need not be either mutually parallel or mutually perpendicular or even along the coordinate axes. During the conduct of that study, those authors discovered a relationship which can be used to compute straightforwardly the Euler angles characterizing a proper-orthogonal direction-cosine matrix for an arbitrary Euler-axis set satisfying n(sub 1) x n(sub 2) = 0 and n(sub 3) x n(sub 1) = 0, which is also satisfied by the more usual Euler angles we encounter commonly in the practice of Astronautics. Rather than leave that relationship hidden in an article with very different focus from the present Engineering note, we present it and the universal algorithm derived from it for extracting the Euler angles from the direction-cosine matrix here. We also offer literal "code" for performing the operations, numerical examples, and general considerations about the extraction of Euler angles which are not universally known, particularly, the treatment of statistical error.

Reactive sputter deposition of piezoelectric Sc 0.12Al 0.88N for contour mode resonators

DOE PAGES

Henry, Michael David; Young, Travis Ryan; Douglas, Erica Ann; ...

2018-05-11

Substitution of Al by Sc has been predicted and demonstrated to improve the piezoelectric response in AlN for commercial market applications in radio frequency filter technologies. Although cosputtering with multiple targets have achieved Sc incorporation in excess of 40%, industrial processes requiring stable single target sputtering are currently limited. A major concern with sputter deposition of ScAl is the control over the presence of non-c-axis oriented crystal growth, referred to as inclusions here, while simultaneously controlling film stress for suspended microelectromechanical systems (MEMS) structures. In this paper, we describe 12.5% ScAl single target reactive sputter deposition process and establishes amore » direct relationship between the inclusion occurrences and compressive film stress allowing for the suppression of the c-axis instability on silicon (100) and Ti/TiN/AlCu seeding layers. An initial high film stress, for suppressing inclusions, is then balanced with a lower film stress deposition to control total film stress to prevent Euler buckling of suspended MEMS devices. Contour mode resonators fabricated using these films demonstrate effective coupling coefficients up to 2.7% with figures of merit of 42. Finally, this work provides a method to establish inclusion free films in ScAlN piezoelectric films for good quality factor devices.« less

Reactive sputter deposition of piezoelectric Sc 0.12Al 0.88N for contour mode resonators

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

Henry, Michael David; Young, Travis Ryan; Douglas, Erica Ann

Substitution of Al by Sc has been predicted and demonstrated to improve the piezoelectric response in AlN for commercial market applications in radio frequency filter technologies. Although cosputtering with multiple targets have achieved Sc incorporation in excess of 40%, industrial processes requiring stable single target sputtering are currently limited. A major concern with sputter deposition of ScAl is the control over the presence of non-c-axis oriented crystal growth, referred to as inclusions here, while simultaneously controlling film stress for suspended microelectromechanical systems (MEMS) structures. In this paper, we describe 12.5% ScAl single target reactive sputter deposition process and establishes amore » direct relationship between the inclusion occurrences and compressive film stress allowing for the suppression of the c-axis instability on silicon (100) and Ti/TiN/AlCu seeding layers. An initial high film stress, for suppressing inclusions, is then balanced with a lower film stress deposition to control total film stress to prevent Euler buckling of suspended MEMS devices. Contour mode resonators fabricated using these films demonstrate effective coupling coefficients up to 2.7% with figures of merit of 42. Finally, this work provides a method to establish inclusion free films in ScAlN piezoelectric films for good quality factor devices.« less

Reactive sputter deposition of piezoelectric Sc 0.12Al 0.88N for contour mode resonators

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

Henry, Michael David; Young, Travis Ryan; Douglas, Erica Ann

Substitution of Al by Sc has been predicted and demonstrated to improve the piezoelectric response in AlN for commercial market applications in radio frequency filter technologies. Although cosputtering with multiple targets have achieved Sc incorporation in excess of 40%, industrial processes requiring stable single target sputtering are currently limited. A major concern with sputter deposition of ScAl is the control over the presence of non-c-axis oriented crystal growth, referred to as inclusions here, while simultaneously controlling film stress for suspended microelectromechanical systems (MEMS) structures. This work describes 12.5% ScAl single target reactive sputter deposition process and establishes a direct relationshipmore » between the inclusion occurrences and compressive film stress allowing for the suppression of the c-axis instability on silicon (100) and Ti/TiN/AlCu seeding layers. An initial high film stress, for suppressing inclusions, is then balanced with a lower film stress deposition to control total film stress to prevent Euler buckling of suspended MEMS devices. Contour mode resonators fabricated using these films demonstrate effective coupling coefficients up to 2.7% with figures of merit of 42. Furthermore, this work provides a method to establish inclusion free films in ScAlN piezoelectric films for good quality factor devices.« less

Propulsion at low Reynolds number via beam extrusion

NASA Astrophysics Data System (ADS)

Gosselin, Frederick; Neetzow, Paul

2014-03-01

We present experimental and theoretical results on the extrusion of a slender beam in a viscous fluid. We are particularly interested in the force necessary to extrude the beam as it buckles with large amplitude due to viscous friction. The problem is inspired by the propulsion of Paramecium via trichocyst extrusion. Self-propulsion in micro-organisms is mostly achieved through the beating of flagella or cilia. However, to avoid a severe aggression, unicellular Paramecium has been observed to extrude trichocysts in the direction of the aggression to burst away. These trichocysts are rod-like organelles which, upon activation, grow to about 40 μm in length in 3 milliseconds before detaching from the animal. The drag force created by these extruding rods pushing against the viscous fluid generates thrust in the opposite direction. We developed an experimental setup to measure the force required to push a steel piano wire into an aquarium filled with corn syrup. This setup offers a near-zero Reynolds number, and allows studying deployments for a range of constant extrusion speeds. The experimental results are reproduced with a numerical model coupling a large amplitude Euler-Bernoulli beam theory with a fluid load model proportional to the local beam velocity. This study was funded in part by the The Natural Sciences and Engineering Research Council of Canada.

Buckling of a stiff thin film on an elastic graded compliant substrate.

PubMed

Chen, Zhou; Chen, Weiqiu; Song, Jizhou

2017-12-01

The buckling of a stiff film on a compliant substrate has attracted much attention due to its wide applications such as thin-film metrology, surface patterning and stretchable electronics. An analytical model is established for the buckling of a stiff thin film on a semi-infinite elastic graded compliant substrate subjected to in-plane compression. The critical compressive strain and buckling wavelength for the sinusoidal mode are obtained analytically for the case with the substrate modulus decaying exponentially. The rigorous finite element analysis (FEA) is performed to validate the analytical model and investigate the postbuckling behaviour of the system. The critical buckling strain for the period-doubling mode is obtained numerically. The influences of various material parameters on the results are investigated. These results are helpful to provide physical insights on the buckling of elastic graded substrate-supported thin film.

A comparison of experimental and calculated thin-shell leading-edge buckling due to thermal stresses

NASA Technical Reports Server (NTRS)

Jenkins, Jerald M.

1988-01-01

High-temperature thin-shell leading-edge buckling test data are analyzed using NASA structural analysis (NASTRAN) as a finite element tool for predicting thermal buckling characteristics. Buckling points are predicted for several combinations of edge boundary conditions. The problem of relating the appropriate plate area to the edge stress distribution and the stress gradient is addressed in terms of analysis assumptions. Local plasticity was found to occur on the specimen analyzed, and this tended to simplify the basic problem since it effectively equalized the stress gradient from loaded edge to loaded edge. The initial loading was found to be difficult to select for the buckling analysis because of the transient nature of thermal stress. Multiple initial model loadings are likely required for complicated thermal stress time histories before a pertinent finite element buckling analysis can be achieved. The basic mode shapes determined from experimentation were correctly identified from computation.

Global Curvature Buckling and Snapping of Spherical Shells.

NASA Astrophysics Data System (ADS)

Pezzulla, Matteo; Stoop, Norbert; Steranka, Mark; Bade, Abdikhalaq; Trejo, Miguel; Holmes, Douglas

A spherical shell under external pressure will eventually buckle locally through the development of a dimple. However, when a free spherical shell is subject to variations in natural curvature, it will either buckle globally or snap towards a buckled configuration. We study the similarities and differences between pressure and curvature instabilities in spherical shells. We show how the critical buckling natural curvature is largely independent of the thinness and half-angle of the shell, while the critical snapping natural curvature grows linearly with the half-angle. As a result, we demonstrate how a critical half-angle, depending only on the thinness of the shell, sets the threshold between two different kinds of snapping: as a rule of thumb, shallow shells snap into everted shells, while deep shells snap into buckled shells. As the developed models are purely geometrical, the results are applicable to a large variety of stimuli and scales. NSF CAREER CMMI-1454153.

Buckling behavior of compression-loaded symmetrically-laminated angle-ply plates with holes

NASA Technical Reports Server (NTRS)

Nemeth, M. P.

1986-01-01

An approximate analysis for buckling of a rectangular specially-orthotropic plate with a central circular hole is applied to symmetrically-laminated angle-ply plates. Results obtained from finite element analyses and experiments indicate that the approximate analysis predicts accurately the buckling loads of (+/-theta sub m)s plates with integer values of m not below 6 and with hole diameters up to 50 percent of the plate width. Moreover, the results indicate that the approximate analysis can be used to predict the buckling trends of plates with hole diameters up to 70 percent of the plate width. Results of a parametric study indicate the influence of hole size, plate aspect ratio, loading conditions, boundary conditions, and orthotropy on the buckling load. Results are also presented that indicate the relationship of the bending stiffness and the prebuckling load distribution to the buckling load of a plate with a hole.

Assuring Life in Composite Systems

NASA Technical Reports Server (NTRS)

Chamis, Christos c.

2008-01-01

A computational simulation method is presented to assure life in composite systems by using dynamic buckling of smart composite shells as an example. The combined use of composite mechanics, finite element computer codes, and probabilistic analysis enable the effective assessment of the dynamic buckling load of smart composite shells. A universal plot is generated to estimate the dynamic buckling load of composite shells at various load rates and probabilities. The shell structure is also evaluated with smart fibers embedded in the plies right below the outer plies. The results show that, on the average, the use of smart fibers improved the shell buckling resistance by about 9% at different probabilities and delayed the buckling occurrence time. The probabilistic sensitivities results indicate that uncertainties in the fiber volume ratio and ply thickness have major effects on the buckling load. The uncertainties in the electric field strength and smart material volume fraction have moderate effects and thereby in the assured life of the shell.

Buckling of a stiff thin film on an elastic graded compliant substrate

NASA Astrophysics Data System (ADS)

Chen, Zhou; Chen, Weiqiu; Song, Jizhou

2017-12-01

The buckling of a stiff film on a compliant substrate has attracted much attention due to its wide applications such as thin-film metrology, surface patterning and stretchable electronics. An analytical model is established for the buckling of a stiff thin film on a semi-infinite elastic graded compliant substrate subjected to in-plane compression. The critical compressive strain and buckling wavelength for the sinusoidal mode are obtained analytically for the case with the substrate modulus decaying exponentially. The rigorous finite element analysis (FEA) is performed to validate the analytical model and investigate the postbuckling behaviour of the system. The critical buckling strain for the period-doubling mode is obtained numerically. The influences of various material parameters on the results are investigated. These results are helpful to provide physical insights on the buckling of elastic graded substrate-supported thin film.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less

Effect of Geometrical Imperfection on Buckling Failure of ITER VVPSS Tank

NASA Astrophysics Data System (ADS)

Jha, Saroj Kumar; Gupta, Girish Kumar; Pandey, Manish Kumar; Bhattacharya, Avik; Jogi, Gaurav; Bhardwaj, Anil Kumar

2017-04-01

The ‘Vacuum Vessel Pressure Suppression System’ (VVPSS) is part of ITER machine, which is designed to protect the ITER Vacuum Vessel and its connected systems, from an over-pressure situation. It is comprised of a partially evacuated tank of stainless steel approximately 46 m long and 6 m in diameter and thickness 30 mm. It is to hold approximately 675 tonnes of water at room temperature to condense the steam resulting from the adverse water leakage into the Vacuum Vessel chamber. For any vacuum vessel, geometrical imperfection has significant effect on buckling failure and structural integrity. Major geometrical imperfection in VVPSS tank depends on form tolerances. To study the effect of geometrical imperfection on buckling failure of VVPSS tank, finite element analysis (FEA) has been performed in line with ASME section VIII division 2 part 5 [1], ‘design by analysis method’. Linear buckling analysis has been performed to get the buckled shape and displacement. Geometrical imperfection due to form tolerance is incorporated in FEA model of VVPSS tank by scaling the resulted buckled shape by a factor ‘60’. This buckled shape model is used as input geometry for plastic collapse and buckling failure assessment. Plastic collapse and buckling failure of VVPSS tank has been assessed by using the elastic-plastic analysis method. This analysis has been performed for different values of form tolerance. The results of analysis show that displacement and load proportionality factor (LPF) vary inversely with form tolerance. For higher values of form tolerance LPF reduces significantly with high values of displacement.

Effects of maintenance operations on track buckling potential

DOT National Transportation Integrated Search

2003-05-04

This paper presents the results of buckling analyses based on data from recent tests determining the influence of track maintenance and consolidation on track lateral resistance. The buckling analyses were performed using the USDOT/Volpe "CWR-SAFE" m...

Analyses of Phase III Dynamic Buckling Tests. Final Report

DOT National Transportation Integrated Search

1990-02-01

Thermal buckling of railroad tracks in the lateral plane is an important problem in the design and maintenance of continuous welded rail (CWR) tracks. The problem is manifested through derailments which are attributable to track buckling, indicating ...

Strategy for the management of uncomplicated retinal detachments: the European vitreo-retinal society retinal detachment study report 1.

PubMed

Adelman, Ron A; Parnes, Aaron J; Ducournau, Didier

2013-09-01

To study success and failure in the treatment of uncomplicated rhegmatogenous retinal detachments (RRDs). Nonrandomized, multicenter retrospective study. One hundred seventy-six surgeons from 48 countries spanning 5 continents provided information on the primary procedures for 7678 cases of RRDs including 4179 patients with uncomplicated RRDs. Reported data included specific clinical findings, the method of repair, and the outcome after intervention. Final failure of retinal detachment repair (level 1 failure rate), remaining silicone oil at the study's conclusion (level 2 failure rate), and need for additional procedures to repair the detachment (level 3 failure rate). Four thousand one hundred seventy-nine uncomplicated cases of RRD were included. Combining phakic, pseudophakic, and aphakic groups, those treated with scleral buckle alone (n = 1341) had a significantly lower final failure rate than those treated with vitrectomy, with or without a supplemental buckle (n = 2723; P = 0.04). In phakic patients, final failure rate was lower in the scleral buckle group compared with those who had vitrectomy, with or without a supplemental buckle (P = 0.028). In pseudophakic patients, the failure rate of the initial procedure was lower in the vitrectomy group compared with the scleral buckle group (P = 3×10(-8)). There was no statistically significant difference in failure rate between segmental (n = 721) and encircling (n = 351) buckles (P = 0.5). Those who underwent vitrectomy with a supplemental scleral buckle (n = 488) had an increased failure rate compared with those who underwent vitrectomy alone (n = 2235; P = 0.048). Pneumatic retinopexy was found to be comparable with scleral buckle when a retinal hole was present (P = 0.65), but not in cases with a flap tear (P = 0.034). In the treatment of uncomplicated phakic retinal detachments, repair using scleral buckle may be a good option. There was no significant difference between segmental versus 360-degree buckle. For pseudophakic uncomplicated retinal detachments, the surgeon should balance the risks and benefits of vitrectomy versus scleral buckle and keep in mind that the single-surgery reattachment rate may be higher with vitrectomy. However, if a vitrectomy is to be performed, these data suggest that a supplemental buckle is not helpful. The author(s) have no proprietary or commercial interest in any materials discussed in this article. Copyright © 2013 American Academy of Ophthalmology. Published by Elsevier Inc. All rights reserved.

Predictions of thermal buckling strengths of hypersonic aircraft sandwich panels using minimum potential energy and finite element methods

NASA Technical Reports Server (NTRS)

Ko, William L.

1995-01-01

Thermal buckling characteristics of hypersonic aircraft sandwich panels of various aspect ratios were investigated. The panel is fastened at its four edges to the substructures under four different edge conditions and is subjected to uniform temperature loading. Minimum potential energy theory and finite element methods were used to calculate the panel buckling temperatures. The two methods gave fairly close buckling temperatures. However, the finite element method gave slightly lower buckling temperatures than those given by the minimum potential energy theory. The reasons for this slight discrepancy in eigensolutions are discussed in detail. In addition, the effect of eigenshifting on the eigenvalue convergence rate is discussed.

Combined-load buckling behavior of metal-matrix composite sandwich panels under different thermal environments

NASA Technical Reports Server (NTRS)

Ko, William L.; Jackson, Raymond H.

1991-01-01

Combined compressive and shear buckling analysis was conducted on flat rectangular sandwich panels with the consideration of transverse shear effects of the core. The sandwich panel is fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that the square panel has the highest combined load buckling strength, and that the buckling strength decreases sharply with the increases of both temperature and panel aspect ratio. The effect of layup (fiber orientation) on the buckling strength of the panels was studied in detail. The metal matrix composite sandwich panel was much more efficient than the sandwich panel with nonreinforced face sheets and had the same specific weight.

Nonlinear mode interaction in equal-leg angle struts susceptible to cellular buckling.

PubMed

Bai, L; Wang, F; Wadee, M A; Yang, J

2017-11-01

A variational model that describes the interactive buckling of a thin-walled equal-leg angle strut under pure axial compression is presented. A formulation combining the Rayleigh-Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Solving the equations using numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weak-axis flexural buckling mode and the strong-axis flexural-torsional buckling mode for the first time-the resulting behaviour being highly unstable. Physical experiments conducted on 10 cold-formed steel specimens are presented and the results show good agreement with the variational model.

Buckling characteristics of hypersonic aircraft wing tubular panels

NASA Technical Reports Server (NTRS)

Ko, William L.; Shideler, John L.; Fields, Roger A.

1986-01-01

The buckling characteristics of Rene 41 tubular panels installed as wing panels on a hypersonic wing test structure (HWTS) were determined nondestructively through use of a force/stiffness technique. The nondestructive buckling tests were carried out under different combined load conditions and different temperature environments. Two panels were subsequently tested to buckling failure in a universal tension compression testing machine. In spite of some data scattering because of large extrapolations of data points resulting from termination of the test at a somewhat low applied load, the overall test data correlated fairly well with theoretically predicted buckling interaction curves. The structural efficiency of the tubular panels was slightly higher than that of the beaded panels which they replaced.

Tensile buckling of advanced turboprops

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Aiello, R. A.

1982-01-01

Theoretical studies were conducted to determine analytically the tensile buckling of advanced propeller blades (turboprops) in centrifugal fields, as well as the effects of tensile buckling on other types of structural behavior, such as resonant frequencies and flutter. Theoretical studies were also conducted to establish the advantages of using high performance composite turboprops as compared to titanium. Results show that the vibration frequencies are not affected appreciably prior to 80 percent of the tensile speed. Some frequencies approach zero as the tensile buckling speed is approached. Composites provide a substantial advantage over titanium on a buckling speed to weight basis. Vibration modes change as the rotor speed is increased and substantial geometric coupling is present.

Effects of thickness and ply orientation on buckling of laminated plates

NASA Technical Reports Server (NTRS)

Jegley, D. C.

1986-01-01

The buckling loads of laminated plates are predicted using a new theory which takes into account transverse shearing effects. This new theory assumes trigonometric terms through-the-thickness in the displacements to take into account transverse shearing effects in thick plates. Buckling loads predicted by the new theory and by traditional theories are compared for isotropic and laminated plates. The effect of ply orientation on the buckling loads predicted by each theory is demonstrated.

Thermal buckling and post-buckling behaviour of continuous welded rail track

NASA Astrophysics Data System (ADS)

Pucillo, Giovanni Pio

2016-12-01

Because thermal expansions are constrained within continuous welded rail track, the track can buckle, and does so mainly in the horizontal plane. In this paper, a parametric finite element model of railway track is presented, and its sensitivity to the variations of the main parameters that characterise the scenario has been investigated and discussed. Comparison with existing literature shows good agreement. It is found that curved tracks suffer from thermal buckling more than tangent tracks do. To simulate a track misalignment defect, a new methodology has been utilised that does not introduce, as is usual, geometrical discontinuities near the same defect, because it takes into account - in a natural way - the bending stiffness of the whole railway track in the horizontal plane. To contribute to a better understanding of the safe utilisation of raw experimental data obtained from in situ tests, a deep analysis of the effects on the thermal track buckling response produced by each parameter characterising the sleeper-ballast lateral resistance curve is presented and discussed. It is found that for current ballasted railway tracks, the minimum buckling temperature depends only on the limit lateral resistance, whereas a high value of the initial stiffness can lead to overestimation of the maximum buckling temperature, also taking into account the 'natural' decrease in the maximum buckling temperature due to an increase in the railway-traffic-induced defect amplitude.

Buckling Design and Imperfection Sensitivity of Sandwich Composite Launch-Vehicle Shell Structures

NASA Technical Reports Server (NTRS)

Schultz, Marc R.; Sleight, David W.; Myers, David E.; Waters, W. Allen, Jr.; Chunchu, Prasad B.; Lovejoy, Andrew W.; Hilburger, Mark W.

2016-01-01

Composite materials are increasingly being considered and used for launch-vehicle structures. For shell structures, such as interstages, skirts, and shrouds, honeycomb-core sandwich composites are often selected for their structural efficiency. Therefore, it is becoming increasingly important to understand the structural response, including buckling, of sandwich composite shell structures. Additionally, small geometric imperfections can significantly influence the buckling response, including considerably reducing the buckling load, of shell structures. Thus, both the response of the theoretically perfect structure and the buckling imperfection sensitivity must be considered during the design of such structures. To address the latter, empirically derived design factors, called buckling knockdown factors (KDFs), were developed by NASA in the 1960s to account for this buckling imperfection sensitivity during design. However, most of the test-article designs used in the development of these recommendations are not relevant to modern launch-vehicle constructions and material systems, and in particular, no composite test articles were considered. Herein, a two-part study on composite sandwich shells to (1) examine the relationship between the buckling knockdown factor and the areal mass of optimized designs, and (2) to interrogate the imperfection sensitivity of those optimized designs is presented. Four structures from recent NASA launch-vehicle development activities are considered. First, designs optimized for both strength and stability were generated for each of these structures using design optimization software and a range of buckling knockdown factors; it was found that the designed areal masses varied by between 6.1% and 19.6% over knockdown factors ranging from 0.6 to 0.9. Next, the buckling imperfection sensitivity of the optimized designs is explored using nonlinear finite-element analysis and the as-measured shape of a large-scale composite cylindrical shell. When compared with the current buckling design recommendations, the results suggest that the current recommendations are overly conservative and that the development of new recommendations could reduce the acreage areal mass of many composite sandwich shell designs by between 4% and 19%, depending on the structure.

The effect of imperfections on the vertical buckling of railroad tracks

DOT National Transportation Integrated Search

1976-06-30

This report deals with an analytical prediction of the effect of geometric imperfections on the post-buckling characteristics of railroad tracks. The analysis is restricted to the case of vertical track buckling due to constrained thermal expansion i...

Mechanical stability analysis on spherical sandwich sheet at low temperature loading conditions

NASA Astrophysics Data System (ADS)

Wang, Shanshuai; Li, Shuhui; Li, Zhimin

2013-12-01

The spherical sandwich sheet (S-S-S) is generally used in the aerospace industry, for example, the airplane, the rocket's fairing, the spacecraft and the satellite for the purpose of heat-insulation, weight-saving and dimension-reducing. The stability of the S-S-S is of general concern because of its particularly thin but large size. For some S-S-S used in fuel tank storing liquid oxygen of the rocket, it must be facing low temperature down to about -183 °C. Low temperature condition affects the stability of the S-S-S and then causes buckling of the structure. In this paper, a finite element (FE) model is established for evaluating the stability of the S-S-S via the sequential coupling mode. The material mechanical properties related to temperature are concerned in the FE model. The buckling modes and critical buckling loading are predicted accurately, since the FE model includes heat transfer simulating, thermal stress computing, buckling and post buckling process. It is found that the thermal stress generated from the low temperature loading reduces the critical buckling loading and changes the buckling modes of the S-S-S.

Buckling Behavior of Substrate Supported Graphene Sheets

PubMed Central

Yang, Kuijian; Chen, Yuli; Pan, Fei; Wang, Shengtao; Ma, Yong; Liu, Qijun

2016-01-01

The buckling of graphene sheets on substrates can significantly degrade their performance in materials and devices. Therefore, a systematic investigation on the buckling behavior of monolayer graphene sheet/substrate systems is carried out in this paper by both molecular mechanics simulations and theoretical analysis. From 70 simulation cases of simple-supported graphene sheets with different sizes under uniaxial compression, two different buckling modes are investigated and revealed to be dominated by the graphene size. Especially, for graphene sheets with length larger than 3 nm and width larger than 1.1 nm, the buckling mode depends only on the length/width ratio. Besides, it is revealed that the existence of graphene substrate can increase the critical buckling stress and strain to 4.39 N/m and 1.58%, respectively, which are about 10 times those for free-standing graphene sheets. Moreover, for graphene sheets with common size (longer than 20 nm), both theoretical and simulation results show that the critical buckling stress and strain are dominated only by the adhesive interactions with substrate and independent of the graphene size. Results in this work provide valuable insight and guidelines for the design and application of graphene-derived materials and nano-electromechanical systems. PMID:28787831

New method for detecting singularities in experimental incompressible flows

NASA Astrophysics Data System (ADS)

Kuzzay, Denis; Saw, Ewe-Wei; Martins, Fabio J. W. A.; Faranda, Davide; Foucaut, Jean-Marc; Daviaud, François; Dubrulle, Bérengère

2017-06-01

We introduce two new criteria based on the work of Duchon and Robert (2000 Nonlinearity 13 249) and Eyink (2006 Phys. Rev. E 74 066302), which allow for the local detection of Navier-Stokes singularities in experimental flows. We discuss the difference between non-dissipative or dissipative Euler quasi-singularities and genuine Navier-Stokes dissipative singularites, and classify them with respect to their Hölder exponent h. We show that our criteria allow us to detect areas in a flow where the velocity field is no more regular than Hölder continuous with some Hölder exponent h ≤slant 1/2 . We illustrate our discussion using classical tomographic particle image velocimetry (TPIV) measurements obtained inside a high Reynolds number flow generated in the boundary layer of a wind tunnel. Our study shows that, in order to detect singularities or quasi-singularities, one does not need to have access to the whole velocity field inside a volume, but can instead look for them from stereoscopic PIV data on a plane. We also provide a discussion about the link between areas detected by our criteria and areas corresponding to large vorticity. We argue that this link might provide either a clue about the genesis of these quasi-singularities or a way to discriminate dissipative Euler quasi-singularities and genuine Navier-Stokes singularities.

Micropolar curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.

Dynamic analysis and control PID path of a model type gantry crane

NASA Astrophysics Data System (ADS)

Ospina-Henao, P. A.; López-Suspes, Framsol

2017-06-01

This paper presents an alternate form for the dynamic modelling of a mechanical system that simulates in real life a gantry crane type, using Euler’s classical mechanics and Lagrange formalism, which allows find the equations of motion that our model describe. Moreover, it has a basic model design system using the SolidWorks software, based on the material and dimensions of the model provides some physical variables necessary for modelling. In order to verify the theoretical results obtained, a contrast was made between solutions obtained by simulation in SimMechanics-Matlab and Euler-Lagrange equations system, has been solved through Matlab libraries for solving equation’s systems of the type and order obtained. The force is determined, but not as exerted by the spring, as this will be the control variable. The objective is to bring the mass of the pendulum from one point to another with a specified distance without the oscillation from it, so that, the answer is overdamped. This article includes an analysis of PID control in which the equations of motion of Euler-Lagrange are rewritten in the state space, once there, they were implemented in Simulink to get the natural response of the system to a step input in F and then draw the desired trajectories.

Stability Results for Idealized Shear Flows on a Rectangular Periodic Domain

NASA Astrophysics Data System (ADS)

Dullin, Holger R.; Worthington, Joachim

2018-06-01

We present a new linearly stable solution of the Euler fluid flow on a torus. On a two-dimensional rectangular periodic domain [0,2π )× [0,2π / κ ) for κ \\in R^+, the Euler equations admit a family of stationary solutions given by the vorticity profiles Ω ^*(x)= Γ cos (p_1x_1+ κ p_2x_2). We show linear stability for such flows when p_2=0 and κ ≥ |p_1| (equivalently p_1=0 and κ {|p_2|}≤ {1}). The classical result due to Arnold is that for p_1 = 1, p_2 = 0 and κ ≥ 1 the stationary flow is nonlinearly stable via the energy-Casimir method. We show that for κ ≥ |p_1| ≥ 2, p_2 = 0 the flow is linearly stable, but one cannot expect a similar nonlinear stability result. Finally we prove nonlinear instability for all steady states satisfying p_1^2+κ ^2{p_2^2}>{3(κ ^2+1)}/4(7-4√{3)}. The modification and application of a structure-preserving Hamiltonian truncation is discussed for the anisotropic case κ ≠ 1. This leads to an explicit Lie-Poisson integrator for the approximate system, which is used to illustrate our analytical results.

Efficient construction of unified continuous and discontinuous Galerkin formulations for the 3D Euler equations

NASA Astrophysics Data System (ADS)

Abdi, Daniel S.; Giraldo, Francis X.

2016-09-01

A unified approach for the numerical solution of the 3D hyperbolic Euler equations using high order methods, namely continuous Galerkin (CG) and discontinuous Galerkin (DG) methods, is presented. First, we examine how classical CG that uses a global storage scheme can be constructed within the DG framework using constraint imposition techniques commonly used in the finite element literature. Then, we implement and test a simplified version in the Non-hydrostatic Unified Model of the Atmosphere (NUMA) for the case of explicit time integration and a diagonal mass matrix. Constructing CG within the DG framework allows CG to benefit from the desirable properties of DG such as, easier hp-refinement, better stability etc. Moreover, this representation allows for regional mixing of CG and DG depending on the flow regime in an area. The different flavors of CG and DG in the unified implementation are then tested for accuracy and performance using a suite of benchmark problems representative of cloud-resolving scale, meso-scale and global-scale atmospheric dynamics. The value of our unified approach is that we are able to show how to carry both CG and DG methods within the same code and also offer a simple recipe for modifying an existing CG code to DG and vice versa.

The lifespan of 3D radial solutions to the non-isentropic relativistic Euler equations

NASA Astrophysics Data System (ADS)

Wei, Changhua

2017-10-01

This paper investigates the lower bound of the lifespan of three-dimensional spherically symmetric solutions to the non-isentropic relativistic Euler equations, when the initial data are prescribed as a small perturbation with compact support to a constant state. Based on the structure of the hyperbolic system, we show the almost global existence of the smooth solutions to Eulerian flows (polytropic gases and generalized Chaplygin gases) with genuinely nonlinear characteristics. While for the Eulerian flows (Chaplygin gas and stiff matter) with mild linearly degenerate characteristics, we show the global existence of the radial solutions, moreover, for the non-strictly hyperbolic system (pressureless perfect fluid) satisfying the mild linearly degenerate condition, we prove the blowup phenomenon of the radial solutions and show that the lifespan of the solutions is of order O(ɛ ^{-1}), where ɛ denotes the width of the perturbation. This work can be seen as a complement of our work (Lei and Wei in Math Ann 367:1363-1401, 2017) for relativistic Chaplygin gas and can also be seen as a generalization of the classical Eulerian fluids (Godin in Arch Ration Mech Anal 177:497-511, 2005, J Math Pures Appl 87:91-117, 2007) to the relativistic Eulerian fluids.

p-Euler equations and p-Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Elastic torsional buckling of thin-walled composite cylinders

NASA Technical Reports Server (NTRS)

Marlowe, D. E.; Sushinsky, G. F.; Dexter, H. B.

1974-01-01

The elastic torsional buckling strength has been determined experimentally for thin-walled cylinders fabricated with glass/epoxy, boron/epoxy, and graphite/epoxy composite materials and composite-reinforced aluminum and titanium. Cylinders have been tested with several unidirectional-ply orientations and several cross-ply layups. Specimens were designed with diameter-to-thickness ratios of approximately 150 and 300 and in two lengths of 10 in. and 20 in. The results of these tests were compared with the buckling strengths predicted by the torsional buckling analysis of Chao.

"Buckle" rib fracture: an artifact following cardio-pulmonary resuscitation detected on postmortem CT.

PubMed

Yang, Kyung-Moo; Lynch, Matthew; O'Donnell, Chris

2011-09-01

Buckle rib fractures are incomplete fractures involving the inner cortex alone, and are rarely detected on routine chest X-ray or at autopsy. The characteristics of these fractures have not been well evaluated in situ although they are commonly observed on postmortem CT images especially following CPR. The postmortem CT findings in 42 cases showing buckle rib fractures caused by CPR were reviewed. The cause of death in all cases was non-traumatic. The shape, number, location, and distribution of these buckle rib fractures and their relationship to other types of rib fractures were evaluated using a novel oblique axial multiplanar reconstruction technique. Almost all incomplete rib fractures associated with CPR are buckle rib fractures (90.5%). All rib fractures were distributed from the second to ninth ribs with over 95% being within the second to seventh ribs. Buckle rib fractures are dominant in the seventh to ninth ribs and the proportion of buckle rib fractures located in the vicinity of the costochondral junctions increases with the lower ribs. Over 97% of all CPR associated rib fractures are located in the anterior one third of the ribs based on a new measurement method utilizing oblique axial multiplanar reconstruction of the CT data. When recognition of incomplete or buckle rib fractures on postmortem CT is taken into account, detection of symmetry and continuity of rib fractures typically associated with CPR is improved compared with the detection of complete fractures alone. Recognition of buckle rib fractures and their characteristics on postmortem CT is of benefit to the forensic pathologist in evaluating the possibility of CPR and the differentiation of resuscitative artifact from forensically significant visceral injury observed at autopsy. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

An Approximate Solution and Master Curves for Buckling of Symmetrically Laminated Composite Cylinders

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2013-01-01

Nondimensional linear-bifurcation buckling equations for balanced, symmetrically laminated cylinders with negligible shell-wall anisotropies and subjected to uniform axial compression loads are presented. These equations are solved exactly for the practical case of simply supported ends. Nondimensional quantities are used to characterize the buckling behavior that consist of a stiffness-weighted length-to-radius parameter, a stiffness-weighted shell-thinness parameter, a shell-wall nonhomogeneity parameter, two orthotropy parameters, and a nondimensional buckling load. Ranges for the nondimensional parameters are established that encompass a wide range of laminated-wall constructions and numerous generic plots of nondimensional buckling load versus a stiffness-weighted length-to-radius ratio are presented for various combinations of the other parameters. These plots are expected to include many practical cases of interest to designers. Additionally, these plots show how the parameter values affect the distribution and size of the festoons forming each response curve and how they affect the attenuation of each response curve to the corresponding solution for an infinitely long cylinder. To aid in preliminary design studies, approximate formulas for the nondimensional buckling load are derived, and validated against the corresponding exact solution, that give the attenuated buckling response of an infinitely long cylinder in terms of the nondimensional parameters presented herein. A relatively small number of "master curves" are identified that give a nondimensional measure of the buckling load of an infinitely long cylinder as a function of the orthotropy and wall inhomogeneity parameters. These curves reduce greatly the complexity of the design-variable space as compared to representations that use dimensional quantities as design variables. As a result of their inherent simplicity, these master curves are anticipated to be useful in the ongoing development of buckling-design technology.

Study of foldable elastic tubes for large space structure applications, phase 3

NASA Technical Reports Server (NTRS)

Jones, I. W.; Mitchell, S. O.

1981-01-01

A bi-convex foldable elastic tube, suitable for use in self deploying space structures, was subjected to a series of buckling tests to deterine initial buckling loads, collapse loads, and the buckling mode. The tube is cylindrical with a cross-section that is lenticular-like with flared edges. It is capable of being flattened in the center and folded compactly, storing up strain energy in the process. Upon removal of constraint, it springs back to its original straight configuration, releasing the stored strain energy. The tests showed that this type of tube has good resistance to buckling, with the initial buckling loads all falling within or above the range of those for comparable circular cylindrical tubes.

Buckling Testing and Analysis of Space Shuttle Solid Rocket Motor Cylinders

NASA Technical Reports Server (NTRS)

Weidner, Thomas J.; Larsen, David V.; McCool, Alex (Technical Monitor)

2002-01-01

A series of full-scale buckling tests were performed on the space shuttle Reusable Solid Rocket Motor (RSRM) cylinders. The tests were performed to determine the buckling capability of the cylinders and to provide data for analytical comparison. A nonlinear ANSYS Finite Element Analysis (FEA) model was used to represent and evaluate the testing. Analytical results demonstrated excellent correlation to test results, predicting the failure load within 5%. The analytical value was on the conservative side, predicting a lower failure load than was applied to the test. The resulting study and analysis indicated the important parameters for FEA to accurately predict buckling failure. The resulting method was subsequently used to establish the pre-launch buckling capability of the space shuttle system.

Effects of Shell-Buckling Knockdown Factors in Large Cylindrical Shells

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.

2012-01-01

Shell-buckling knockdown factors (SBKF) have been used in large cylindrical shell structures to account for uncertainty in buckling loads. As the diameter of the cylinder increases, achieving the manufacturing tolerances becomes increasingly more difficult. Knockdown factors account for manufacturing imperfections in the shell geometry by decreasing the allowable buckling load of the cylinder. In this paper, large-diameter (33 ft) cylinders are investigated by using various SBKF's. An investigation that is based on finite-element analysis (FEA) is used to develop design sensitivity relationships. Different manufacturing imperfections are modeled into a perfect cylinder to investigate the effects of these imperfections on buckling. The analysis results may be applicable to large- diameter rockets, cylindrical tower structures, bulk storage tanks, and silos.

Buckling analysis of carbon nanotube bundles under axial compressive, bending and torsional loadings via a structural mechanics model

NASA Astrophysics Data System (ADS)

Lashkari Zadeh, Ali; Shariati, Mahmoud; Torabi, Hamid

2012-11-01

A structural mechanics model is employed for the investigation of the buckling behavior of carbon nanotube bundles of three single-walled carbon nanotubes (SWCNTs) under axial compressive, bending and torsional loadings. The effects of van der Waals (vdW) forces are further modeled using a nonlinear spring element.The effects of different types of boundary conditions are studied for nanotubes with various aspect ratios. The results reveal that bundles comprising longer SWCNTs exhibit lower critical buckling load. Moreover, for the fixed-free boundary condition the rate of critical buckling load reduction is highest, while the lowest critical buckling load occurs. Simulations show good agreement between our model and molecular dynamics results.

Buckling and Failure of Compression-loaded Composite Cylindrical Shells with Reinforced Cutouts

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Nemeth, Michael P.

2005-01-01

Results from a numerical and experimental study that illustrate the effects of selected cutout reinforcement configurations on the buckling and failure response of compression-loaded composite cylindrical shells with a cutout are presented. The effects of reinforcement size, thickness, and orthotropy on the overall response of compression-loaded shells are described. In general, reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response and material failure near the cutout and increase the buckling load of the shell. However, some results show that certain reinforcement configurations can cause a significant increase in the local interlaminar failures that can accumulate near the free edges of a cutout during a local buckling event.

Buckling and Failure of Compression-Loaded Composite Laminated Shells With Cutouts

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.

2007-01-01

Results from a numerical and experimental study that illustrate the effects of laminate orthotropy on the buckling and failure response of compression-loaded composite cylindrical shells with a cutout are presented. The effects of orthotropy on the overall response of compression-loaded shells is described. In general, preliminary numerical results appear to accurately predict the buckling and failure characteristics of the shell considered herein. In particular, some of the shells exhibit stable post-local-buckling behavior accompanied by interlaminar material failures near the free edges of the cutout. In contrast another shell with a different laminate stacking sequence appears to exhibit catastrophic interlaminar material failure at the onset of local buckling near the cutout and this behavior correlates well with corresponding experimental results.

Seismic rehabilitation of skewed and curved bridges using a new generation of buckling restrained braces : research brief.

DOT National Transportation Integrated Search

2016-12-01

Damage to skewed and curved bridges during strong earthquakes is documented. This project investigates whether such damage could be mitigated by using buckling restrained braces. Nonlinear models show that using buckling restrained braces to mitigate...

Buckling analysis of orthotropic protein microtubules under axial and radial compression based on couple stress theory.

PubMed

Beni, Yaghoub Tadi; Zeverdejani, M Karimi; Mehralian, Fahimeh

2017-10-01

Protein microtubules (MTs) are one of the important intercellular components and have a vital role in the stability and strength of the cells. Due to applied external loads, protein microtubules may be involved buckling phenomenon. Due to impact of protein microtubules in cell reactions, it is important to determine their critical buckling load. Considering nature of protein microtubules, various parameters are effective on microtubules buckling. The small size of microtubules and also lack of uniformity of MTs properties in different directions caused the necessity of accuracy in the analysis of these bio-structure. In fact, microtubules must be considered as a size dependent cylinder, which behave as an orthotropic material. Hence, in the present work using first-order shear deformation model (FSDT), the buckling equations of anisotropic MTs are derived based on new modified couple stress theory (NMCST). After solving the stability equations, the influences of various parameters are measured on the MTs critical buckling load. Copyright © 2017 Elsevier Inc. All rights reserved.

Buckling analysis of Big Dee Vacuum Vessel

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

Lightner, S.; Gallix, R.

1983-12-01

A simplified three-dimensional shell buckling analysis of the GA Technologies Inc., Big Dee Vacuum Vessel (V/V) was performed using the finite element program TRICO. A coarse-mesh linear elastic model, which accommodated the support boundary conditions, was used to determine the buckling mode shape under a uniform external pressure. Using this buckling mode shape, refined models were used to calculate the linear buckling load (P/sub crit/) more accurately. Several different designs of the Big Dee V/V were considered in this analysis. The supports for the V/V were equally-spaced radial pins at the outer diameter of the mid-plane. For all the casesmore » considered, the buckling mode was axisymmetric in the toroidal direction. Therefore, it was possible to use only a small angular sector of a toric shell for the refined analysis. P/sub crit/ for the Big Dee is about 60 atm for a uniform external pressure. Also investigated in this analysis were the effects of geometrical imperfections and non-uniform pressure distributions.« less

Static Buckling Model Tests and Elasto-plastic Finite Element Analysis of a Pile in Layers with Various Thicknesses

NASA Astrophysics Data System (ADS)

Okajima, Kenji; Imai, Junichi; Tanaka, Tadatsugu; Iida, Toshiaki

Damage to piles in the liquefied ground is frequently reported. Buckling by the excess vertical load could be one of the causes of the pile damage, as well as the lateral flow of the ground and the lateral load at the pile head. The buckling mechanism is described as a complicated interaction between the pile deformation by the vertical load and the earth pressure change cased by the pile deformation. In this study, series of static buckling model tests of a pile were carried out in dried sand ground with various thickness of the layer. Finite element analysis was applied to the test results to verify the effectiveness of the elasto-plastic finite element analysis combining the implicit-explicit mixed type dynamic relaxation method with the return mapping method to the pile buckling problems. The test results and the analysis indicated the possibility that the buckling load of a pile decreases greatly where the thickness of the layer increases.

Active buckling control of a beam-column with circular cross-section using piezo-elastic supports and integral LQR control

NASA Astrophysics Data System (ADS)

Schaeffner, Maximilian; Götz, Benedict; Platz, Roland

2016-06-01

Buckling of slender beam-columns subject to axial compressive loads represents a critical design constraint for light-weight structures. Active buckling control provides a possibility to stabilize slender beam-columns by active lateral forces or bending moments. In this paper, the potential of active buckling control of an axially loaded beam-column with circular solid cross-section by piezo-elastic supports is investigated experimentally. In the piezo-elastic supports, lateral forces of piezoelectric stack actuators are transformed into bending moments acting in arbitrary directions at the beam-column ends. A mathematical model of the axially loaded beam-column is derived to design an integral linear quadratic regulator (LQR) that stabilizes the system. The effectiveness of the stabilization concept is investigated in an experimental test setup and compared with the uncontrolled system. With the proposed active buckling control it is possible to stabilize the beam-column in arbitrary lateral direction for axial loads up to the theoretical critical buckling load of the system.

A Biomechanical Model of Artery Buckling

PubMed Central

Han, Hai-Chao

2010-01-01

The stability of arteries under blood pressure load is essential to the maintenance of normal arterial function and the loss of stability can lead to tortuosity and kinking that are associated with significant clinical complications. However, mechanical analysis of arterial bent buckling is lacking. To address this issue, this paper presents a biomechanical model of arterial buckling. Using a linear elastic cylindrical arterial model, the mechanical equations for arterial buckling were developed and the critical buckling pressure was found to be a function of the wall stiffness (Young’s modulus), arterial radius, length, wall thickness, and the axial strain. Both the model equations and experimental results demonstrated that the critical pressure is related to the axial strain. Arteries may buckle and become tortuous due to reduced (sub-physiological) axial strain, hypertensive pressure, and a weakened wall. These results are in accordance with, and provide a possible explanation to the clinical observations that these changes are the risk factors for arterial tortuosity and kinking. The current model is also applicable to veins and ureters. PMID:17689541

Critical thickness ratio for buckled and wrinkled fruits and vegetables

NASA Astrophysics Data System (ADS)

Dai, Hui-Hui; Liu, Yang

2014-11-01

This work aims at establishing the geometrical constraint for buckled and wrinkled shapes by modeling a fruit/vegetable with exocarp and sarcocarp as a hyperelastic layer-substrate structure subjected to uniaxial compression. A careful analysis on the derived bifurcation condition leads to the finding of a critical thickness ratio which separates the buckling and wrinkling modes, and remarkably, which is independent of the material stiffnesses. More specifically, it is found that if the thickness ratio is smaller than this critical value a fruit/vegetable should be in a buckled shape (under a sufficient stress); if a fruit/vegetable is in a wrinkled shape the thickness ratio is always larger than this critical value. To verify the theoretical prediction, we consider four types of buckled fruits/vegetables and four types of wrinkled fruits/vegetables with three samples in each type. The geometrical parameters for the 24 samples are measured and it is found that indeed all the data fall into the theoretically predicted buckling or wrinkling domains.

Microelectromechanical (MEM) thermal actuator

DOEpatents

Garcia, Ernest J [Albuquerque, NM; Fulcher, Clay W. G. [Sandia Park, NM

2012-07-31

Microelectromechanical (MEM) buckling beam thermal actuators are disclosed wherein the buckling direction of a beam is constrained to a desired direction of actuation, which can be in-plane or out-of-plane with respect to a support substrate. The actuators comprise as-fabricated, linear beams of uniform cross section supported above the substrate by supports which rigidly attach a beam to the substrate. The beams can be heated by methods including the passage of an electrical current through them. The buckling direction of an initially straight beam upon heating and expansion is controlled by incorporating one or more directional constraints attached to the substrate and proximal to the mid-point of the beam. In the event that the beam initially buckles in an undesired direction, deformation of the beam induced by contact with a directional constraint generates an opposing force to re-direct the buckling beam into the desired direction. The displacement and force generated by the movement of the buckling beam can be harnessed to perform useful work, such as closing contacts in an electrical switch.

Preliminary Sizing Study of Ares-I and Ares-V Liquid Hydrogen Tanks

NASA Technical Reports Server (NTRS)

Oliver, Stanley T.; Harper, David W.

2012-01-01

A preliminary sizing study of two cryogenic propellant tanks was performed using a FORTRAN optimization program to determine weight efficient orthogrid designs for the tank barrels sections only. Various tensile and compressive failure modes were considered, including general buckling of cylinders with a shell buckling knockdown factor. Eight independent combinations of three design requirements were also considered and their effects on the tanks weight. The approach was to investigate each design case with a variable shell buckling knockdown factor, determining the most weight efficient combination of orthogrid design parameters. Numerous optimization analyses were performed, and the results presented herein compare the effects of the different design requirements and shell buckling knockdown factor. Through a series of comparisons between design requirements or shell buckling knockdown factors, the relative change in overall tank barrel weights is shown. The findings indicate that the design requirements can substantually increase the tank weight while a less conservative shell buckling knockdown factor can modestly reduce the tank weight.

Numerical analysis of light extraction enhancement of GaN-based thin-film flip-chip light-emitting diodes with high-refractive-index buckling nanostructures

NASA Astrophysics Data System (ADS)

Yue, Qing-Yang; Yang, Yang; Cheng, Zhen-Jia; Guo, Cheng-Shan

2018-06-01

In this work, the light extraction efficiency enhancement of GaN-based thin-film flip-chip (TFFC) light-emitting diodes (LEDs) with high-refractive-index (TiO2) buckling nanostructures was studied using the three-dimensional finite difference time domain method. Compared with 2-D photonic crystals, the buckling structures have the advantages of a random directionality and a broad distribution in periodicity, which can effectively extract the guided light propagating in all azimuthal directions over a wide spectrum. Numerical studies revealed that the light extraction efficiency of buckling-structured LEDs reaches 1.1 times that of triangular lattice photonic crystals. The effects of the buckling structure feature sizes and the thickness of the N-GaN layer on the light extraction efficiency for TFFC LEDs were also investigated systematically. With optimized structural parameters, a significant light extraction enhancement of about 2.6 times was achieved for TiO2 buckling-structured TFFC LEDs compared with planar LEDs.

VizieR Online Data Catalog: l Car radial velocity curves (Anderson, 2016)

NASA Astrophysics Data System (ADS)

Anderson, R. I.

2018-02-01

Line-of-sight (radial) velocities of the long-period classical Cepheid l Carinae were measured from 925 high-quality optical spectra recorded using the fiber-fed high-resolution (R~60,000) Coralie spectrograph located at the Euler telescope at La Silla Observatory, Chile. The data were taken between 2014 and 2016. This is the full version of Tab. 2 presented partially in the paper. Line shape parameters (depth, width, asymmetry) are listed for the computed cross-correlation profiles (CCFs). Radial velocities were determined using different techniques (Gaussian, bi-Gaussian) and measured on CCFs computed using three different numerical masks (G2, weak lines, strong lines). (1 data file).

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Poisson structure on a space with linear SU(2) fuzziness

NASA Astrophysics Data System (ADS)

Khorrami, Mohammad; Fatollahi, Amir H.; Shariati, Ahmad

2009-07-01

The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which the counterpart of the angular momentum as well as the Euler parametrization of the phase space are introduced. SU(2)-invariant classical systems are discussed, and it is observed that the path of particle can be obtained by the solution of a first-order equation, as the case with such models on commutative spaces. The examples of free particle, rotationally invariant potentials, and specially the isotropic harmonic oscillator are investigated in more detail.

Opto-mechanical design of a buckling cavity in a novel high-performance outside-plant robust field installable single-mode fibre connector

NASA Astrophysics Data System (ADS)

Ebraert, Evert; Van Erps, Jürgen; Beri, Stefano; Watté, Jan; Thienpont, Hugo

2014-05-01

Fibre-to-the-home (FTTH) networks provide an ideal means to reach the goal the European Union has set to provide 50 % of the households with a broadband connection faster than 100 Mb/s. Deployment of FTTH networks, which is still costly today, could be significantly boosted by novel ferrule-less connectors which don't require highly skilled personnel and allow installation in the field. We propose a ferrule-less connector in which two single-mode fibres (SMFs) are aligned and maintain physical contact by ensuring that at least one fibre is in a buckled state. To this end, we design a cavity in which a fibre can buckle in a controlled way. Using finite element analysis simulations to investigate the shape of the formed buckle for various buckling cavity lengths, we show that it can be accurately approximated by a cosine function. In addition, the optical performance of a buckled SMF is investigated by bending loss calculations and simulations. We show a good agreement between the analytical and the simulated bending loss results for a G.652 fibre at a wavelength of 1550 nm. Buckling cavity lengths smaller than 20 mm should be avoided to keep the optical bending loss due to buckling below 0.1 dB. In this case the cavity height should at least be 2 mm to avoid mechanical confinement of the fibre.

Buckling and bone modeling as factors in the development of idiopathic scoliosis.

PubMed

Goto, Manabu; Kawakami, Noriaki; Azegami, Hideyuki; Matsuyama, Yukihiro; Takeuchi, Kenzen; Sasaoka, Ryu

2003-02-15

Computational analysis using the finite-element method was used to examine a possible etiology of idiopathic scoliosis. To compare changes in the coronal and the transverse planes of idiopathic thoracic scoliosis with changes produced in a finite-element buckling model, and to investigate the influence of bone modeling on the buckling spine. Although it is now widely accepted that growth is related strongly to the onset and progression of scoliosis, the pathomechanism or etiology of idiopathic scoliosis still is not clear. A previous study showed that a buckling phenomenon caused by anterior spinal overgrowth can produce scoliosis, and that the fourth buckling mode matched the clinical characteristics associated with the thoracic type of idiopathic scoliosis. The fourth buckling mode occurs when the first, second, and third buckling modes are prevented. The spinal finite-element model used in this study consisted of 68,582 elements and 84,603 nodes. The transverse changes seen in the computed tomography images of 41 patients with idiopathic thoracic scoliosis (apex, T8; average Cobb angle, 52.5 degrees) were compared with those produced in the fourth buckling mode. Bone modeling (bone formation and resorption) was simulated as heat deformation caused by changes in temperature. The bone formation and resorption were simulated, respectively, by positive and negative volume changes in proportion to the stress that occurred in the buckling spine. Computed tomography images of scoliosis show that as the scoliosis becomes more severe, the thoracic cage decreases on the convex side of the curve and increases on the concave side. The opposite thoracic cage deformation was obtained in the fourth buckling mode. In patients with scoliosis, the sternum essentially remains in its original position with respect to the vertebrae, but in the linear buckling model, it shifted in the direction of vertebral body rotation. In contrast to clinical data, the incremental deformation resulting from bone formation corrected the original curve, and the thoracic cage distorted. On the other hand, incremental deformation resulting from bone resorption worsened the original curve, and the thoracic cage distorted in a manner similar to that described by the clinical data. This computational investigation suggests that scoliotic changes in the spinal column triggered by the buckling phenomenon are counteracted by bone formation, but worsened by bone resorption. The authors hypothesized that scoliosis progressed with resorption of loaded bone. However, it is unclear whether this hypothesis applies to a living body in practice because of the effects from additional factors.

Conditions for Symmetries in the Buckle Patterns of Laminated-Composite Plates

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2012-01-01

Conditions for the existence of certain symmetries to exist in the buckle patterns of symmetrically laminated composite plates are presented. The plates considered have a general planform with cutouts, variable thickness and stiffnesses, and general support and loading conditions. The symmetry analysis is based on enforcing invariance of the corresponding eigenvalue problem for a group of coordinate transformations associated with buckle patterns commonly exhibited by symmetrically laminated plates. The buckle-pattern symmetries examined include a central point of inversion symmetry, one plane of reflective symmetry, and two planes of reflective symmetry.

Optimal Design of Grid-Stiffened Composite Panels Using Global and Local Buckling Analysis

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.; Jaunky, Navin; Knight, Norman F., Jr.

1996-01-01

A design strategy for optimal design of composite grid-stiffened panels subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. The design optimization process is adapted to identify the lightest-weight stiffening configuration and pattern for grid stiffened composite panels given the overall panel dimensions, design in-plane loads, material properties, and boundary conditions of the grid-stiffened panel.

The Lateral Compressive Buckling Performance of Aluminum Honeycomb Panels for Long-Span Hollow Core Roofs

PubMed Central

Zhao, Caiqi; Zheng, Weidong; Ma, Jun; Zhao, Yangjian

2016-01-01

To solve the problem of critical buckling in the structural analysis and design of the new long-span hollow core roof architecture proposed in this paper (referred to as a “honeycomb panel structural system” (HSSS)), lateral compression tests and finite element analyses were employed in this study to examine the lateral compressive buckling performance of this new type of honeycomb panel with different length-to-thickness ratios. The results led to two main conclusions: (1) Under the experimental conditions that were used, honeycomb panels with the same planar dimensions but different thicknesses had the same compressive stiffness immediately before buckling, while the lateral compressive buckling load-bearing capacity initially increased rapidly with an increasing honeycomb core thickness and then approached the same limiting value; (2) The compressive stiffnesses of test pieces with the same thickness but different lengths were different, while the maximum lateral compressive buckling loads were very similar. Overall instability failure is prone to occur in long and flexible honeycomb panels. In addition, the errors between the lateral compressive buckling loads from the experiment and the finite element simulations are within 6%, which demonstrates the effectiveness of the nonlinear finite element analysis and provides a theoretical basis for future analysis and design for this new type of spatial structure. PMID:28773567

Fluid-structure interaction modeling of aneurysmal arteries under steady-state and pulsatile blood flow: a stability analysis.

PubMed

Sharzehee, Mohammadali; Khalafvand, Seyed Saeid; Han, Hai-Chao

2018-02-01

Tortuous aneurysmal arteries are often associated with a higher risk of rupture but the mechanism remains unclear. The goal of this study was to analyze the buckling and post-buckling behaviors of aneurysmal arteries under pulsatile flow. To accomplish this goal, we analyzed the buckling behavior of model carotid and abdominal aorta with aneurysms by utilizing fluid-structure interaction (FSI) method with realistic waveforms boundary conditions. FSI simulations were done under steady-state and pulsatile flow for normal (1.5) and reduced (1.3) axial stretch ratios to investigate the influence of aneurysm, pulsatile lumen pressure and axial tension on stability. Our results indicated that aneurysmal artery buckled at the critical buckling pressure and its deflection nonlinearly increased with increasing lumen pressure. Buckling elevates the peak stress (up to 118%). The maximum aneurysm wall stress at pulsatile FSI flow was (29%) higher than under static pressure at the peak lumen pressure of 130 mmHg. Buckling results show an increase in lumen shear stress at the inner side of the maximum deflection. Vortex flow was dramatically enlarged with increasing lumen pressure and artery diameter. Aneurysmal arteries are more susceptible than normal arteries to mechanical instability which causes high stresses in the aneurysm wall that could lead to aneurysm rupture.

Band Gaps for Elastic Wave Propagation in a Periodic Composite Beam Structure Incorporating Microstructure and Surface Energy Effects

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

Zhang, G. Y.; Gao, X. -L.; Bishop, J. E.

Here, a new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a non-classical Bernoulli–Euler beam model that incorporates the microstructure, surface energy and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticity-based model when both the microstructure and surface energy effects are not considered. The band gaps predicted by the new model depend on the microstructure and surface elasticity of each constituent material, the unit cell size, the rotational inertia, and the volumemore » fraction. To quantitatively illustrate the effects of these factors, a parametric study is conducted. The numerical results reveal that the band gap predicted by the current non-classical model is always larger than that predicted by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the effect of the rotational inertia is larger when the exciting frequency is higher and the unit cell length is smaller. Furthermore, it is seen that the volume fraction has a significant effect on the band gap size, and large band gaps can be obtained by tailoring the volume fraction and material parameters.« less

Band Gaps for Elastic Wave Propagation in a Periodic Composite Beam Structure Incorporating Microstructure and Surface Energy Effects

DOE PAGES

Zhang, G. Y.; Gao, X. -L.; Bishop, J. E.; ...

2017-11-20

Here, a new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a non-classical Bernoulli–Euler beam model that incorporates the microstructure, surface energy and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticity-based model when both the microstructure and surface energy effects are not considered. The band gaps predicted by the new model depend on the microstructure and surface elasticity of each constituent material, the unit cell size, the rotational inertia, and the volumemore » fraction. To quantitatively illustrate the effects of these factors, a parametric study is conducted. The numerical results reveal that the band gap predicted by the current non-classical model is always larger than that predicted by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the effect of the rotational inertia is larger when the exciting frequency is higher and the unit cell length is smaller. Furthermore, it is seen that the volume fraction has a significant effect on the band gap size, and large band gaps can be obtained by tailoring the volume fraction and material parameters.« less

Room Temperature Silicene Field-Effect Transistors

NASA Astrophysics Data System (ADS)

Akinwande, Deji

Silicene, a buckled Si analogue of graphene, holds significant promise for future electronics beyond traditional CMOS. In our predefined experiments via encapsulated delamination with native electrodes approach, silicene devices exhibit an ambipolar charge transport behavior, corroborating theories on Dirac band in Ag-free silicene. Monolayer silicene device has extracted field-effect mobility within the theoretical expectation and ON/OFF ratio greater than monolayer graphene, while multilayer silicene devices show decreased mobility and gate modulation. Air-stability of silicene devices depends on the number of layers of silicene and intrinsic material structure determined by growth temperature. Few or multi-layer silicene devices maintain their ambipolar behavior for days in contrast to minutes time scale for monolayer counterparts under similar conditions. Multilayer silicene grown at different temperatures below 300oC possess different intrinsic structures and yield different electrical property and air-stability. This work suggests a practical prospect to enable more air-stable silicene devices with layer and growth condition control, which can be leveraged for other air-sensitive 2D materials. In addition, we describe quantum and classical transistor device concepts based on silicene and related buckled materials that exploit the 2D topological insulating phenomenon. The transistor device physics offer the potential for ballistic transport that is robust against scattering and can be employed for both charge and spin transport. This work was supported by the ARO.

Ground state of dipolar hard spheres confined in channels

NASA Astrophysics Data System (ADS)

Deißenbeck, Florian; Löwen, Hartmut; Oǧuz, Erdal C.

2018-05-01

We investigate the ground state of a classical two-dimensional system of hard-sphere dipoles confined between two hard walls. Using lattice sum minimization techniques we reveal that at fixed wall separations, a first-order transition from a vacuum to a straight one-dimensional chain of dipoles occurs upon increasing the density. Further increase in the density yields the stability of an undulated chain as well as nontrivial buckling structures. We explore the close-packed configurations of dipoles in detail, and we find that, in general, the densest packings of dipoles possess complex magnetizations along the principal axis of the slit. Our predictions serve as a guideline for experiments with granular dipolar and magnetic colloidal suspensions confined in slitlike channel geometry.

On new non-modal hydrodynamic stability modes and resulting non-exponential growth rates - a Lie symmetry approach

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan

2016-11-01

Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.

Research on transient thermal process of a friction brake during repetitive cycles of operation

NASA Astrophysics Data System (ADS)

Slavchev, Yanko; Dimitrov, Lubomir; Dimitrov, Yavor

2017-12-01

Simplified models are used in the classical engineering analyses of the friction brake heating temperature during repetitive cycles of operation to determine basically the maximum and minimum brake temperatures. The objective of the present work is to broaden and complement the possibilities for research through a model that is based on the classical scheme of the Newton's law of cooling and improves the studies by adding a disturbance function for a corresponding braking process. A general case of braking in non-periodic repetitive mode is considered, for which a piecewise function is defined to apply pulse thermal loads to the system. Cases with rectangular and triangular waveforms are presented. Periodic repetitive braking process is also studied using a periodic rectangular waveform until a steady thermal state is achieved. Different numerical methods such as the Euler's method, the classical fourth order Runge-Kutta (RK4) and the Runge-Kutta-Fehlberg 4-5 (RKF45) are used to solve the non-linear differential equation of the model. The constructed model allows during pre-engineering calculations to be determined effectively the time for reaching the steady thermal state of the brake, to be simulated actual braking modes in vehicles and material handling machines, and to be accounted for the thermal impact when performing fatigue calculations.

The buckling response of symmetrically laminated composite plates having a trapezoidal planform area. M.S. Thesis Interim Report No. 98, Aug. 1990 - May 1994

NASA Technical Reports Server (NTRS)

Radloff, H. D., II; Hyer, M. W.; Nemeth, M. P.

1994-01-01

The focus of this work is the buckling response of symmetrically laminated composite plates having a planform area in the shape of an isosceles trapezoid. The loading is assumed to be inplane and applied perpendicular to the parallel ends of the plate. The tapered edges of the plate are assumed to have simply supported boundary conditions, while the parallel ends are assumed to have either simply supported or clamped boundary conditions. A semi-analytic closed-form solution based on energy principles and the Trefftz stability criterion is derived and solutions are obtained using the Rayleigh-Ritz method. Intrinsic in this solution is a simplified prebuckling analysis which approximates the inplane force resultant distributions by the forms Nx=P/W(x) and Ny=Nxy=0, where P is the applied load and W(x) is the plate width which, for the trapezoidal planform, varies linearly with the lengthwise coordinate x. The out-of-plane displacement is approximated by a double trigonometric series. This analysis is posed in terms of four nondimensional parameters representing orthotropic and anisotropic material properties, and two nondimensional parameters representing geometric properties. For comparison purposes, a number of specific plate geometry, ply orientation, and stacking sequence combinations are investigated using the general purpose finite element code ABAQUS. Comparison of buckling coefficients calculated using the semi-analytical model and the finite element model show agreement within 5 percent, in general, and within 15 percent for the worst cases. In order to verify both the finite element and semi-analytical analyses, buckling loads are measured for graphite/epoxy plates having a wide range of plate geometries and stacking sequences. Test fixtures, instrumentation system, and experimental technique are described. Experimental results for the buckling load, the buckled mode shape, and the prebuckling plate stiffness are presented and show good agreement with the analytical results regarding the buckling load and the prebuckling plate stiffness. However, the experimental results show that for some cases the analysis underpredicts the number of halfwaves in the buckled mode shape. In the context of the definitions of taper ratio and aspect ratio used in this study, it is concluded that the buckling load always increases as taper ratio increases for a given aspect ratio for plates having simply supported boundary conditions on the parallel ends. There are combinations of plate geometry and ply stackling sequences, however, that reverse this trend for plates having clamped boundary conditions on the parallel ends such that an increase in the taper ratio causes a decrease in the buckling load. The clamped boundary conditions on the parallel ends of the plate are shown to increase the buckling load compared to simply supported boundary conditions. Also, anisotropy (the D16 and D26 terms) is shown to decrease the buckling load and skew the buckled mode shape for both the simply supported and clamped boundary conditions.

Computer program for stresses and buckling of heated composite-stiffened panels and other structures (BUCLASP 3)

NASA Technical Reports Server (NTRS)

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

1974-01-01

General-purpose program is intended for thermal stress and instability analyses of structures such as axially-stiffened curved panels. Two types of instability analyses can be effected by program: (1) thermal buckling with temperature variation as specified and (2) buckling due to in-plane biaxial loading.

Buckling of beams supported by Pasternak foundation.

NASA Technical Reports Server (NTRS)

Murthy, G. K. N.

1973-01-01

The determination of buckling loads for infinitely long beams resting on a Pasternak (1954) foundation is considered. It is assumed that the onset of buckling takes place at neutral equilibrium. The effect of extending the foundation beyond the width of the beam is determined by comparing the results obtained for two- and three-dimensional foundations.

Buckling Behavior of Long Anisotropic Plates Subjected to Fully Restrained Thermal Expansion

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2003-01-01

An approach for synthesizing buckling results and behavior for thin, balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and which are fully-restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined mechanical loads and is based on useful nondimensional parameters. In addition, stiffness-weighted laminate thermal-expansion parameters are derived and used to determine critical temperature changes in terms of physically intuitive mechanical buckling coefficients. The effects of membrane orthotropy and anisotropy are included. 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 that are presented in the paper. Several generic buckling design curves are presented that provide physical insight into buckling response and provide useful design data. Examples are presented that demonstrate the use of generic design curves. The analysis approach and generic results indicate the effects and characteristics of laminate thermal expansion, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general, unifying manner.

Shear and compression buckling analysis for anisotropic panels with centrally located elliptical cutouts

NASA Technical Reports Server (NTRS)

Britt, V. O.

1993-01-01

An approximate analysis for buckling of biaxial- and shear-loaded anisotropic panels with centrally located elliptical cutouts is presented in the present paper. The analysis is composed of two parts, a prebuckling analysis and a buckling analysis. The prebuckling solution is determined using Lekhnitskii's complex variable equations of plane elastostatics combined with a Laurent series approximation and a boundary collocation method. The buckling solution is obtained using the principle of minimum potential energy. A by-product of the minimum potential energy equation is an integral equation which is solved using Gaussian quadrature. Comparisons with documented experimental results and finite element analyses indicate that the approximate analysis accurately predicts the buckling loads of square biaxial- and shear-loaded panels having elliptical cutouts with major axes up to sixty percent of the panel width. Results of a parametric study are presented for shear- and compression-loaded rectangular anisotropic panels with elliptical cutouts. The effects of panel aspect ratio, cutout shape, cutout size, cutout orientation, laminate anisotropy, and combined loading on the buckling load are examined.

A study of fluid-structure problems

NASA Astrophysics Data System (ADS)

Lam, Dennis Kang-Por

The stability of structures with and without fluid load is investigated. A method is developed for determining the fluid load in terms of added structural mass. Finite element methods are employed to study the buckling of a cylindrical shell under axial compression and liquid storage tanks under hydrodynamic load. Both linear and nonlinear analyses are performed. Diamond modes are found to be the possible postbuckling shapes of the cylindrical shell. Local buckling including elephant-foot buckle and diamond buckle are found for the liquid storage tank models. Comparison between the linear and nonlinear results indicates a substantial difference in buckling mode shapes, though the buckling loads are close to each other. The method for determining the hydrodynamic mass is applied to the impeller stage of a centrifugal pump. The method is based on a linear perturbation technique which assumes that the disturbance in the flow boundaries and velocities caused by the motion of the structure is small. A potential method is used to estimate the velocity flow field. The hydrodynamic mass is then obtained by calculating the total force which results from the pressure induced by a perturbation of the structure.

Buckling-dependent switching behaviours in shifted bilayer germanene nanoribbons: A computational study

NASA Astrophysics Data System (ADS)

Arjmand, T.; Tagani, M. Bagheri; Soleimani, H. Rahimpour

2018-01-01

Bilayer germanene nanoribbons are investigated in different stacks like buckled and flat armchair and buckled zigzag germanene nanoribbons by performing theoretical calculations using the nonequilibrium Greens function method combined with density functional theory. In these bilayer types, the current oscillates with change of interlayer distances or intra-layer overlaps and is dependent on the type of the bilayer. Band gap of AA-stacked of shifted flat bilayer armchair germanene nanoribbon oscillates by change of interlayer distance which is in contrast to buckled bilayer armchair germanene nanoribbon. So, results show the buckling makes system tend to be a semiconductor with wide band gap. Therefore, AA-stacked of shifted flat bilayer armchair germanene nanoribbon has properties between zigzag and armchair edges, the higher current under bias voltages similar to zigzag edge and also oscillations in current like buckled armchair edges. Also, it is found that HOMO-LUMO band gap strongly affects oscillation in currents and their I-V characteristic. This kind of junction improves the switching properties at low voltages around the band gap.

Solution of steady and unsteady transonic-vortex flows using Euler and full-potential equations

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Chuang, Andrew H.; Hu, Hong

1989-01-01

Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The rotating frame of reference solution is potentially efficient as compared with the space fixed reference formulation with dynamic gridding. The integral equation solution with embedded Euler domain is computationally efficient and as accurate as the Euler equations.

Predicting the Influence of Nano-Scale Material Structure on the In-Plane Buckling of Orthotropic Plates

NASA Technical Reports Server (NTRS)

Gates, Thomas S.; Odegard, Gregory M.; Nemeth, Michael P.; Frankland, Sarah-Jane V.

2004-01-01

A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the non-functionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.

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.

An epibulbar chocolate cyst: a rare complication of silicone-based scleral buckle

PubMed Central

Venkatesh, Pradeep; Gogia, Varun; Gupta, Shikha; Nayak, Bhagabat

2015-01-01

A patient with a history of vitreoretinal surgery presented with nasal dystopia, diplopia and epibulbar bluish black mass simulating a chocolate cyst in the right eye. After a non-conclusive ocular examination, he underwent CT of the orbit along with volume rendition and three-dimensional reconstruction, which demonstrated intact globe with laterally displaced band-buckle assembly along with peri-scleral buckle element (SBE) soft tissue proliferation. Imaging-assisted exploration of the lesion was performed and retained scleral buckle element (SBE) was removed in toto; thus relieving the patient long-standing dystopia. PMID:26240109

An epibulbar chocolate cyst: a rare complication of silicone-based scleral buckle.

PubMed

Venkatesh, Pradeep; Gogia, Varun; Gupta, Shikha; Nayak, Bhagabat

2015-08-03

A patient with a history of vitreoretinal surgery presented with nasal dystopia, diplopia and epibulbar bluish black mass simulating a chocolate cyst in the right eye. After a non-conclusive ocular examination, he underwent CT of the orbit along with volume rendition and three-dimensional reconstruction, which demonstrated intact globe with laterally displaced band-buckle assembly along with peri-scleral buckle element (SBE) soft tissue proliferation. Imaging-assisted exploration of the lesion was performed and retained scleral buckle element (SBE) was removed in toto; thus relieving the patient long-standing dystopia. 2015 BMJ Publishing Group Ltd.

Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics

NASA Astrophysics Data System (ADS)

Farajpour, Ali; Danesh, Mohammad; Mohammadi, Moslem

2011-12-01

This paper presents an investigation on the buckling characteristics of nanoscale rectangular plates under bi-axial compression considering non-uniformity in the thickness. Based on the nonlocal continuum mechanics, governing differential equations are derived. Numerical solutions for the buckling loads are obtained using the Galerkin method. The present study shows that the buckling behaviors of single-layered graphene sheets (SLGSs) are strongly sensitive to the nonlocal and non-uniform parameters. The influence of percentage change of thickness on the stability of SLGSs is more significant in the strip-type nonoplates (nanoribbons) than in the square-type nanoplates.

Spontaneous Periodic Delamination of Thin Films To Form Crack-Free Metal and Silicon Ribbons with High Stretchability.

PubMed

Zhang, Qiuting; Tang, Yichao; Hajfathalian, Maryam; Chen, Chunxu; Turner, Kevin T; Dikin, Dmitriy A; Lin, Gaojian; Yin, Jie

2017-12-27

Design of electronic materials with high stretchability is of great importance for realizing soft and conformal electronics. One strategy of realizing stretchable metals and semiconductors is to exploit the buckling of materials bonded to elastomers. However, the level of stretchability is often limited by the cracking and fragmentation of the materials that occurs when constrained buckling occurs while bonded to the substrate. Here, we exploit a failure mechanism, spontaneous buckling-driven periodic delamination, to achieve high stretchability in metal and silicon films that are deposited on prestrained elastomer substrates. We find that both globally periodic buckle-delaminated pattern and ordered cracking patterns over large areas are observed in the spontaneously buckle-delaminated thin films. The geometry of periodic delaminated buckles and cracking periodicity can be predicted by theoretical models. By patterning the films into ribbons with widths smaller than the predicted cracking periodicity, we demonstrate the design of crack-free and spontaneous delaminated ribbons on highly prestrained elastomer substrates, which provides a high stretchability of about 120% and 400% in Si and Au ribbons, respectively. We find that the high stretchability is mainly attributed to the largely relaxed strain in the ribbons via spontaneous buckling-driven delamination, as made evident by the small maximum tensile strain in both ribbons, which is measured to be over 100 times smaller than that of the substrate prestrain.

A New Sutureless Illuminated Macular Buckle Designed for Myopic Macular Hole Retinal Detachment

PubMed Central

Bedda, Ahmed M.; Lolah, Mohamed; Abd Al Shafy, Muhammad S.

2017-01-01

Purpose. To report the anatomic and visual results of a new sutureless illuminated macular buckle designed for patients with macular hole retinal detachment related to high myopia (MMHRD). Design. Prospective nonrandomized comparative interventional trial. Methods. Twenty myopic eyes of 20 patients (mean age, 51.4 years; range, 35–65 years) presenting with MMHRD with a posterior staphyloma, in whom the new buckle was used, were evaluated. The buckle used was assembled from a 5 mm wide sponge and a 7 mm wide silicone tire; it was fixed utilizing the sterile topical adhesive Histoacryl Blue (B Braun, TS1050044FP) which polymerizes in seconds upon being exposed to water-containing substances. The primary outcomes measured included aided visual acuity (BCVA) and optical coherence tomography (OCT) findings. The mean follow-up period was 6 months. Results. Postoperatively, the MH closure was identified by OCT in 8 (40%) eyes. The mean BCVA increased from 0.11 to 0.21 (p < 0.005). The axial length of the eyes included decreased from 30.5 mm preoperatively to 29.8 mm (p = 0.002) postoperatively. Conclusion. Preparation of the new sutureless macular buckle is simple and easy. Illumination of the terminal part of the buckle ensures proper placement. Histoacryl Blue is effective in fixing the buckle in its place for at least 6 months with no reported intra- or postoperative complications. PMID:28409023

Enhancement of quasi-static strain energy harvesters using non-uniform cross-section post-buckled beams

NASA Astrophysics Data System (ADS)

Jiao, Pengcheng; Borchani, Wassim; Hasni, Hassene; Lajnef, Nizar

2017-08-01

Thanks to their efficiency enhancement systems based on post-buckled structural elements have been extensively used in many applications such as actuation, remote sensing and energy harvesting. The post-buckling snap-through behavior of bilaterally constrained beams has been exploited to create sensing or energy harvesting mechanisms for quasi-static applications. The conversion mechanism has been used to transform low-rate and low-frequency excitations into high-rate motions. Electric energy has been generated from such high-rate motions using piezoelectric transducers. However, lack of control over the post-buckling behavior severely limits the mechanism’s efficiency. This study aims to maximize the levels of harvestable power by controlling the location of snap-throughs along the beam at different buckling transitions. Since the snap-through location cannot be controlled by tuning the geometric properties of a uniform beam, non-uniform cross-sections are examined. An energy-based theoretical model is herein developed to predict the post-buckling response of non-prismatic beams. The total potential energy is minimized under constraints that represent the physical confinement of the beam between the lateral boundaries. The experimentally validated results show that changing the shape and geometric dimensions of non-uniform beams allows for the accurate controlling of the snap-through location at different buckling transitions. A 78.59% improvement in harvested energy levels has been achieved by optimization of beam shape.

A Non-Linear Simulation for an Autonomous Unmanned Air Vehicle

DTIC Science & Technology

1993-09-01

4D cos T cos 4D cos T r These equations can now be integrated to find the time history of the Euler angles . 2. Quaternions Another choice for the...is associated with the Euler angles . Quaternions haxe been in 15 use for quite some time. having been discovered by Euler in a search for complex... quaternions has the following advantages over Euler angles in repre- senting spatial orientation of a rigid body: "* Four states required to express the

Nonlinear Buckling Analysis of Functionally Graded Graphene Reinforced Composite Shallow Arches with Elastic Rotational Constraints under Uniform Radial Load.

PubMed

Huang, Yonghui; Yang, Zhicheng; Liu, Airong; Fu, Jiyang

2018-05-28

The buckling behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) shallow arches with elastic rotational constraints under uniform radial load is investigated in this paper. The nonlinear equilibrium equation of the FG-GPLRC shallow arch with elastic rotational constraints under uniform radial load is established using the Halpin-Tsai micromechanics model and the principle of virtual work, from which the critical buckling load of FG-GPLRC shallow arches with elastic rotational constraints can be obtained. This paper gives special attention to the effect of the GPL distribution pattern, weight fraction, geometric parameters, and the constraint stiffness on the buckling load. The numerical results show that all of the FG-GPLRC shallow arches with elastic rotational constraints have a higher buckling load-carrying capacity compared to the pure epoxy arch, and arches of the distribution pattern X have the highest buckling load among four distribution patterns. When the GPL weight fraction is constant, the thinner and larger GPL can provide the better reinforcing effect to the FG-GPLRC shallow arch. However, when the value of the aspect ratio is greater than 4, the flakiness ratio is greater than 103, and the effect of GPL's dimensions on the buckling load of the FG-GPLRC shallow arch is less significant. In addition, the buckling model of FG-GPLRC shallow arch with elastic rotational constraints is changed as the GPL distribution patterns or the constraint stiffness changes. It is expected that the method and the results that are presented in this paper will be useful as a reference for the stability design of this type of arch in the future.

The association between antagonist hamstring coactivation and episodes of knee joint shifting and buckling

PubMed Central

Segal, N.A.; Nevitt, M.C.; Welborn, R.D.; Nguyen, U.-S.D.T.; Niu, J.; Lewis, C.E.; Felson, D.T.; Frey-Law, L.

2016-01-01

SUMMARY Objective Hamstring coactivation during quadriceps activation is necessary to counteract the quadriceps pull on the tibia, but coactivation can be elevated with symptomatic knee osteoarthritis (OA). To guide rehabilitation to attenuate risk for mobility limitations and falls, this study evaluated whether higher antagonistic open kinetic chain hamstring coactivation is associated with knee joint buckling (sudden loss of support) and shifting (a sensation that the knee might give way). Design At baseline, median hamstring coactivation was assessed during maximal isokinetic knee extensor strength testing and at baseline and 24-month follow-up, knee buckling and shifting was self-reported. Associations between tertiles of co-activation and knee (1) buckling, (2) shifting and (3) either buckling or shifting were assessed using logistic regression, adjusted for age, sex, knee OA and pain. Results 1826 participants (1089 women) were included. Mean ± SD age was 61.7 ± 7.7 years, BMI was 30.3 ± 5.5 kg/m2 and 38.2% of knees had OA. There were no consistent statistically significant associations between hamstring coactivation and ipsilateral prevalent or incident buckling or the combination of buckling and shifting. The odds ratios for incident shifting in the highest in comparison with the lowest tertile of coactivation had similar magnitudes in the combined and medial hamstrings, but only reached statistical significance for lateral hamstring coactivation, OR(95%CI) 1.53 (0.99, 2.36). Conclusions Hamstring coactivation during an open kinetic chain quadriceps exercise was not consistently associated with prevalent or incident self-reported knee buckling or shifting in older adults with or at risk for knee OA. PMID:25765501

Embedding methods for the steady Euler equations

NASA Technical Reports Server (NTRS)

Chang, S. H.; Johnson, G. M.

1983-01-01

An approach to the numerical solution of the steady Euler equations is to embed the first-order Euler system in a second-order system and then to recapture the original solution by imposing additional boundary conditions. Initial development of this approach and computational experimentation with it were previously based on heuristic physical reasoning. This has led to the construction of a relaxation procedure for the solution of two-dimensional steady flow problems. The theoretical justification for the embedding approach is addressed. It is proven that, with the appropriate choice of embedding operator and additional boundary conditions, the solution to the embedded system is exactly the one to the original Euler equations. Hence, solving the embedded version of the Euler equations will not produce extraneous solutions.

Site-Specific Pre-Swelling-Directed Morphing Structures of Patterned Hydrogels.

PubMed

Wang, Zhi Jian; Hong, Wei; Wu, Zi Liang; Zheng, Qiang

2017-12-11

Morphing materials have promising applications in various fields, yet how to program the self-shaping process for specific configurations remains a challenge. Herein we show a versatile approach to control the buckling of individual domains and thus the outcome configurations of planar-patterned hydrogels. By photolithography, high-swelling disc gels were positioned in a non-swelling gel sheet; the swelling mismatch resulted in out-of-plain buckling of the disc gels. To locally control the buckling direction, masks with holes were used to guide site-specific swelling of the high-swelling gel under the holes, which built a transient through-thickness gradient and thus directed the buckling during the subsequent unmasked swelling process. Therefore, various configurations of an identical patterned hydrogel can be programmed by the pre-swelling step with different masks to encode the buckling directions of separate domains. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Test and Analysis of a Buckling-Critical Large-Scale Sandwich Composite Cylinder

NASA Technical Reports Server (NTRS)

Schultz, Marc R.; Sleight, David W.; Gardner, Nathaniel W.; Rudd, Michelle T.; Hilburger, Mark W.; Palm, Tod E.; Oldfield, Nathan J.

2018-01-01

Structural stability is an important design consideration for launch-vehicle shell structures and it is well known that the buckling response of such shell structures can be very sensitive to small geometric imperfections. As part of an effort to develop new buckling design guidelines for sandwich composite cylindrical shells, an 8-ft-diameter honeycomb-core sandwich composite cylinder was tested under pure axial compression to failure. The results from this test are compared with finite-element-analysis predictions and overall agreement was very good. In particular, the predicted buckling load was within 1% of the test and the character of the response matched well. However, it was found that the agreement could be improved by including composite material nonlinearity in the analysis, and that the predicted buckling initiation site was sensitive to the addition of small bending loads to the primary axial load in analyses.

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

NASA Technical Reports Server (NTRS)

Shuart, M. J.

1985-01-01

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

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.

Enhancement of Buckling Load with the Use of Active Materials

NASA Technical Reports Server (NTRS)

Yuan, F. G.

2002-01-01

In this paper, active buckling control of a beam using piezoelectric materials is investigated. Under small deformation, mathematical models are developed to describe the behavior of the beams subjected to an axial compressive load with geometric imperfections and load eccentricities under piezoelectric force. Two types of supports, simply supported and clamped, of the beam with a partially bonded piezoelectric actuator are used to illustrate the concept. For the beam with load eccentricities and initial geometric imperfections, the load- carrying capacity can be significantly enhanced by counteracting moments from the piezoelectric actuator. For the single piezoelectric actuator, using static feedback closed-loop control, the first buckling load can be eliminated. In the case of initially straight beams, analytical solutions of the enhanced first critical buckling load due to the increase of bending stiffness by piezoelectric actuators are derived based on linearized buckling analysis.

Compressive and shear buckling analysis of metal matrix composite sandwich panels under different thermal environments

NASA Technical Reports Server (NTRS)

Ko, William L.; Jackson, Raymond H.

1993-01-01

Combined inplane compressive and shear buckling analysis was conducted on flat rectangular sandwich panels using the Raleigh-Ritz minimum energy method with a consideration of transverse shear effect of the sandwich core. The sandwich panels were fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that slightly slender (along unidirectional compressive loading axis) rectangular sandwich panels have the most desirable stiffness-to-weight ratios for aerospace structural applications; the degradation of buckling strength of sandwich panels with rising temperature is faster in shear than in compression; and the fiber orientation of the face sheets for optimum combined-load buckling strength of sandwich panels is a strong function of both loading condition and panel aspect ratio. Under the same specific weight and panel aspect ratio, a sandwich panel with metal matrix composite face sheets has much higher buckling strength than one having monolithic face sheets.

On Euler's Theorem for Homogeneous Functions and Proofs Thereof.

ERIC Educational Resources Information Center

Tykodi, R. J.

1982-01-01

Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)

Mechanical and Thermal Analysis of Classical Functionally Graded Coated Beam

NASA Astrophysics Data System (ADS)

Toudehdehghan, Abdolreza; Mujibur Rahman, Md.; Tarlochan, Faris

2018-03-01

The governing equation of a classical rectangular coated beam made of two layers subjected to thermal and uniformly distributed mechanical loads are derived by using the principle of virtual displacements and based on Euler-Bernoulli deformation beam theory (EBT). The aim of this paper was to analyze the static behavior of clamped-clamped thin coated beam under thermo-mechanical load using MATLAB. Two models were considered for composite coated. The first model was consisting of ceramic layer as a coated and substrate which was metal (HC model). The second model was consisting of Functionally Graded Material (FGM) as a coated layer and metal substrate (FGC model). From the result it was apparent that the superiority of the FGC composite against conventional coated composite has been demonstrated. From the analysis, the stress level throughout the thickness at the interface of the coated beam for the FGC was reduced. Yet, the deflection in return was observed to increase. Therefore, this could cater to various new engineering applications where warrant the utilization of material that has properties that are well-beyond the capabilities of the conventional or yesteryears materials.

Sound Emission of Rotor Induced Deformations of Generator Casings

NASA Technical Reports Server (NTRS)

Polifke, W.; Mueller, B.; Yee, H. C.; Mansour, Nagi (Technical Monitor)

2001-01-01

The casing of large electrical generators can be deformed slightly by the rotor's magnetic field. The sound emission produced by these periodic deformations, which could possibly exceed guaranteed noise emission limits, is analysed analytically and numerically. From the deformation of the casing, the normal velocity of the generator's surface is computed. Taking into account the corresponding symmetry, an analytical solution for the acoustic pressure outside the generator is round in terms of the Hankel function of second order. The normal velocity or the generator surface provides the required boundary condition for the acoustic pressure and determines the magnitude of pressure oscillations. For the numerical simulation, the nonlinear 2D Euler equations are formulated In a perturbation form for low Mach number Computational Aeroacoustics (CAA). The spatial derivatives are discretized by the classical sixth-order central interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a characteristic-based artificial compression method (ACM) filter. The time derivatives are approximated by the classical 4th-order Runge-Kutta method. The numerical results are In excellent agreement with the analytical solution.

Experimental Comparison Between Mahoney and Complementary Sensor Fusion Algorithm for Attitude Determination by Raw Sensor Data of Xsens Imu on Buoy

NASA Astrophysics Data System (ADS)

Jouybari, A.; Ardalan, A. A.; Rezvani, M.-H.

2017-09-01

The accurate measurement of platform orientation plays a critical role in a range of applications including marine, aerospace, robotics, navigation, human motion analysis, and machine interaction. We used Mahoney filter, Complementary filter and Xsens Kalman filter for achieving Euler angle of a dynamic platform by integration of gyroscope, accelerometer, and magnetometer measurements. The field test has been performed in Kish Island using an IMU sensor (Xsens MTi-G-700) that installed onboard a buoy so as to provide raw data of gyroscopes, accelerometers, magnetometer measurements about 25 minutes. These raw data were used to calculate the Euler angles by Mahoney filter and Complementary filter, while the Euler angles collected by XSense IMU sensor become the reference of the Euler angle estimations. We then compared Euler angles which calculated by Mahoney Filter and Complementary Filter with reference to the Euler angles recorded by the XSense IMU sensor. The standard deviations of the differences between the Mahoney Filter, Complementary Filter Euler angles and XSense IMU sensor Euler angles were about 0.5644, 0.3872, 0.4990 degrees and 0.6349, 0.2621, 2.3778 degrees for roll, pitch, and heading, respectively, so the numerical result assert that Mahoney filter is precise for roll and heading angles determination and Complementary filter is precise only for pitch determination, it should be noted that heading angle determination by Complementary filter has more error than Mahoney filter.

Root-sum-square structural strength verification approach

NASA Technical Reports Server (NTRS)

Lee, Henry M.

1994-01-01

Utilizing a proposed fixture design or some variation thereof, this report presents a verification approach to strength test space flight payload components, electronics boxes, mechanisms, lines, fittings, etc., which traditionally do not lend themselves to classical static loading. The fixture, through use of ordered Euler rotation angles derived herein, can be mounted on existing vibration shakers and can provide an innovative method of applying single axis flight load vectors. The versatile fixture effectively loads protoflight or prototype components in all three axes simultaneously by use of a sinusoidal burst of desired magnitude at less than one-third the first resonant frequency. Cost savings along with improved hardware confidence are shown. The end product is an efficient way to verify experiment hardware for both random vibration and strength.

Vortex Dynamics and Shear-Layer Instability in High-Intensity Cyclotrons.

PubMed

Cerfon, Antoine J

2016-04-29

We show that the space-charge dynamics of high-intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam breakup behavior observed in experiments and in simulations. Specifically, we demonstrate that beam breakup is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of beams subject to it. Our work suggests that cyclotrons may be uniquely suited for the experimental study of shear layers and vortex distributions that are not achievable in Penning-Malmberg traps.

Molecular symmetry with quaternions.

PubMed

Fritzer, H P

2001-09-01

A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra are discussed. The correlation of the unit quaternions with both the Cayley-Klein and the Euler parameters through the group SU(2) is presented. Besides rotations the extension of quaternions to other important symmetry operations, reflections and the spatial inversion, is given. Finally, the power of the quaternion calculus for molecular symmetry problems is revealed by treating some examples applied to icosahedral symmetry.

The Effect of Internal Pressure on the Buckling Stress of Thin-Walled Circular Cylinders Under Torsion

NASA Technical Reports Server (NTRS)

Crate, Harold; Batdorf, S B; Baab, George W

1944-01-01

The results of a series of tests to determine the effect of internal pressure on the buckling load of a thin cylinder under an applied torque indicated that internal pressure raises the shear buckling stress. The experimental results were analyzed with the aid of previously developed theory and a simple interaction formula was derived. (author)

Mesoscale studies of ionic closed membranes with polyhedral geometries

DOE PAGES

Olvera de la Cruz, Monica

2016-06-01

Large crystalline molecular shells buckle spontaneously into icosahedra while multicomponent shells buckle into various polyhedra. Continuum elastic theory explains the buckling of closed shells with one elastic component into icosahedra. A generalized elastic model, on the other hand, describes the spontaneous buckling of inhomogeneous shells into regular and irregular polyhedra. By coassembling water-insoluble anionic (–1) amphiphiles with cationic (3+) amphiphiles, we realized ionic vesicles. Results revealed that surface crystalline domains and the unusual shell shapes observed arise from the competition of ionic correlations with charge-regulation. We explain here the mechanism by which these ionic membranes generate a mechanically heterogeneous vesicle.

Local stress determination in chromia-former thanks to micro-Raman spectroscopy: A way to investigate spontaneous delamination processes

NASA Astrophysics Data System (ADS)

Guerain, M.; Goudeau, P.; Panicaud, B.; Grosseau-Poussard, J. L.

2013-02-01

Spontaneous delamination process for α-Cr2O3 thermal oxide films growing on NiCr-30 alloys is studied thanks to micro Raman spectroscopy. In particular, stress maps are performed through and around buckles developed on chromia films. Depending on the cooling rate at the end of the oxidation process, different buckle types appear which are investigated. Associated residual stress distribution clearly evidences the stress release field. In addition, geometrical features are determined for the different buckle types, and from comparison with modelling describing buckle formation and propagation, it is possible to get the interface toughness distribution.

The cutting of metals via plastic buckling

PubMed Central

Viswanathan, Koushik; Ho, Yeung; Chandrasekar, Srinivasan

2017-01-01

The cutting of metals has long been described as occurring by laminar plastic flow. Here we show that for metals with large strain-hardening capacity, laminar flow mode is unstable and cutting instead occurs by plastic buckling of a thin surface layer. High speed in situ imaging confirms that the buckling results in a small bump on the surface which then evolves into a fold of large amplitude by rotation and stretching. The repeated occurrence of buckling and folding manifests itself at the mesoscopic scale as a new flow mode with significant vortex-like components—sinuous flow. The buckling model is validated by phenomenological observations of flow at the continuum level and microstructural characteristics of grain deformation and measurements of the folding. In addition to predicting the conditions for surface buckling, the model suggests various geometric flow control strategies that can be effectively implemented to promote laminar flow, and suppress sinuous flow in cutting, with implications for industrial manufacturing processes. The observations impinge on the foundations of metal cutting by pointing to the key role of stability of laminar flow in determining the mechanism of material removal, and the need to re-examine long-held notions of large strain deformation at surfaces. PMID:28690406

The cutting of metals via plastic buckling.

PubMed

Udupa, Anirudh; Viswanathan, Koushik; Ho, Yeung; Chandrasekar, Srinivasan

2017-06-01

The cutting of metals has long been described as occurring by laminar plastic flow. Here we show that for metals with large strain-hardening capacity, laminar flow mode is unstable and cutting instead occurs by plastic buckling of a thin surface layer. High speed in situ imaging confirms that the buckling results in a small bump on the surface which then evolves into a fold of large amplitude by rotation and stretching. The repeated occurrence of buckling and folding manifests itself at the mesoscopic scale as a new flow mode with significant vortex-like components-sinuous flow. The buckling model is validated by phenomenological observations of flow at the continuum level and microstructural characteristics of grain deformation and measurements of the folding. In addition to predicting the conditions for surface buckling, the model suggests various geometric flow control strategies that can be effectively implemented to promote laminar flow, and suppress sinuous flow in cutting, with implications for industrial manufacturing processes. The observations impinge on the foundations of metal cutting by pointing to the key role of stability of laminar flow in determining the mechanism of material removal, and the need to re-examine long-held notions of large strain deformation at surfaces.

The cutting of metals via plastic buckling

NASA Astrophysics Data System (ADS)

Udupa, Anirudh; Viswanathan, Koushik; Ho, Yeung; Chandrasekar, Srinivasan

2017-06-01

The cutting of metals has long been described as occurring by laminar plastic flow. Here we show that for metals with large strain-hardening capacity, laminar flow mode is unstable and cutting instead occurs by plastic buckling of a thin surface layer. High speed in situ imaging confirms that the buckling results in a small bump on the surface which then evolves into a fold of large amplitude by rotation and stretching. The repeated occurrence of buckling and folding manifests itself at the mesoscopic scale as a new flow mode with significant vortex-like components-sinuous flow. The buckling model is validated by phenomenological observations of flow at the continuum level and microstructural characteristics of grain deformation and measurements of the folding. In addition to predicting the conditions for surface buckling, the model suggests various geometric flow control strategies that can be effectively implemented to promote laminar flow, and suppress sinuous flow in cutting, with implications for industrial manufacturing processes. The observations impinge on the foundations of metal cutting by pointing to the key role of stability of laminar flow in determining the mechanism of material removal, and the need to re-examine long-held notions of large strain deformation at surfaces.

Modal parameter identification of a compression-loaded CFRP stiffened plate and correlation with its buckling behaviour

NASA Astrophysics Data System (ADS)

Chaves-Vargas, M.; Dafnis, A.; Reimerdes, H.-G.; Schröder, K.-U.

2015-10-01

In order to study the dynamic response and the buckling behaviour of several load-carrying structural components of civil aircraft when subjected to transient load scenarios such as gusts or a landing impact, a generic mid-size aircraft is defined within the European research project DAEDALOS. From this aircraft, several sections or panels in different regions such as wing, vertical tailplane and fuselage are defined. The stiffened carbon-fibre-reinforced plastic (CFRP) plate investigated within the present work represents a simplified version of the wing panel selected from the generic aircraft. As part of the current work, the buckling behaviour and the modal properties of the stiffened plate under the effect of a static in-plane compression load are studied. This is accomplished by means of a test series including quasi-static buckling tests and an experimental modal analysis (EMA). One of the key objectives pursued is the correlation of the modal properties to the buckling behaviour by studying the relationship between the natural frequencies of the stiffened plate and its corresponding buckling load. The experimental work is verified by a finite element analysis.

Effects of Initial Geometric Imperfections On the Non-Linear Response of the Space Shuttle Superlightweight Liquid-Oxygen Tank

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H., Jr.

2002-01-01

The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.

Experimental investigation of graphite/polyimide sandwich panels in edgewise compression

NASA Technical Reports Server (NTRS)

Camarda, C. J.

1980-01-01

The local and general buckling behavior of graphite/polyimide sandwich panels simply supported along all four edges and loaded in uniaxial edgewise compression was investigated. Material properties of adhesive and facings were determined from flatwise tension and sandwich beam flexure tests. Tensile and compressive material properties of the facings were determined at 116, R.T., and 589 K (-250, R.T., and 600 F) using the sandwich beam flexure test method. Results indicate that Gr/PI is a usable structural material for short term use at temperatures as high as 589 K (600 F). Buckling specimens were 30.5 X 33.0 cm (12 x 13 in.), had quasi-isotropic symmetric facings and a glass/polyimide honeycomb core. Core thicknesses varied and three panels of each thickness were tested in edgewise compression at room temperature to investigate failure modes and corresponding buckling formulas. Specimens 0.635 cm (0.25 in.) thick failed by overall buckling at loads close to the analytically predicted buckling load; all other panels failed by face wrinkling. Results of the winkling tests indicate that several buckling formulas were unconservative and therefore not suitable for design purposes; recommended wrinkling equations are presented.

Variational Principles for Buckling of Microtubules Modeled as Nonlocal Orthotropic Shells

PubMed Central

2014-01-01

A variational principle for microtubules subject to a buckling load is derived by semi-inverse method. The microtubule is modeled as an orthotropic shell with the constitutive equations based on nonlocal elastic theory and the effect of filament network taken into account as an elastic surrounding. Microtubules can carry large compressive forces by virtue of the mechanical coupling between the microtubules and the surrounding elastic filament network. The equations governing the buckling of the microtubule are given by a system of three partial differential equations. The problem studied in the present work involves the derivation of the variational formulation for microtubule buckling. The Rayleigh quotient for the buckling load as well as the natural and geometric boundary conditions of the problem is obtained from this variational formulation. It is observed that the boundary conditions are coupled as a result of nonlocal formulation. It is noted that the analytic solution of the buckling problem for microtubules is usually a difficult task. The variational formulation of the problem provides the basis for a number of approximate and numerical methods of solutions and furthermore variational principles can provide physical insight into the problem. PMID:25214886

Buckling Behavior of Long Anisotropic Plates Subjected to Fully Restrained Thermal Expansion

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2001-01-01

An approach for synthesizing buckling results and behavior for thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and fully restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined mechanical loads and is based on useful nondimensional parameters. In addition, stiffness-weighted laminate thermal-expansion parameters are derived that are used to determine critical temperatures in terms of physically intuitive mechanical buckling coefficients, and the effects of membrane orthotropy and membrane anisotropy are included. 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 that are presented in the paper. Several generic buckling design curves are presented 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 analysis approach and generic results indicate the effects and characteristics of laminate thermal expansion, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general and unifying manner.

Buckling Behavior of Compression-Loaded Composite Cylindrical Shells With Reinforced Cutouts

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Sarnes, James H., Jr.

2004-01-01

Results from a numerical study of the response of thin-walled compression-loaded quasi-isotropic laminated composite cylindrical shells with unreinforced and reinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The results indicate that a local buckling response occurs in the shell near the cutout when subjected to load and is caused by a nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, reinforcement around a cutout in a compression-loaded shell is shown to retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell. However, some results show that certain reinforcement configurations can cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved buckling response characteristics.

Application of the ideas and techniques of classical fluid mechanics to some problems in physical oceanography.

PubMed

Johnson, R S

2018-01-28

This review makes a case for describing many of the flows observed in our oceans, simply based on the Euler equation, with (piecewise) constant density and with suitable boundary conditions. The analyses start from the Euler and mass conservation equations, expressed in a rotating, spherical coordinate system (but the f -plane and β -plane approximations are also mentioned); five examples are discussed. For three of them, a suitable non-dimensionalization is introduced, and a single small parameter is identified in each case. These three examples lead straightforwardly and directly to new results for: waves on the Pacific Equatorial Undercurrent (EUC) with a thermocline (in the f -plane); a nonlinear, three-dimensional model for EUC-type flows (in the β -plane); and a detailed model for large gyres. The other two examples are exact solutions of the complete system: a flow which corresponds to the underlying structure of the Pacific EUC; and a flow based on the necessary requirement to use a non-conservative body force, which produces the type of flow observed in the Antarctic Circumpolar Current. (All these examples have been discussed in detail in the references cited.) This review concludes with a few comments on how these solutions can be extended and expanded.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).

Couple stress theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

On the Application of the Energy Method to Stability Problems

NASA Technical Reports Server (NTRS)

Marguerre, Karl

1947-01-01

Since stability problems have come into the field of vision of engineers, energy methods have proved to be one of the most powerful aids in mastering them. For finding the especially interesting critical loads special procedures have evolved that depart somewhat from those customary in the usual elasticity theory. A clarification of the connections seemed desirable,especially with regard to the post-critical region, for the treatment of which these special methods are not suited as they are. The present investigation discusses this question-complex (made important by shell construction in aircraft) especially in the classical example of the Euler strut, because in this case - since the basic features are not hidden by difficulties of a mathematical nature - the problem is especially clear. The present treatment differs from that appearing in the Z.f.a.M.M. (1938) under the title "Uber die Behandlung von Stabilittatsproblemen mit Hilfe der energetischen Methode" in that, in order to work out the basic ideas still more clearly,it dispenses with the investigation of behavior at large deflections and of the elastic foundation;in its place the present version gives an elaboration of the 6th section and (in its 7 th and 8th secs.)a new example that shows the applicability of the general criterion to a stability problem that differs from that of Euler in many respects.

Planar incompressible Navier-Stokes and Euler equations: A geometric formulation

NASA Astrophysics Data System (ADS)

Dimitriou, Ioannis

2017-11-01

In this paper, a novel geometric approach for studying steady, two-dimensional, incompressible flows has been thoroughly developed. The continuity and momentum equations were expressed in the flow's intrinsic coordinate system in order to "accommodate" the geometric parameters characterizing it, namely, the local curvatures of the streamlines and their orthogonal trajectories. As a result, a new description of the governing equations was obtained, in which the concerned variables are the velocity magnitude v and a new quantity which was named geometric vorticity, Γ. The latter is defined by the curl of the global curvature vector KG and can be interpreted as the geometric signature of the known vorticity Ω. This approach leads to a new formulation of the Navier-Stokes and Euler equations, the so-called "velocity-curvature" formulation. In this framework, an expression for the flow velocity as a function of geometric parameters only was developed. This reveals that the physical information of a steady incompressible flow is imprinted in its geometry. It is this insight that makes the aforementioned formulation not only conceptually different to the existing classical descriptions, traditionally employed in both analytical and numerical applications, but also attractive, due to the advantages that it could provide at a theoretical and an experimental level. Finally, the derived results are briefly discussed, while emphasizing the implications that the identified geometry-physics interface might have in the future for planar flow analysis.

An energy harvesting solution based on the post-buckling response of non-prismatic slender beams

NASA Astrophysics Data System (ADS)

Jiao, Pengcheng; Borchani, Wassim; Hasni, Hassene; Alavi, Amir H.; Lajnef, Nizar

2017-04-01

Systems based on post-buckled structural elements have been extensively used in many applications such as actuation, remote sensing and energy harvesting thanks to their efficiency enhancement. The post-buckling snap- through behavior of bilaterally constrained beams has been used to create an efficient energy harvesting mechanism under quasi-static excitations. The conversion mechanism has been used to transform low-rate and low-frequency excitations into high-rate motions. Electric energy can be generated from such high-rate motions using piezoelectric transducers. However, lack of control over the post-buckling behavior severely limits the mechanism's efficiency. This study aims to maximize the levels of the harvestable power by controlling the location of the snapping point along the beam at different buckling transitions. Since the snap-through location cannot be controlled by tuning the geometry properties of a uniform cross-section beam, non-uniform cross sections are examined. An energy-based theoretical model is herein developed to predict the post-buckling response of non-uniform cross-section beams. The total potential energy is minimized under constraints that represent the physical confinement of the beam between the lateral boundaries. Experimentally validated results show that changing the shape and geometry dimensions of non- uniform cross-section beams allows for the accurate control of the snap-through location at different buckling transitions. A 78.59% increase in harvested energy levels is achieved by optimizing the beam's shape.

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

NASA Astrophysics Data System (ADS)

Thompson, J. Michael T.; Hutchinson, John W.; Sieber, Jan

2017-12-01

This paper addresses testing of compressed structures, such as shells, that exhibit catastrophic buckling and notorious imperfection sensitivity. The central concept is the probing of a loaded structural specimen by a controlled lateral displacement to gain quantitative insight into its buckling behavior and to measure the energy barrier against buckling. This can provide design information about a structure’s stiffness and robustness against buckling in terms of energy and force landscapes. Developments in this area are relatively new but have proceeded rapidly with encouraging progress. Recent experimental tests on uniformly compressed spherical shells, and axially loaded cylinders, show excellent agreement with theoretical solutions. The probing technique could be a valuable experimental procedure for testing prototype structures, but before it can be used a range of potential problems must be examined and solved. The probing response is highly nonlinear and a variety of complications can occur. Here, we make a careful assessment of unexpected limit points and bifurcations, that could accompany probing, causing complications and possibly even collapse of a test specimen. First, a limit point in the probe displacement (associated with a cusp instability and fold) can result in dynamic buckling as probing progresses, as demonstrated in the buckling of a spherical shell under volume control. Second, various types of bifurcations which can occur on the probing path which result in the probing response becoming unstable are also discussed. To overcome these problems, we outline the extra controls over the entire structure that may be needed to stabilize the response.

Leonhard Euler and his contributions to fluid mechanics

NASA Technical Reports Server (NTRS)

Salas, M. D.

1988-01-01

The career of Leonhard Euler, one of the world's most gifted scientists, is reviewed. The paper focuses on Euler's contributions to fluid mechanics and gives a perspective of how this science was born. A bibliography is included to provide the history enthusiast with a starting point for further study.

Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course

ERIC Educational Resources Information Center

Kull, Trent C.

2011-01-01

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

A new Euler scheme based on harmonic-polygon approach for solving first order ordinary differential equation

NASA Astrophysics Data System (ADS)

Yusop, Nurhafizah Moziyana Mohd; Hasan, Mohammad Khatim; Wook, Muslihah; Amran, Mohd Fahmi Mohamad; Ahmad, Siti Rohaidah

2017-10-01

There are many benefits to improve Euler scheme for solving the Ordinary Differential Equation Problems. Among the benefits are simple implementation and low-cost computational. However, the problem of accuracy in Euler scheme persuade scholar to use complex method. Therefore, the main purpose of this research are show the construction a new modified Euler scheme that improve accuracy of Polygon scheme in various step size. The implementing of new scheme are used Polygon scheme and Harmonic mean concept that called as Harmonic-Polygon scheme. This Harmonic-Polygon can provide new advantages that Euler scheme could offer by solving Ordinary Differential Equation problem. Four set of problems are solved via Harmonic-Polygon. Findings show that new scheme or Harmonic-Polygon scheme can produce much better accuracy result.

76 FR 11935 - Death of Army Corporal Frank W. Buckles, the Last Surviving American Veteran of World War I

Federal Register 2010, 2011, 2012, 2013, 2014

2011-03-03

... of Army Corporal Frank W. Buckles, the Last Surviving American Veteran of World War I By the... Corporal Frank W. Buckles, the last surviving American veteran of World War I, and in remembrance of the generation of American veterans of World War I, I hereby order, by the authority vested in me by the...

Manifestly covariant classical correlation dynamics I. General theory

NASA Astrophysics Data System (ADS)

Lin, Shiru; Wang, Yanchao; Chen, Zhongfang

2018-06-01

By means of density functional theory (DFT) computations and particle-swarm optimization (PSO) structure searches, we herein predict five low-lying energy structures of two-dimensional (2D) aluminum monoxide (AlO) nanosheets. Their high cohesive energy, absence of imaginary phonon dispersion, and good thermal stability make them feasible targets for experimental realization. These monolayers exhibit diverse structural topologies, for instance, PmA- and Pmm-AlO possess buckled four- and six-membered AlO rings, whereas P62-, PmB-, and P6 m-AlO have pores of varied sizes. Interestingly, the most energetically preferred monolayers, PmA- and Pmm-AlO, feature wide band gaps (2.45 and 5.13 eV, respectively), which are promising for green and blue light-emitting devices (LEDs) and photodetectors.

Timoshenko-Type Theory in the Stability Analysis of Corrugated Cylindrical Shells

NASA Astrophysics Data System (ADS)

Semenyuk, N. P.; Neskhodovskaya, N. A.

2002-06-01

A technique is proposed for stability analysis of longitudinally corrugated shells under axial compression. The technique employs the equations of the Timoshenko-type nonlinear theory of shells. The geometrical parameters of shells are specified on discrete set of points and are approximated by segments of Fourier series. Infinite systems of homogeneous algebraic equations are derived from a variational equation written in displacements to determine the critical loads and buckling modes. Specific types of corrugated isotropic metal and fiberglass shells are considered. The calculated results are compared with those obtained within the framework of the classical theory of shells. It is shown that the Timoshenko-type theory extends significantly the possibility of exact allowance for the geometrical parameters and material properties of corrugated shells compared with Kirchhoff-Love theory.

Compression failure mechanisms of uni-ply composite plates with a circular cutout

NASA Technical Reports Server (NTRS)

Khamseh, A. R.; Waas, A. M.

1992-01-01

The effect of circular-hole size on the failure mode of uniply graphite-epoxy composite plates is investigated experimentally and analytically for uniaxial compressive loading. The test specimens are sandwiched between polyetherimide plastic for nondestructive evaluations of the uniply failure mechanisms associated with a range of hole sizes. Finite-element modeling based on classical lamination theory is conducted for the corresponding materials and geometries to reproduce the experimental results analytically. The type of compressive failure is found to be a function of hole size, with fiber buckling/kinking at the hole being the dominant failure mechanism for hole diam/plate width ratios exceeding 0.062. The results of the finite-element analysis supported the experimental data for these failure mechanisms and for those corresponding to smaller hole sizes.

Post-Buckling and Ultimate Strength Analysis of Stiffened Composite Panel Base on Progressive Damage

NASA Astrophysics Data System (ADS)

Zhang, Guofan; Sun, Xiasheng; Sun, Zhonglei

Stiffened composite panel is the typical thin wall structure applied in aerospace industry, and its main failure mode is buckling subjected to compressive loading. In this paper, the development of an analysis approach using Finite Element Method on post-buckling behavior of stiffened composite structures under compression was presented. Then, the numerical results of stiffened panel are obtained by FE simulations. A thorough comparison were accomplished by comparing the load carrying capacity and key position strains of the specimen with test. The comparison indicates that the FEM results which adopted developed methodology could meet the demand of engineering application in predicting the post-buckling behavior of intact stiffened structures in aircraft design stage.

Buckling-Induced Kirigami

NASA Astrophysics Data System (ADS)

Rafsanjani, Ahmad; Bertoldi, Katia

2017-02-01

We investigate the mechanical response of thin sheets perforated with a square array of mutually orthogonal cuts, which leaves a network of squares connected by small ligaments. Our combined analytical, experimental and numerical results indicate that under uniaxial tension the ligaments buckle out of plane, inducing the formation of 3D patterns whose morphology is controlled by the load direction. We also find that by largely stretching the buckled perforated sheets, plastic strains develop in the ligaments. This gives rise to the formation of kirigami sheets comprising periodic distribution of cuts and permanent folds. As such, the proposed buckling-induced pop-up strategy points to a simple route for manufacturing complex morphable structures out of flat perforated sheets.

Buckling Analysis of Single and Multi Delamination In Composite Beam Using Finite Element Method

NASA Astrophysics Data System (ADS)

Simanjorang, Hans Charles; Syamsudin, Hendri; Giri Suada, Muhammad

2018-04-01

Delamination is one type of imperfection in structure which found usually in the composite structure. Delamination may exist due to some factors namely in-service condition where the foreign objects hit the composite structure and creates inner defect and poor manufacturing that causes the initial imperfections. Composite structure is susceptible to the compressive loading. Compressive loading leads the instability phenomenon in the composite structure called buckling. The existence of delamination inside of the structure will cause reduction in buckling strength. This paper will explain the effect of delamination location to the buckling strength. The analysis will use the one-dimensional modelling approach using two- dimensional finite element method.

Buckling of Fiber Reinforced Composite Plates with Nanofiber Reinforced Matrices

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Murthy, Pappu L. N.

2010-01-01

Anisotropic composite plates were evaluated with nanofiber reinforced matrices (NFRM). The nanofiber reinforcement volumes ratio in the matrix was 0.01. The plate dimensions were 20 by 10 by 1.0 in. (508 by 254 by 25.4 mm). Seven different loading condition cases were evaluated: three for uniaxial loading, three for pairs of combined loading, and one with three combined loadings. The anisotropy arose from the unidirectional plates having been at 30 from the structural axis. The anisotropy had a full 6 by 6 rigidities matrix which were satisfied and solved by a Galerkin buckling algorithm. The buckling results showed that the NFRM plates buckled at about twice those with conventional matrix.

Euler force actuation mechanism for siphon valving in compact disk-like microfluidic chips.

PubMed

Deng, Yongbo; Fan, Jianhua; Zhou, Song; Zhou, Teng; Wu, Junfeng; Li, Yin; Liu, Zhenyu; Xuan, Ming; Wu, Yihui

2014-03-01

Based on the Euler force induced by the acceleration of compact disk (CD)-like microfluidic chip, this paper presents a novel actuation mechanism for siphon valving. At the preliminary stage of acceleration, the Euler force in the tangential direction of CD-like chip takes the primary place compared with the centrifugal force to function as the actuation of the flow, which fills the siphon and actuates the siphon valving. The Euler force actuation mechanism is demonstrated by the numerical solution of the phase-field based mathematical model for the flow in siphon valve. In addition, experimental validation is implemented in the polymethylmethacrylate-based CD-like microfluidic chip manufactured using CO2 laser engraving technique. To prove the application of the proposed Euler force actuation mechanism, whole blood separation and plasma extraction has been conducted using the Euler force actuated siphon valving. The newly introduced actuation mechanism overcomes the dependence on hydrophilic capillary filling of siphon by avoiding external manipulation or surface treatments of polymeric material. The sacrifice for highly integrated processing in pneumatic pumping technique is also prevented by excluding the volume-occupied compressed air chamber.

Design, Optimization and Evaluation of Integrally Stiffened Al 7050 Panel with Curved Stiffeners

NASA Technical Reports Server (NTRS)

Slemp, Wesley C. H.; Bird, R. Keith; Kapania, Rakesh K.; Havens, David; Norris, Ashley; Olliffe, Robert

2011-01-01

A curvilinear stiffened panel was designed, manufactured, and tested in the Combined Load Test Fixture at NASA Langley Research Center. The panel was optimized for minimum mass subjected to constraints on buckling load, yielding, and crippling or local stiffener failure using a new analysis tool named EBF3PanelOpt. The panel was designed for a combined compression-shear loading configuration that is a realistic load case for a typical aircraft wing panel. The panel was loaded beyond buckling and strains and out-of-plane displacements were measured. The experimental data were compared with the strains and out-of-plane deflections from a high fidelity nonlinear finite element analysis and linear elastic finite element analysis of the panel/test-fixture assembly. The numerical results indicated that the panel buckled at the linearly elastic buckling eigenvalue predicted for the panel/test-fixture assembly. The experimental strains prior to buckling compared well with both the linear and nonlinear finite element model.

Anisotropic carrier mobility in buckled two-dimensional GaN.

PubMed

Tong, Lijia; He, Junjie; Yang, Min; Chen, Zheng; Zhang, Jing; Lu, Yanli; Zhao, Ziyuan

2017-08-30

Developing nanoelectronic engineering requires two-dimensional (2d) materials with both usable carrier mobility and proper large band-gap. In this study, we present a detailed theoretical investigation of the intrinsic carrier mobilities of buckled 2d GaN. This buckled 2d GaN is accessed by hydrofluorination (FGaNH) and hydrogenation (HGaNH). We predict that the anisotropic carrier mobilities of buckled 2d GaN can exceed those of 2d MoS 2 and can be altered by an alterable surface chemical bond (convert from a Ga-F-Ga bond of FGaNH to a Ga-H bond of HGaNH). Moreover, converting FGaNH to HGaNH can significantly suppress hole mobility (even close to zero) and result in a transition from a p-type-like semiconductor (FGaNH) to an n-type-like semiconductor (HGaNH). These features make buckled 2d GaN a promising candidate for application in future conductivity-adjustable electronics.

Hierarchical macroscopic fibrillar adhesives: in situ study of buckling and adhesion mechanisms on wavy substrates.

PubMed

Bauer, Christina T; Kroner, Elmar; Fleck, Norman A; Arzt, Eduard

2015-10-23

Nature uses hierarchical fibrillar structures to mediate temporary adhesion to arbitrary substrates. Such structures provide high compliance such that the flat fibril tips can be better positioned with respect to asperities of a wavy rough substrate. We investigated the buckling and adhesion of hierarchically structured adhesives in contact with flat smooth, flat rough and wavy rough substrates. A macroscopic model for the structural adhesive was fabricated by molding polydimethylsiloxane into pillars of diameter in the range of 0.3-4.8 mm, with up to three different hierarchy levels. Both flat-ended and mushroom-shaped hierarchical samples buckled at preloads one quarter that of the single level structures. We explain this behavior by a change in the buckling mode; buckling leads to a loss of contact and diminishes adhesion. Our results indicate that hierarchical structures can have a strong influence on the degree of adhesion on both flat and wavy substrates. Strategies are discussed that achieve highly compliant substrates which adhere to rough substrates.

Investigation of Buckling Phenomenon Induced by Growth of Vertebral Bodies Using a Mechanical Spine Model

NASA Astrophysics Data System (ADS)

Sasaoka, Ryu; Azegami, Hideyuki; Murachi, Shunji; Kitoh, Junzoh; Ishida, Yoshito; Kawakami, Noriaki; Makino, Mitsunori; Matsuyama, Yukihiro

A hypothesis that idiopathic scoliosis is a buckling phenomenon of the fourth or sixth mode, which is the second or third lateral bending mode, induced by the growth of vertebral bodies was presented in a previous paper by the authors using numerical simulations with a finite-element model of the spine. This paper presents experimental proof of the buckling phenomenon using mechanical spine models constructed with the geometrical data of the finite-element model used in a previous work. Using three spine mechanical models with different materials at intervertebral joints, the change in the natural vibration eigenvalue of the second lateral bending mode with the growth of vertebral bodies was measured by experimental modal analysis. From the result, it was observed that natural vibration eigenvalue decreased with the growth of vertebral bodies. Since the increase in primary factor inducing the buckling phenomenon decreases natural vibration eigenvalue, the obtained result confirms the buckling hypothesis.

Buckling in serpentine microstructures and applications in elastomer-supported ultra-stretchable electronics with high areal coverage

PubMed Central

Zhang, Yihui; Xu, Sheng; Fu, Haoran; Lee, Juhwan; Su, Jessica; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang

2014-01-01

Lithographically defined electrical interconnects with thin, filamentary serpentine layouts have been widely explored for use in stretchable electronics supported by elastomeric substrates. We present a systematic and thorough study of buckling physics in such stretchable serpentine microstructures, and a strategic design of serpentine layout for ultra-stretchable electrode, via analytical models, finite element method (FEM) computations, and quantitative experiments. Both the onset of buckling and the postbuckling behaviors are examined, to determine scaling laws for the critical buckling strain and the limits of elastic behavior. Two buckling modes, namely the symmetric and anti-symmetric modes, are identified and analyzed, with experimental images and numerical results that show remarkable levels of agreement for the associated postbuckling processes. Based on these studies and an optimization in design layout, we demonstrate routes for application of serpentine interconnects in an ultra-stretchable electrode that offer, simultaneously, an areal coverage as high as 81%, and a biaxial stretchability as large as ~170%. PMID:25309616

Buckling in serpentine microstructures and applications in elastomer-supported ultra-stretchable electronics with high areal coverage.

PubMed

Zhang, Yihui; Xu, Sheng; Fu, Haoran; Lee, Juhwan; Su, Jessica; Hwang, Keh-Chih; Rogers, John A; Huang, Yonggang

2013-01-01

Lithographically defined electrical interconnects with thin, filamentary serpentine layouts have been widely explored for use in stretchable electronics supported by elastomeric substrates. We present a systematic and thorough study of buckling physics in such stretchable serpentine microstructures, and a strategic design of serpentine layout for ultra-stretchable electrode, via analytical models, finite element method (FEM) computations, and quantitative experiments. Both the onset of buckling and the postbuckling behaviors are examined, to determine scaling laws for the critical buckling strain and the limits of elastic behavior. Two buckling modes, namely the symmetric and anti-symmetric modes, are identified and analyzed, with experimental images and numerical results that show remarkable levels of agreement for the associated postbuckling processes. Based on these studies and an optimization in design layout, we demonstrate routes for application of serpentine interconnects in an ultra-stretchable electrode that offer, simultaneously, an areal coverage as high as 81%, and a biaxial stretchability as large as ~170%.

Non-Deterministic Dynamic Instability of Composite Shells

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Abumeri, Galib H.

2004-01-01

A computationally effective method is described to evaluate the non-deterministic dynamic instability (probabilistic dynamic buckling) of thin composite shells. The method is a judicious combination of available computer codes for finite element, composite mechanics, and probabilistic structural analysis. The solution method is incrementally updated Lagrangian. It is illustrated by applying it to thin composite cylindrical shell subjected to dynamic loads. Both deterministic and probabilistic buckling loads are evaluated to demonstrate the effectiveness of the method. A universal plot is obtained for the specific shell that can be used to approximate buckling loads for different load rates and different probability levels. Results from this plot show that the faster the rate, the higher the buckling load and the shorter the time. The lower the probability, the lower is the buckling load for a specific time. Probabilistic sensitivity results show that the ply thickness, the fiber volume ratio and the fiber longitudinal modulus, dynamic load and loading rate are the dominant uncertainties, in that order.

Dynamic Probabilistic Instability of Composite Structures

NASA Technical Reports Server (NTRS)

Chamis, Christos C.

2009-01-01

A computationally effective method is described to evaluate the non-deterministic dynamic instability (probabilistic dynamic buckling) of thin composite shells. The method is a judicious combination of available computer codes for finite element, composite mechanics and probabilistic structural analysis. The solution method is incrementally updated Lagrangian. It is illustrated by applying it to thin composite cylindrical shell subjected to dynamic loads. Both deterministic and probabilistic buckling loads are evaluated to demonstrate the effectiveness of the method. A universal plot is obtained for the specific shell that can be used to approximate buckling loads for different load rates and different probability levels. Results from this plot show that the faster the rate, the higher the buckling load and the shorter the time. The lower the probability, the lower is the buckling load for a specific time. Probabilistic sensitivity results show that the ply thickness, the fiber volume ratio and the fiber longitudinal modulus, dynamic load and loading rate are the dominant uncertainties in that order.

Effect of plasticity and atmospheric pressure on the formation of donut- and croissantlike buckles.

PubMed

Hamade, S; Durinck, J; Parry, G; Coupeau, C; Cimetière, A; Grilhé, J; Colin, J

2015-01-01

The formation of donut- and croissantlike buckles has been observed onto the free surface of gold thin films deposited on silicon substrates. Numerical simulations clearly evidence that the coupling effect between the atmospheric pressure acting on the free surface and the plastic folding of the ductile film is responsible for the circular blister destabilization and the formation of the donut- and croissantlike buckling patterns.

Nondimensional parameters and equations for buckling of symmetrically laminated thin elastic shallow shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

1991-01-01

A method of deriving nondimensional equations and identifying the fundamental parameters associated with bifurcation buckling of anisotropic shells subjected to combined loads is presented. The procedure and rationale used to obtain useful nondimensional forms of the transverse equilibrium and compatibility equations for buckling are presented. Fundamental parameters are identified that represent the importance of both membrane and bending orthotropy and anisotropy on the results.

Effect of end-ring stiffness on buckling of pressure-loaded stiffened conical shells

NASA Technical Reports Server (NTRS)

Davis, R. C.; Williams, J. G.

1977-01-01

Buckling studies were conducted on truncated 120 deg conical shells having large end rings and many interior reinforcing rings that are typical of aeroshells used as spacecraft decelerators. Changes in base-end-ring stiffness were accomplished by simply machining away a portion of the base ring between successive buckling tests. Initial imperfection measurements from the test cones were included in the analytical model.

The stability of the compression cover of box beams stiffened by posts

NASA Technical Reports Server (NTRS)

Seide, Paul; Barrett, Paul F

1951-01-01

An investigation is made of the buckling of the compression cover of post-stiffened box beams subjected to end moments. Charts are presented for the determination of the minimum post axial stiffnesses and the corresponding compressive buckling loads required for the compression cover to buckle with nodes through the posts. Application of the charts to design and analysis and the limitations of their use are discussed.

What happens between pure hydraulic and buckling mechanisms of blowout fractures?

PubMed

Nagasao, Tomohisa; Miyamoto, Junpei; Shimizu, Yusuke; Jiang, Hua; Nakajima, Tatsuo

2010-06-01

The present study aims to evaluate how the ratio of the hydraulic and buckling mechanisms affects blowout fracture patterns, when these two mechanisms work simultaneously. Three-dimensional computer-aided-design (CAD)models were generated simulating ten skulls. To simulate impact, 1.2J was applied on the orbital region of these models in four patterns. Pattern 1: All the energy works to cause the hydraulic effect. Pattern 2: Two-thirds of the energy works to cause the hydraulic effect; one-third of the energy works to cause the buckling effect. Pattern 3: One-third of the energy works to cause the hydraulic effect; two-thirds of the energy works to cause the buckling effect. Pattern 4: The entire energy quantum works to cause the buckling effect. Using the finite element method, the regions where fractures were theoretically expected to occur were calculated and were compared between the four patterns. More fracture damage occurred for Pattern 1 than Pattern 2, and for Pattern 3 than for Pattern 4. The hydraulic and buckling mechanisms interact with one another. When these two mechanisms are combined, the orbital walls tend to develop serious fractures. Copyright (c) 2009 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rights reserved.

Interaction of hydraulic and buckling mechanisms in blowout fractures.

PubMed

Nagasao, Tomohisa; Miyamoto, Junpei; Jiang, Hua; Tamaki, Tamotsu; Kaneko, Tsuyoshi

2010-04-01

The etiology of blowout fractures is generally attributed to 2 mechanisms--increase in the pressure of the orbital contents (the hydraulic mechanism) and direct transmission of impacts on the orbital walls (the buckling mechanism). The present study aims to elucidate whether or not an interaction exists between these 2 mechanisms. We performed a simulation experiment using 10 Computer-Aided-Design skull models. We applied destructive energy to the orbits of the 10 models in 3 different ways. First, to simulate pure hydraulic mechanism, energy was applied solely on the internal walls of the orbit. Second, to simulate pure buckling mechanism, energy was applied solely on the inferior rim of the orbit. Third, to simulate the combined effect of the hydraulic and buckling mechanisms, energy was applied both on the internal wall of the orbit and inferior rim of the orbit. After applying the energy, we calculated the areas of the regions where fracture occurred in the models. Thereafter, we compared the areas among the 3 energy application patterns. When the hydraulic and buckling mechanisms work simultaneously, fracture occurs on wider areas of the orbital walls than when each of these mechanisms works separately. The hydraulic and buckling mechanisms interact, enhancing each other's effect. This information should be taken into consideration when we examine patients in whom blowout fracture is suspected.

Active buckling control of an imperfect beam-column with circular cross-section using piezo-elastic supports and integral LQR control

NASA Astrophysics Data System (ADS)

Schaeffner, Maximilian; Platz, Roland

2016-09-01

For slender beam-columns loaded by axial compressive forces, active buckling control provides a possibility to increase the maximum bearable axial load above that of a purely passive structure. In this paper, the potential of active buckling control of an imperfect beam-column with circular cross-section using piezo-elastic supports is investigated numerically. Imperfections are given by an initial deformation of the beam-column caused by a constant imperfection force. With the piezo-elastic supports, active bending moments in arbitrary directions orthogonal to the beam-column's longitudinal axis can be applied at both beam- column's ends. The imperfect beam-column is loaded by a gradually increasing axial compressive force resulting in a lateral deformation of the beam-column. First, a finite element model of the imperfect structure for numerical simulation of the active buckling control is presented. Second, an integral linear-quadratic regulator (LQR) that compensates the deformation via the piezo-elastic supports is derived for a reduced modal model of the ideal beam-column. With the proposed active buckling control it is possible to stabilize the imperfect beam-column in arbitrary lateral direction for axial loads above the theoretical critical buckling load and the maximum bearable load of the passive structure.

Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

NASA Astrophysics Data System (ADS)

Ye, Hong-Ling; Wang, Wei-Wei; Chen, Ning; Sui, Yun-Kang

2017-10-01

The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.

Buckling behavior of long symmetrically laminated plates subjected to combined loadings

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

1992-01-01

A parametric study is presented of the buckling behavior of infinitely long, symmetrically laminated anisotropic plates subjected to combined loadings. The loading conditions considered are axial tension and compression transverse tension and compression, and shear. Results obtained using a special-purpose analysis, well-suited for parametric studies, are presented for clamped and simply supported plates. Moreover, results are presented for some common laminate constructions, and generic buckling design charts are presented for a wide range of parameters. The generic design charts are presented in terms of useful nondimensional parameters, and the dependence of the nondimensional parameters on laminate fiber orientation, stacking sequence, and material properties is discussed. An important finding of the study is that the effects of anisotropy are much more pronounced in shear-loaded plates than in compression-loaded plates. In addition, the effects of anisotropy on plates subjected to combined loadings are generally manifested as a phase shift of self-similar buckling interaction curves. A practical application of this phase shift is that the buckling resistance of long plates can be improved by applying a shear loading with a specific orientation. In all cases considered in the study, the buckling coefficients of infinitely long plates are found to be independent of the bending stiffness ratio (D sub 11/D sub 22)(1/4).

Buckling behavior of long symmetrically laminated plates subjected to combined loads

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

1992-01-01

A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loadings is presented. The loading conditions considered are axial tension and compression, transverse tension and compression, and shear. Results obtained using a special purpose analysis, well suited for parametric studies are presented for clamped and simply supported plates. Moreover, results are presented for some common laminate constructions, and generic buckling design charts are presented for a wide range of parameters. The generic design charts are presented in terms of useful nondimensional parameters, and dependence of the nondimensional parameters on laminate fiber orientation, stacking sequence, and material properties is discussed. An important finding of the study is that the effects of anisotropy are much more pronounced in shear-loaded plates than in compression loaded plates. In addition, the effects of anisotropy on plates subjected to combined loadings are generally manifested as a phase shift of self-similar buckling interaction curves. A practical application of this phase shift is the buckling resistance of long plates can be improved by applying a shear loading with a specific orientation. In all cases considered, it is found that the buckling coefficients of infinitely long plates are independent of the bending stiffness ratio (D sub 11/D sub 22) sup 1/4.

Influence of carbon nanotubes on the buckling of microtubule bundles in viscoelastic cytoplasm using nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Farajpour, A.; Rastgoo, A.

Carbon nanotubes are a new class of microtubule-stabilizing agents since they interact with protein microtubules in living cells, interfering with cell division and inducing apoptosis. In the present work, a modified beam model is developed to investigate the effect of carbon nanotubes on the buckling of microtubule bundles in living cell. A realistic interaction model is employed using recent experimental data on the carbon nanotube-stabilized microtubules. Small scale and surface effects are taken into account applying the nonlocal strain gradient theory and surface elasticity theory. Pasternak model is used to describe the normal and shearing effects of enclosing filament matrix on the buckling behavior of the system. An exact solution is obtained for the buckling growth rates of the mixed bundle in viscoelastic surrounding cytoplasm. The present results are compared with those reported in the open literature for single microtubules and an excellent agreement is found. Finally, the effects of different parameters such as the size, chirality, position and surface energy of carbon nanotubes on the buckling growth rates of microtubule bundles are studied. It is found that the buckling growth rate may increase or decrease by adding carbon nanotubes, depending on the diameter and chirality of carbon nanotubes.

Engineering electronic states of periodic and quasiperiodic chains by buckling

NASA Astrophysics Data System (ADS)

Mukherjee, Amrita; Nandy, Atanu; Chakrabarti, Arunava

2017-07-01

The spectrum of spinless, non-interacting electrons on a linear chain that is buckled in a non-uniform, quasiperiodic manner is investigated within a tight binding formalism. We have addressed two specific cases, viz., a perfectly periodic chain wrinkled in a quasiperiodic Fibonacci pattern, and a quasiperiodic Fibonacci chain, where the buckling also takes place in a Fibonacci pattern. The buckling brings distant neighbors in the parent chain to close proximity, which is simulated by a tunnel hopping amplitude. It is seen that, in the perfectly ordered case, increasing the strength of the tunnel hopping (that is, bending the segments more) absolutely continuous density of states is retained towards the edges of the band, while the central portion becomes fragmented and host subbands of narrowing widths containing extended, current carrying states, and multiple isolated bound states formed as a result of the bending. A switching ;on; and ;off; of the electronic transmission can thus be engineered by buckling. On the other hand, in the second example of a quasiperiodic Fibonacci chain, imparting a quasiperiodic buckling is found to generate continuous subband(s) destroying the usual multifractality of the energy spectrum. We present exact results based on a real space renormalization group analysis, that is corroborated by explicit calculation of the two terminal electronic transport.

An experiment for determining the Euler load by direct computation

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.; Stein, Peter A.

1986-01-01

A direct algorithm is presented for computing the Euler load of a column from experimental data. The method is based on exact inextensional theory for imperfect columns, which predicts two distinct deflected shapes at loads near the Euler load. The bending stiffness of the column appears in the expression for the Euler load along with the column length, therefore the experimental data allows a direct computation of bending stiffness. Experiments on graphite-epoxy columns of rectangular cross-section are reported in the paper. The bending stiffness of each composite column computed from experiment is compared with predictions from laminated plate theory.

Misuse of Booster Cushions – An Observation Study of Children’s Performance during Buckling Up

PubMed Central

Osvalder, Anna-Lisa; Bohman, Katarina

2008-01-01

Booster cushions are effective tools to protect children from injuries in car crashes, but there remains a large amount of misuse. The aim of this study was to assess potential misuse of booster cushions in an observational laboratory study, and to identify whether booster cushion design, age or clothing had any effect. 130 Swedish children from the ages of 4–12 years participated. Each child buckled up on an integrated and on an aftermarket booster cushion in the rear seat. The older children also buckled up with seat belt only. Interviews, observations and body measurements were performed. Time to buckle up and amount of belt slack were registered. Photographs were taken to document misuse. Results showed that 77% failed to perform correct belt routing on the aftermarket cushion, independent of age, although they were familiar with this system. The misuse rate for the integrated cushion was only 4%. No misuse was found for seat belt only. Few children tightened the belt. The belt slack increased when wearing winter jackets. This indicates the importance of adding pretensioners to the rear seat. Sled tests with HIII&TNO 6y dummies were also performed for the most frequent misuse situations found. The main conclusion is that an integrated booster cushion has many advantages compared to an aftermarket cushion regarding both safety and comfort. It is easy and quick to handle, has few possibilities for misuse, has an intuitive design, the buckling up sequence is equal to buckling up with an ordinary seat belt, and younger children can buckle up correctly. PMID:19026222

Stability of carotid artery under steady-state and pulsatile blood flow: a fluid-structure interaction study.

PubMed

Saeid Khalafvand, Seyed; Han, Hai-Chao

2015-06-01

It has been shown that arteries may buckle into tortuous shapes under lumen pressure, which in turn could alter blood flow. However, the mechanisms of artery instability under pulsatile flow have not been fully understood. The objective of this study was to simulate the buckling and post-buckling behaviors of the carotid artery under pulsatile flow using a fully coupled fluid-structure interaction (FSI) method. The artery wall was modeled as a nonlinear material with a two-fiber strain-energy function. FSI simulations were performed under steady-state flow and pulsatile flow conditions with a prescribed flow velocity profile at the inlet and different pressures at the outlet to determine the critical buckling pressure. Simulations were performed for normal (160 ml/min) and high (350 ml/min) flow rates and normal (1.5) and reduced (1.3) axial stretch ratios to determine the effects of flow rate and axial tension on stability. The results showed that an artery buckled when the lumen pressure exceeded a critical value. The critical mean buckling pressure at pulsatile flow was 17-23% smaller than at steady-state flow. For both steady-state and pulsatile flow, the high flow rate had very little effect (<5%) on the critical buckling pressure. The fluid and wall stresses were drastically altered at the location with maximum deflection. The maximum lumen shear stress occurred at the inner side of the bend and maximum tensile wall stresses occurred at the outer side. These findings improve our understanding of artery instability in vivo.

Stability of Carotid Artery Under Steady-State and Pulsatile Blood Flow: A Fluid–Structure Interaction Study

PubMed Central

Saeid Khalafvand, Seyed; Han, Hai-Chao

2015-01-01

It has been shown that arteries may buckle into tortuous shapes under lumen pressure, which in turn could alter blood flow. However, the mechanisms of artery instability under pulsatile flow have not been fully understood. The objective of this study was to simulate the buckling and post-buckling behaviors of the carotid artery under pulsatile flow using a fully coupled fluid–structure interaction (FSI) method. The artery wall was modeled as a nonlinear material with a two-fiber strain-energy function. FSI simulations were performed under steady-state flow and pulsatile flow conditions with a prescribed flow velocity profile at the inlet and different pressures at the outlet to determine the critical buckling pressure. Simulations were performed for normal (160 ml/min) and high (350 ml/min) flow rates and normal (1.5) and reduced (1.3) axial stretch ratios to determine the effects of flow rate and axial tension on stability. The results showed that an artery buckled when the lumen pressure exceeded a critical value. The critical mean buckling pressure at pulsatile flow was 17–23% smaller than at steady-state flow. For both steady-state and pulsatile flow, the high flow rate had very little effect (<5%) on the critical buckling pressure. The fluid and wall stresses were drastically altered at the location with maximum deflection. The maximum lumen shear stress occurred at the inner side of the bend and maximum tensile wall stresses occurred at the outer side. These findings improve our understanding of artery instability in vivo. PMID:25761257

Controlled elastic postbuckling of bilaterally constrained non-prismatic columns: application to enhanced quasi-static energy harvesters

NASA Astrophysics Data System (ADS)

Liu, Suihan; Burgueño, Rigoberto

2016-12-01

Axially compressed bilaterally constrained columns, which can attain multiple snap-through buckling events in their elastic postbuckling response, can be used as energy concentrators and mechanical triggers to transform external quasi-static displacement input to local high-rate motions and excite vibration-based piezoelectric transducers for energy harvesting devices. However, the buckling location with highest kinetic energy release along the element, and where piezoelectric oscillators should be optimally placed, cannot be controlled or isolated due to the changing buckling configurations. This paper proposes the concept of stiffness variations along the column to gain control of the buckling location for optimal placement of piezoelectric transducers. Prototyped non-prismatic columns with piece-wise varying thickness were fabricated through 3D printing for experimental characterization and numerical simulations were conducted using the finite element method. A simple theoretical model was also developed based on the stationary potential energy principle for predicting the critical line contact segment that triggers snap-through events and the buckling morphologies as compression proceeds. Results confirm that non-prismatic column designs allow control of the buckling location in the elastic postbuckling regime. Compared to prismatic columns, non-prismatic designs can attain a concentrated kinetic energy release spot and a higher number of snap-buckling mode transitions under the same global strain. The direct relation between the column’s dynamic response and the output voltage from piezoelectric oscillator transducers allows the tailorable postbuckling response of non-prismatic columns to be used as multi-stable energy concentrators with enhanced performance in micro-energy harvesters.

Large-scale mechanical buckle fold development and the initiation of tensile fractures

NASA Astrophysics Data System (ADS)

Eckert, Andreas; Connolly, Peter; Liu, Xiaolong

2014-11-01

failure associated with buckle folding is commonly associated to the distribution of outer arc extension but has also been observed on fold limbs. This study investigates whether tensile stresses and associated failure can be explained by the process of buckling under realistic in situ stress conditions. A 2-D plane strain finite element modeling approach is used to study single-layer buckle folds with a Maxwell viscoelastic rheology. A variety of material parameters are considered and their influence on the initiation of tensile stresses during the various stages of deformation is analyzed. It is concluded that the buckling process determines the strain distribution within the fold layer but is not solely responsible for the initiation of tensile stresses. The modeling results show that tensile stresses are most dependent on the permeability, viscosity, and overburden thickness. Low permeability (<10-19 m2), high viscosity (≥1021 Pa s), and low overburden pressure can explain tensile failure at the fold hinge. Tensile stresses in the limb of the fold cannot (in general) be explained by buckling. Rather, it develops due to a combination of compression and erosional unloading. The modeling results show that erosion of high permeability rocks can explain the generation of tensile stresses at significant depths (˜2 km) both at the hinge of the fold and throughout the limb of the fold. This study shows that tensile stresses and associated failure within buckle folds is directly dependent on the distribution of material parameters but moreover to the strain history of the geologic system.

Mathematical Investigation of Fluid Flow, Mass Transfer, and Slag-steel Interfacial Behavior in Gas-stirred Ladles

NASA Astrophysics Data System (ADS)

Cao, Qing; Nastac, Laurentiu

2018-06-01

In this study, the Euler-Euler and Euler-Lagrange modeling approaches were applied to simulate the multiphase flow in the water model and gas-stirred ladle systems. Detailed comparisons of the computational and experimental results were performed to establish which approach is more accurate for predicting the gas-liquid multiphase flow phenomena. It was demonstrated that the Euler-Lagrange approach is more accurate than the Euler-Euler approach. The Euler-Lagrange approach was applied to study the effects of the free surface setup, injected bubble size, gas flow rate, and slag layer thickness on the slag-steel interaction and mass transfer behavior. Detailed discussions on the flat/non-flat free surface assumption were provided. Significant inaccuracies in the prediction of the surface fluid flow characteristics were found when the flat free surface was assumed. The variations in the main controlling parameters (bubble size, gas flow rate, and slag layer thickness) and their potential impact on the multiphase fluid flow and mass transfer characteristics (turbulent intensity, mass transfer rate, slag-steel interfacial area, flow patterns, etc.,) in gas-stirred ladles were quantitatively determined to ensure the proper increase in the ladle refining efficiency. It was revealed that by injecting finer bubbles as well as by properly increasing the gas flow rate and the slag layer thickness, the ladle refining efficiency can be enhanced significantly.

Gaussian Curvature as an Identifier of Shell Rigidity

NASA Astrophysics Data System (ADS)

Harutyunyan, Davit

2017-11-01

In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shell for zero or periodic Dirichlet, Neumann, and Robin type boundary conditions. We prove that if the Gaussian curvature is positive, then the optimal constant in the first Korn inequality scales like h, and if the Gaussian curvature is negative, then the Korn constant scales like h 4/3, where h is the thickness of the shell. These results have a classical flavour in continuum mechanics, in particular shell theory. The Korn first inequalities are the linear version of the famous geometric rigidity estimate by Friesecke et al. for plates in Arch Ration Mech Anal 180(2):183-236, 2006 (where they show that the Korn constant in the nonlinear Korn's first inequality scales like h 2), extended to shells with nonzero curvature. We also recover the uniform Korn-Poincaré inequality proven for "boundary-less" shells by Lewicka and Müller in Annales de l'Institute Henri Poincare (C) Non Linear Anal 28(3):443-469, 2011 in the setting of our problem. The new estimates can also be applied to find the scaling law for the critical buckling load of the shell under in-plane loads as well as to derive energy scaling laws in the pre-buckled regime. The exponents 1 and 4/3 in the present work appear for the first time in any sharp geometric rigidity estimate.

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

NASA Astrophysics Data System (ADS)

Paimushin, V. N.

2017-11-01

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

Imperfection sensitivity of pressured buckling of biopolymer spherical shells

NASA Astrophysics Data System (ADS)

Zhang, Lei; Ru, C. Q.

2016-06-01

Imperfection sensitivity is essential for mechanical behavior of biopolymer shells [such as ultrasound contrast agents (UCAs) and spherical viruses] characterized by high geometric heterogeneity. In this work, an imperfection sensitivity analysis is conducted based on a refined shell model recently developed for spherical biopolymer shells of high structural heterogeneity and thickness nonuniformity. The influence of related parameters (including the ratio of radius to average shell thickness, the ratio of transverse shear modulus to in-plane shear modulus, and the ratio of effective bending thickness to average shell thickness) on imperfection sensitivity is examined for pressured buckling. Our results show that the ratio of effective bending thickness to average shell thickness has a major effect on the imperfection sensitivity, while the effect of the ratio of transverse shear modulus to in-plane shear modulus is usually negligible. For example, with physically realistic parameters for typical imperfect spherical biopolymer shells, the present model predicts that actual maximum external pressure could be reduced to as low as 60% of that of a perfect UCA spherical shell or 55%-65% of that of a perfect spherical virus shell, respectively. The moderate imperfection sensitivity of spherical biopolymer shells with physically realistic imperfection is largely attributed to the fact that biopolymer shells are relatively thicker (defined by smaller radius-to-thickness ratio) and therefore practically realistic imperfection amplitude normalized by thickness is very small as compared to that of classical elastic thin shells which have much larger radius-to-thickness ratio.

Euler and His Contribution Number Theory

ERIC Educational Resources Information Center

Len, Amy; Scott, Paul

2004-01-01

Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…

CFD validation needs for advanced concepts at Northrop Corporation

NASA Technical Reports Server (NTRS)

George, Michael W.

1987-01-01

Information is given in viewgraph form on the Computational Fluid Dynamics (CFD) Workshop held July 14 - 16, 1987. Topics covered include the philosophy of CFD validation, current validation efforts, the wing-body-tail Euler code, F-20 Euler simulated oil flow, and Euler Navier-Stokes code validation for 2D and 3D nozzle afterbody applications.

The small length scale effect for a non-local cantilever beam: a paradox solved.

PubMed

Challamel, N; Wang, C M

2008-08-27

Non-local continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with microstructures or nanostructures. This paper presents some simplified non-local elastic beam models, for the bending analyses of small scale rods. Integral-type or gradient non-local models abandon the classical assumption of locality, and admit that stress depends not only on the strain value at that point but also on the strain values of all points on the body. There is a paradox still unresolved at this stage: some bending solutions of integral-based non-local elastic beams have been found to be identical to the classical (local) solution, i.e. the small scale effect is not present at all. One example is the Euler-Bernoulli cantilever nanobeam model with a point load which has application in microelectromechanical systems and nanoelectromechanical systems as an actuator. In this paper, it will be shown that this paradox may be overcome with a gradient elastic model as well as an integral non-local elastic model that is based on combining the local and the non-local curvatures in the constitutive elastic relation. The latter model comprises the classical gradient model and Eringen's integral model, and its application produces small length scale terms in the non-local elastic cantilever beam solution.

Determination of regional Euler pole parameters for Eastern Austria

NASA Astrophysics Data System (ADS)

Umnig, Elke; Weber, Robert; Schartner, Matthias; Brueckl, Ewald

2017-04-01

The horizontal motion of lithospheric plates can be described as rotations around a rotation axes through the Earth's center. The two possible points where this axes intersects the surface of the Earth are called Euler poles. The rotation is expressed by the Euler parameters in terms of angular velocities together with the latitude and longitude of the Euler pole. Euler parameters were calculated from GPS data for a study area in Eastern Austria. The observation network is located along the Mur-Mürz Valley and the Vienna Basin. This zone is part of the Vienna Transfer Fault, which is the major fault system between the Eastern Alps and the Carpathians. The project ALPAACT (seismological and geodetic monitoring of ALpine-PAnnonian ACtive Tectonics) investigated intra plate tectonic movements within the Austrian part in order to estimate the seismic hazard. Precise site coordinate time series established from processing 5 years of GPS observations are available for the regional network spanning the years from 2010.0 to 2015.0. Station velocities with respect to the global reference frame ITRF2008 have been computed for 23 sites. The common Euler vector was estimated on base of a subset of reliable site velocities, for stations directly located within the area of interest. In a further step a geokinematic interpretation shall be carried out. Therefore site motions with respect to the Eurasian Plate are requested. To obtain this motion field different variants are conceivable. In a simple approach the mean ITRF2008 velocity of IGS site GRAZ can be adopted as Eurasian rotational velocity. An improved alternative is to calculate site-specific velocity differences between the Euler rotation and the individual site velocities. In this poster presentation the Euler parameters, the residual motion field as well as first geokinematic interpretation results are presented.

High intensity acoustic tests of a thermally stressed aluminum plate in TAFA

NASA Technical Reports Server (NTRS)

Ng, Chung Fai; Clevenson, Sherman A.

1989-01-01

An investigation was conducted in the Thermal Acoustic Fatigue Apparatus at the Langley Research Center to study the acoustically excited random motion of an aluminum plate which is buckled due to thermal stresses. The thermal buckling displacements were measured and compared with theory. The general trends of the changes in resonances frequencies and random responses of the plate agree with previous theoretical prediction and experimental results for a mechanically buckled plate.

Torsion Tests of Stiffened Circular Cylinders

NASA Technical Reports Server (NTRS)

Moore, R L; Wescoat, C

1944-01-01

The design of curved sheet panels to resist shear involves a consideration of several factors: the buckling resistance of the sheet, the stress at which buckling becomes permanent, and the strength which may be developed beyond the buckling limit by tension-field action. Although some experimental as well as theoretical work has been done on the buckling and tension-field phases of this problem, neither of these types of action appears to be very well understood. The problem is of sufficient importance from the standpoint of aircraft design, it is believed, to warrant further experimental investigation. This report presents the results of the first series of torsion tests of stiffened circular cylinders to be completed in connection with this study at Aluminum Research Laboratories. (author)

Electric field effects on the optical properties of buckled GaAs monolayer

NASA Astrophysics Data System (ADS)

Bahuguna, Bhagwati Prasad; Saini, L. K.; Sharma, Rajesh O.

2018-04-01

Buckled GaAs monolayer has a direct band gap semiconductor with energy gap of 1.31 eV in the absence of electric field. When we applied transverse electric field, the value of band gap decreases with increasing of electric field strength. In our previous work [1], it is observed that the buckled GaAs monolayer becomes metallic at 1.3 V/Å. In the present work, we investigate the optical properties such as photon energy-dependent dielectric functions, extinction coefficient, refractive index, absorption spectrum and reflectivity of buckled GaAs monolayer in the semiconducting phase i.e. absence of external electric field and metallic phase i.e. presence of external electric field using density functional theory.

Redeposition of a straight-sided buckle under pressure.

PubMed

Colin, Jérôme; Coupeau, Christophe; Durinck, Julien; Cimetière, Alain; Grilhé, Jean

2014-03-01

The unilateral buckling of a stressed thin film on a substrate has been investigated theoretically in the framework of the Föppl-von Kármán theory of thin plates when an increasing overpressure is considered onto the upper free surface of the film. It is found that, depending on the initial stress in the film and overpressure, two scenarios of evolution may occur. The snap-through of the one-dimensional buckle leading to the full redeposition should take place for low values of the initial stress. When the initial stress exceeds a critical value, a partial redeposition of the buckle should proceed as the overpressure increases. A snap-through while the redeposition mechanism has taken place should also occur for higher values of the overpressure.

Large Area Silicon Sheet by EFG

NASA Technical Reports Server (NTRS)

Wald, F. V.

1979-01-01

Displaced die concepts were explored along with some initial work on buckle characterization. Convective impurity redistribution was further studied. Growth from single cartridges was continued to create a quality baseline to allow comparison of the results with those in the upcoming multiple run and to choose the most appropriate die design. Fabrication and assembly work on the actual five ribbon furnace continued. Progress was made toward the development of the video optical system for edge position and meniscus height control. In preparation for a detailed program, designed to explore the buckling problem, ribbon guidance in the machine was improved. Buckle free, full width ribbon was grown under stable conditions without a cold shoe, an achievement essential to finally arrive at quantitative correlations between growth conditions and buckle formation.

Leonhard Euler and the mechanics of rigid bodies

NASA Astrophysics Data System (ADS)

Marquina, J. E.; Marquina, M. L.; Marquina, V.; Hernández-Gómez, J. J.

2017-01-01

In this work we present the original ideas and the construction of the rigid bodies theory realised by Leonhard Euler between 1738 and 1775. The number of treatises written by Euler on this subject is enormous, including the most notorious Scientia Navalis (1749), Decouverte d’un noveau principe de mecanique (1752), Du mouvement de rotation des corps solides autour d’un axe variable (1765), Theoria motus corporum solidorum seu rigidorum (1765) and Nova methodus motu corporum rigidorum determinandi (1776), in which he developed the ideas of the instantaneous rotation axis, the so-called Euler equations and angles, the components of what is now known as the inertia tensor, the principal axes of inertia, and, finally, the generalisation of the translation and rotation movement equations for any system. Euler, the man who ‘put most of mechanics into its modern form’ (Truesdell 1968 Essays in the History of Mechanics (Berlin: Springer) p 106).

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

NASA Astrophysics Data System (ADS)

Drivas, Theodore D.; Eyink, Gregory L.

2017-12-01

We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also vanish for such Euler solutions, unless the same singularity conditions are satisfied. It is shown furthermore that strong limits of solutions of compressible Navier-Stokes equations that are bounded and exhibit anomalous dissipation are weak Euler solutions. These inviscid limit solutions have non-negative anomalous entropy production and kinetic energy dissipation, with both vanishing when solutions are above the critical degree of Besov regularity. Stationary, planar shocks in Euclidean space with an ideal-gas equation of state provide simple examples that satisfy the conditions of our theorems and which demonstrate sharpness of our L 3-based conditions. These conditions involve space-time Besov regularity, but we show that they are satisfied by Euler solutions that possess similar space regularity uniformly in time.

Localization instability and the origin of regularly- spaced faults in planetary lithospheres

NASA Astrophysics Data System (ADS)

Montesi, Laurent Gilbert Joseph

2002-10-01

Brittle deformation is not distributed uniformly in planetary lithospheres but is instead localized on faults and ductile shear zones. In some regions such as the Central Indian Basin or martian ridged plains, localized shear zones display a characteristic spacing. This pattern can constrain the mechanical structure of the lithosphere if a model that includes the development of localized shear zones and their interaction with the non- localizing levels of the lithosphere is available. I construct such a model by modifying the buckling analysis of a mechanically-stratified lithosphere idealization, by allowing for rheologies that have a tendency to localize. The stability of a rheological system against localization is indicated by its effective stress exponent, ne. That quantity must be negative for the material to have a tendency to localize. I show that a material deforming brittly or by frictional sliding has ne < 0. Localization by shear heating or grain size feedback in the ductile field requires significant deviations from non-localized deformation conditions. The buckling analysis idealizes the lithosphere as a series of horizontal layers of different mechanical properties. When this model is subjected to horizontal extension or compression, infinitesimal perturbation of its interfaces grow at a rate that depends on their wavelength. Two superposed instabilities develop if ne < 0 in a layer overlying a non-localizing substratum. One is the classical buckling/necking instability. The other gives rise to regularly-spaced localized shear zones, with a spacing proportional to the thickness of the localizing layer, and dependent on n e. I call that second instability the localization instability. Using the localization instability, the depth to which fault penetrate in the Indian Ocean and in martian ridged plains can be constrained from the ridge spacing. The result are consistent with earthquake data in the Indian Ocean and radiogenic heat production on Mars. It is therefore possible that the localization instability exerts a certain control on the formation of fault patterns in planetary lithospheres. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253- 1690.)

Uniaxial, Pure Bending, and Column Buckling Experiments on Superelastic NiTi Rods and Tubes

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

Watkins, Ryan T.; Reedlunn, Benjamin; Daly, Samantha

Many existing shape memory alloy (SMA) devices consist of slender beams and frames. To better understand SMA beam behavior, we experimentally examined the isothermal, room temperature response of superelastic NiTi rods and tubes, of similar outer diameters, subjected to four different modes of loading. Pure tension, pure compression, and pure bending experiments were first performed to establish and compare the baseline uniaxial and bending behaviors of rods and tubes. Column buckling experiments were then performed on rod and tube columns of several slenderness ratios to investigate their mechanical responses, phase transformation kinetics under combined uniaxial and bending deformation, and themore » interaction between material and structural instabilities. In all experiments, stereo digital image correlation measured local displacement fields in order to capture phenomena such as strain localization and propagating phase boundaries. Superelastic mechanical behavior and the nature of stress-induced phase transformation were found to be strongly affected by specimen geometry and the deformation mode. Under uniaxial tension, both the rod and tube had well-defined loading and unloading plateaus in their superelastic responses, during which stress-induced phase transformation propagated along the length of the specimen in the form of a high/low strain front. Due to the dependence of strain localization on kinematic compatibility, the high/low strain front morphologies differed between the rod and tube: for the rod, the high/low strain front consisted of a diffuse “neck”, while the high/low strain front in the tube consisted of distinct, criss-crossing “fingers.” During uniaxial compression, both cross-sectional forms exhibited higher transformation stresses and smaller transformation strains than uniaxial tension, highlighting the now well-known tension-compression asymmetry of SMAs. Additionally, phase transformation localization and propagation were absent under compressive loading. During pure bending, the moment-curvature response of both forms exhibited plateaus and strain localization during forward and reverse transformations. Rod specimens developed localized, high-curvature regions that propagated along the specimen axis and caused shear strain near the high/low curvature interface; whereas, the tube specimens exhibited finger/wedge-like high strain regions over the tensile side of the tube which caused nonlinear strain profiles through the thickness of the specimen that did not propagate. Here, it was therefore found that classical beam theory assumptions did not hold in the presence of phase transformation localization (although, the assumptions did hold on average for the tube). During column buckling, the structures were loaded into the post-buckling regime yet recovered nearly-straight forms upon unloading. Strain localization was observed only for high aspect ratio (slender) tubes, but the mechanical responses were similar to that of rods of the same slenderness ratio. Also, an interesting “unbuckling” phenomenon was discovered in certain low aspect ratio (stout) columns, where late post-buckling straightening was observed despite continuous monotonic loading. Thus, these behaviors are some of the challenging phenomena which must be captured when developing SMA constitutive models and executing structural simulations.« less

Uniaxial, Pure Bending, and Column Buckling Experiments on Superelastic NiTi Rods and Tubes

DOE PAGES

Watkins, Ryan T.; Reedlunn, Benjamin; Daly, Samantha; ...

2018-03-23

Many existing shape memory alloy (SMA) devices consist of slender beams and frames. To better understand SMA beam behavior, we experimentally examined the isothermal, room temperature response of superelastic NiTi rods and tubes, of similar outer diameters, subjected to four different modes of loading. Pure tension, pure compression, and pure bending experiments were first performed to establish and compare the baseline uniaxial and bending behaviors of rods and tubes. Column buckling experiments were then performed on rod and tube columns of several slenderness ratios to investigate their mechanical responses, phase transformation kinetics under combined uniaxial and bending deformation, and themore » interaction between material and structural instabilities. In all experiments, stereo digital image correlation measured local displacement fields in order to capture phenomena such as strain localization and propagating phase boundaries. Superelastic mechanical behavior and the nature of stress-induced phase transformation were found to be strongly affected by specimen geometry and the deformation mode. Under uniaxial tension, both the rod and tube had well-defined loading and unloading plateaus in their superelastic responses, during which stress-induced phase transformation propagated along the length of the specimen in the form of a high/low strain front. Due to the dependence of strain localization on kinematic compatibility, the high/low strain front morphologies differed between the rod and tube: for the rod, the high/low strain front consisted of a diffuse “neck”, while the high/low strain front in the tube consisted of distinct, criss-crossing “fingers.” During uniaxial compression, both cross-sectional forms exhibited higher transformation stresses and smaller transformation strains than uniaxial tension, highlighting the now well-known tension-compression asymmetry of SMAs. Additionally, phase transformation localization and propagation were absent under compressive loading. During pure bending, the moment-curvature response of both forms exhibited plateaus and strain localization during forward and reverse transformations. Rod specimens developed localized, high-curvature regions that propagated along the specimen axis and caused shear strain near the high/low curvature interface; whereas, the tube specimens exhibited finger/wedge-like high strain regions over the tensile side of the tube which caused nonlinear strain profiles through the thickness of the specimen that did not propagate. Here, it was therefore found that classical beam theory assumptions did not hold in the presence of phase transformation localization (although, the assumptions did hold on average for the tube). During column buckling, the structures were loaded into the post-buckling regime yet recovered nearly-straight forms upon unloading. Strain localization was observed only for high aspect ratio (slender) tubes, but the mechanical responses were similar to that of rods of the same slenderness ratio. Also, an interesting “unbuckling” phenomenon was discovered in certain low aspect ratio (stout) columns, where late post-buckling straightening was observed despite continuous monotonic loading. Thus, these behaviors are some of the challenging phenomena which must be captured when developing SMA constitutive models and executing structural simulations.« less

The importance of Leonhard Euler's discoveries in the field of shipbuilding for the scientific evolution of academician A. N. Krylov

NASA Astrophysics Data System (ADS)

Sharkov, N. A.; Sharkova, O. A.

2018-05-01

The paper identifies the importance of the Leonhard Euler's discoveries in the field of shipbuilding for the scientific evolution of academician A. N. Krylov and for the modern knowledge in survivability and safety of ships. The works by Leonard Euler "Marine Science" and "The Moon Motion New Theory" are discussed.

On the statistical mechanics of the 2D stochastic Euler equation

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

The dynamics of vortices and large scale structures is qualitatively very different in two dimensional flows compared to its three dimensional counterparts, due to the presence of multiple integrals of motion. These are believed to be responsible for a variety of phenomena observed in Euler flow such as the formation of large scale coherent structures, the existence of meta-stable states and random abrupt changes in the topology of the flow. In this paper we study stochastic dynamics of the finite dimensional approximation of the 2D Euler flow based on Lie algebra su(N) which preserves all integrals of motion. In particular, we exploit rich algebraic structure responsible for the existence of Euler's conservation laws to calculate the invariant measures and explore their properties and also study the approach to equilibrium. Unexpectedly, we find deep connections between equilibrium measures of finite dimensional su(N) truncations of the stochastic Euler equations and random matrix models. Our work can be regarded as a preparation for addressing the questions of large scale structures, meta-stability and the dynamics of random transitions between different flow topologies in stochastic 2D Euler flows.

3D GIS spatial operation based on extended Euler operators

NASA Astrophysics Data System (ADS)

Xu, Hongbo; Lu, Guonian; Sheng, Yehua; Zhou, Liangchen; Guo, Fei; Shang, Zuoyan; Wang, Jing

2008-10-01

The implementation of 3 dimensions spatial operations, based on certain data structure, has a lack of universality and is not able to treat with non-manifold cases, at present. ISO/DIS 19107 standard just presents the definition of Boolean operators and set operators for topological relationship query, and OGC GeoXACML gives formal definitions for several set functions without implementation detail. Aiming at these problems, based mathematical foundation on cell complex theory, supported by non-manifold data structure and using relevant research in the field of non-manifold geometry modeling for reference, firstly, this paper according to non-manifold Euler-Poincaré formula constructs 6 extended Euler operators and inverse operators to carry out creating, updating and deleting 3D spatial elements, as well as several pairs of supplementary Euler operators to convenient for implementing advanced functions. Secondly, we change topological element operation sequence of Boolean operation and set operation as well as set functions defined in GeoXACML into combination of extended Euler operators, which separates the upper functions and lower data structure. Lastly, we develop underground 3D GIS prototype system, in which practicability and credibility of extended Euler operators faced to 3D GIS presented by this paper are validated.

Euler force actuation mechanism for siphon valving in compact disk-like microfluidic chips

PubMed Central

Deng, Yongbo; Fan, Jianhua; Zhou, Song; Zhou, Teng; Wu, Junfeng; Li, Yin; Liu, Zhenyu; Xuan, Ming; Wu, Yihui

2014-01-01

Based on the Euler force induced by the acceleration of compact disk (CD)-like microfluidic chip, this paper presents a novel actuation mechanism for siphon valving. At the preliminary stage of acceleration, the Euler force in the tangential direction of CD-like chip takes the primary place compared with the centrifugal force to function as the actuation of the flow, which fills the siphon and actuates the siphon valving. The Euler force actuation mechanism is demonstrated by the numerical solution of the phase-field based mathematical model for the flow in siphon valve. In addition, experimental validation is implemented in the polymethylmethacrylate-based CD-like microfluidic chip manufactured using CO2 laser engraving technique. To prove the application of the proposed Euler force actuation mechanism, whole blood separation and plasma extraction has been conducted using the Euler force actuated siphon valving. The newly introduced actuation mechanism overcomes the dependence on hydrophilic capillary filling of siphon by avoiding external manipulation or surface treatments of polymeric material. The sacrifice for highly integrated processing in pneumatic pumping technique is also prevented by excluding the volume-occupied compressed air chamber. PMID:24753736

Transverse vibration of Bernoulli Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

NASA Astrophysics Data System (ADS)

Maiz, Santiago; Bambill, Diana V.; Rossit, Carlos A.; Laura, P. A. A.

2007-06-01

The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of the machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. An exact solution for the title problem is obtained in closed-form fashion, considering general boundary conditions by means of translational and rotatory springs at both ends. The model allows to analyze the influence of the masses and their rotatory inertia on the dynamic behavior of beams with all the classic boundary conditions, and also, as particular cases, to determine the frequencies of continuous beams.

"Cosmomorphistic geometry" in the unconscious geometry of Johannes Kepler

NASA Astrophysics Data System (ADS)

Adam, Adolf

Some mathematical aspects of the Music theory by Johannes Kepler are discussed, paying a special attention to the book "De harmonice mundi". Other scientists interested in Music theory are mentioned throughout the paper: The Pythagorean school, Klaudios Ptolemaios, Leonard Euler, Gottfried Wilhelm Leibniz, Christian von Goldbach, Hermann Ludwig Ferdinand von Helmholz, Karl Friedrich Gauss. The relation with the ancient chinese schools of cosmography has been discussed: From the the Pythagorean to the ancient Chinese schools of cosmography we find arithmo-geometrical applications of numbers which are emblematic, hold meaning or represent the essence of things, the author writes. It was Johannes Kepler who taught us this "transconstructive method" of forming classical and ancient begginings of structuralistic thinking into a system from which deductions can readily be made.

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

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

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

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

Kozlov, I K

In this paper we study topological properties of an integrable case for Euler's equations on the Lie algebra so(4), which can be regarded as an analogue of the classical Kovalevskaya case in rigid body dynamics. In particular, for all values of the parameters of the system under consideration, the bifurcation diagrams of the momentum mapping are constructed, the types of critical points of rank 0 are determined, the bifurcations of Liouville tori are described, and the loop molecules are computed for all singular points of the bifurcation diagrams. It follows from the obtained results that some topological properties of the classicalmore » Kovalevskaya case can be obtained from the corresponding properties of the considered integrable case on the Lie algebra so(4) by taking a natural limit. Bibliography: 21 titles.« less

A free boundary approach to the Rosensweig instability of ferrofluids

NASA Astrophysics Data System (ADS)

Parini, Enea; Stylianou, Athanasios

2018-04-01

We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid undergoing normal field instability. The starting point is the ferrohydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. These constitute the strong form for the Euler-Lagrange equations of a convex-concave functional, which we extend to include interfaces that are not necessarily graphs of functions. Saddle points are then found by iterating the direct method of the calculus of variations and applying classical results of convex analysis. For the existence part, we assume a general nonlinear magnetization law; for a linear law, we also show, via convex duality, that the saddle point is a constrained minimizer of the relevant energy functional.

Application of Finite Element Method of Numerical Modelling to Understand Toe Buckling Deformation in the Southern Alps of New Zealand.

NASA Astrophysics Data System (ADS)

Ridl, Romy; Bell, David; Villeneuve, Marlene

2017-04-01

Toe buckling deformation is a temporal product of induced stresses concentrated at the base of a slope. Prolonged induced stresses may lead to yielding of an anisotropic rock mass, either through rheological creep deformation (flexural toe buckling) or brittle failure (hinge buckling). Progressive deformation can lead to the breakout at the buckled toe and ultimately result in deep seated displacements on a mountain range scale, referred to as deep seated gravitational slope deformation (DSGSD). DSGSD can have a considerable impact on civil infrastructure and should be well understood for hazard identification, to inform civil engineering design and for resource management purposes. Toe buckling deformation was identified beneath the basal sliding zone of three large (≥50 Mm3) landslides in the Cromwell Gorge, New Zealand. This area was subjected to extensive geotechnical investigations for the Clyde Hydropower Scheme. During these investigations seventeen major landslides were identified in the Cromwell Gorge and subsequently stabilised. The data from the landslide stabilisation project, including 26.7 km of boreholes and 9 km of tunnels, for the three landslides exhibiting toe buckling was made available for this study. This comprehensive database has enabled comparison and validation of numerical simulations carried out for the Cromwell Gorge. The application of numerical modelling has demonstrated that toe buckling within the Cromwell Gorge is a result of the combination of induced stresses acting on an anisotropic schistose rock mass. The induced stresses comprise: i) topographically-induced gravitational stresses parallel to the slope, associated with the evolution of the Cromwell Gorge from a relatively low relief surface to present day topography (1400 m deep valley), and ii) active far-field tectonic stresses associated with the obliquely convergent stress regime of the Australian-Pacific continent plate boundary. Finite Element Method (FEM) numerical models were used to model the anisotropic nature of the schist rock mass, and a sequential unloading method was adopted to simulate valley evolution. Far-field tectonics were incorporated into the model by comparing topographically induced gravitational stresses with in situ field stress measurements. The results of sensitivity analyses demonstrate that the dominant parameters governing toe buckling deformation in the Cromwell Gorge are a function of the anisotropy of the schist (foliation orientation and stiffness), and the intersection of the two induced stress fields near the base of the slopes.

Gain-scheduled {{\\mathscr{H}}}_{\\infty } buckling control of a circular beam-column subject to time-varying axial loads

NASA Astrophysics Data System (ADS)

Schaeffner, Maximilian; Platz, Roland

2018-06-01

For slender beam-columns loaded by axial compressive forces, active buckling control provides a possibility to increase the maximum bearable axial load above that of a purely passive structure. In this paper, an approach for gain-scheduled {{\\mathscr{H}}}∞ buckling control of a slender beam-column with circular cross-section subject to time-varying axial loads is investigated experimentally. Piezo-elastic supports with integrated piezoelectric stack actuators at the beam-column ends allow an active stabilization in arbitrary lateral directions. The axial loads on the beam-column influence its lateral dynamic behavior and, eventually, cause the beam-column to buckle. A reduced modal model of the beam-column subject to axial loads including the dynamics of the electrical components is set up and calibrated with experimental data. Particularly, the linear parameter-varying open-loop plant is used to design a model-based gain-scheduled {{\\mathscr{H}}}∞ buckling control that is implemented in an experimental test setup. The beam-column is loaded by ramp- and step-shaped time-varying axial compressive loads that result in a lateral deformation of the beam-column due to imperfections, such as predeformation, eccentric loading or clamping moments. The lateral deformations and the maximum bearable loads of the beam-column are analyzed and compared for the beam-column with and without gain-scheduled {{\\mathscr{H}}}∞ buckling control or, respectively, active and passive configuration. With the proposed gain-scheduled {{\\mathscr{H}}}∞ buckling control it is possible to increase the maximum bearable load of the active beam-column by 19% for ramp-shaped axial loads and to significantly reduce the beam-column deformations for step-shaped axial loads compared to the passive structure.

Lithospheric buckling and intra-arc stresses: A mechanism for arc segmentation

NASA Technical Reports Server (NTRS)

Nelson, Kerri L.

1989-01-01

Comparison of segment development of a number of arcs has shown that consistent relationships between segmentation, volcanism and variable stresses exists. Researchers successfully modeled these relationships using the conceptual model of lithospheric buckling of Yamaoka et al. (1986; 1987). Lithosphere buckling (deformation) provides the needed mechanism to explain segmentation phenomenon; offsets in volcanic fronts, distribution of calderas within segments, variable segment stresses and the chemical diversity seen between segment boundary and segment interior magmas.

Influence of Scleral Buckling Surgery with Encircling Band on Subfoveal Choroidal Thickness in Long-Term Observations

PubMed Central

Laudańska-Olszewska, Iwona; Gozdek, Piotr; Maroszyński, Mariusz; Amon, Michael

2013-01-01

Purpose. The aim of this study is the presentation of subfoveal choroidal thickness with enhanced depth imaging spectral-domain optical coherence tomography (EDI-OCT) several months after scleral buckling with encircling band surgery. Methods. 48 patients who underwent scleral buckling with encircling band surgery for unilateral rhegmatogenous retinal detachment were included in the retrospective observational study. The mean time from scleral buckling surgery to the final EDI-OCT examination was 22±6.7 months. We compare choroidal thickness between operated and fellow eyes. Results. In all patients, the macula was detached before the surgery. The subfoveal choroidal thickness in 48 treated eyes was 260.9±45.8 µm (range 155–383 µm) and in the fellow eyes was 217.5±36.7 µm (range 98–326 µm). The subfoveal choroidal thickness of eyes after scleral buckling surgery in long-term EDI-OCT examination was significantly thicker (P<0.001) than in fellow eyes. Conclusions. The subfoveal choroid in eyes undergoing encircling band surgery was significantly thicker than in fellow eyes. We suspect that this may be the result of reduced choroidal blood flow. It also seems that the width and size of the material used in scleral buckling surgery may affect a change in the choroid circulation and increase subfoveal choroidal thickness. PMID:23841077

Mathematical modeling and full-scale shaking table tests for multi-curve buckling restrained braces

NASA Astrophysics Data System (ADS)

Tsai, C. S.; Lin, Yungchang; Chen, Wenshin; Su, H. C.

2009-09-01

Buckling restrained braces (BRBs) have been widely applied in seismic mitigation since they were introduced in the 1970s. However, traditional BRBs have several disadvantages caused by using a steel tube to envelope the mortar to prevent the core plate from buckling, such as: complex interfaces between the materials used, uncertain precision, and time consumption during the manufacturing processes. In this study, a new device called the multi-curve buckling restrained brace (MC-BRB) is proposed to overcome these disadvantages. The new device consists of a core plate with multiple neck portions assembled to form multiple energy dissipation segments, and the enlarged segment, lateral support elements and constraining elements to prevent the BRB from buckling. The enlarged segment located in the middle of the core plate can be welded to the lateral support and constraining elements to increase buckling resistance and to prevent them from sliding during earthquakes. Component tests and a series of shaking table tests on a full-scale steel structure equipped with MC-BRBs were carried out to investigate the behavior and capability of this new BRB design for seismic mitigation. The experimental results illustrate that the MC-BRB possesses a stable mechanical behavior under cyclic loadings and provides good protection to structures during earthquakes. Also, a mathematical model has been developed to simulate the mechanical characteristics of BRBs.

"Astronomica" in the Correspondence between Leonhard Euler and Daniel Bernoull (German Title: "Astronomica" im Briefwechsel zwischen Leonhard Euler und Daniel Bernoulli)

NASA Astrophysics Data System (ADS)

Verdun, Andreas

2010-12-01

The Euler Commission of the Swiss Academy of Sciences intends to terminate the edition of Leonhard Euler's works in the next year 2011 after nearly one hundred years since the beginning of the editorial works. These works include, e.g., Volume 3 of the Series quarta A which will contain the correspondence between Leonhard Euler (1707-1783) and Daniel Bernoulli (1700-1783) and which is currently being edited by Dr. Emil A. Fellmann (Basel) and Prof. Dr. Gleb K. Mikhailov (Moscow). This correspondence contains more than hundred letters, principally from Daniel Bernoulli to Euler. Parts of this correspondence were published uncommented already in 1843. It is astonishing that, apart from mathematics and physics (mainly mechanics and hydrodynamics), many topics addressed concern astronomy. The major part of the preserved correspondence between Euler and Daniel Bernoulli, in which astronomical themes are discussed, concerns celestial mechanics as the dominant discipline of theoretical astronomy of the eighteenth century. It was triggered and coined mainly by the prize questions of the Paris Academy of Science. In more than two thirds of the letters current problems and questions concerning celestial mechanics of that time are treated, focusing on the lunar theory and the great inequality in the motions of Jupiter and Saturn as special applications of the three body problem. In the remaining letters, problems concerning spherical astronomy are solved and attempts are made to explain certain phenomena in the field of "cosmic physics" concerning astronomical observations.

Buckling shells are also swimmers

NASA Astrophysics Data System (ADS)

Quilliet, Catherine; Dyfcom Bubbleboost Team

We present an experimental and numerical study on the displacement of shells undergoing deformations in a fluid. When submitted to cycles of pressure difference between outside and inside, a shell buckles and debuckles, showing a succession of shapes and a dynamics that are different during the two phases. Hence such objects are likely to swim, including at low Reynolds (microscopic scale). We studied the swimming of buckling/debuckling shells at macroscopic scale using different approaches (force quantization, shape recording, displacement along a frictionless rail, study of external flow using PIV), and showed that inertia plays a role in propulsion, even in situations where dimensionless numbers correspond also to microswimmers in water. Different fluid viscosities were explored, showing an optimum for the displacement. Interestingly, the most favorable cases lead to displacements in the same direction and sense during both motor stroke (buckling phase) and recovery stroke (de-buckling phase). This work opens the route for the synthesis with high throughput of abusively simple synthetic swimmers, possibly gathered into nanorobots, actuated by a scalar field such as the pressure in echographic devices. Universite Grenoble Alpes, CNRS, European Research Council.

Finite Element Modeling of the Buckling Response of Sandwich Panels

NASA Technical Reports Server (NTRS)

Rose, Cheryl A.; Moore, David F.; Knight, Norman F., Jr.; Rankin, Charles C.

2002-01-01

A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.

Selective buckling via states of self-stress in topological metamaterials

PubMed Central

Paulose, Jayson; Meeussen, Anne S.; Vitelli, Vincenzo

2015-01-01

States of self-stress—tensions and compressions of structural elements that result in zero net forces—play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self-stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely hinged joints, they leave a distinct signature in the nonlinear buckling behavior of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices. PMID:26056303

Buckling Analysis of Angle-ply Composite and Sandwich Plates by Combination of Geometric Stiffness Matrix

NASA Astrophysics Data System (ADS)

Zhen, Wu; Wanji, Chen

2007-05-01

Buckling response of angle-ply laminated composite and sandwich plates are analyzed using the global-local higher order theory with combination of geometric stiffness matrix in this paper. This global-local theory completely fulfills the free surface conditions and the displacement and stress continuity conditions at interfaces. Moreover, the number of unknowns in this theory is independent of the number of layers in the laminate. Based on this global-local theory, a three-noded triangular element satisfying C1 continuity conditions has also been proposed. The bending part of this element is constructed from the concept of DKT element. In order to improve the accuracy of the analysis, a method of modified geometric stiffness matrix has been introduced. Numerical results show that the present theory not only computes accurately the buckling response of general laminated composite plates but also predicts the critical buckling loads of soft-core sandwiches. However, the global higher-order theories as well as first order theories might encounter some difficulties and overestimate the critical buckling loads for soft-core sandwich plates.

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.

Buckling behavior of origami unit cell facets under compressive loads

NASA Astrophysics Data System (ADS)

Kshad, Mohamed Ali Emhmed; Naguib, Hani E.

2018-03-01

Origami structures as cores for sandwich structures are designed to withstand the compressive loads and to dissipate compressive energy. The deformation of the origami panels and the unit cell facets are the primary factors behind the compressive energy dissipation in origami structures. During the loading stage, the origami structures deform through the folding and unfolding process of the unit cell facets, and also through the plastic deformation of the facets. This work presents a numerical study of the buckling behavior of different origami unit cell elements under compressive loading. The studied origami configurations were Miura and Ron-Resch-like origami structures. Finite element package was used to model the origami structures. The study investigated the buckling behavior of the unit cell facets of two types of origami structures Miura origami and Ron-Resch-Like origami structures. The simulation was conducted using ANSYS finite element software, in which the model of the unit cell represented by shell elements, and the eigenvalues buckling solver was used to predict the theoretical buckling of the unit cell elements.

Use of Buckling Instabilities in Micro Pumps, Valves, and Mixers

NASA Astrophysics Data System (ADS)

Tavakol, Behrouz; Chawan, Aschvin; Holmes, Douglas

2014-03-01

We use the buckling of thin, flexible plates for pumping fluids, controlling the flow rate, and mixing different media within a microfluidic channel. A dielectric elastomeric film with a confined geometry buckles out of the plane when exposed to an electric field. Solid or grease electrodes have traditionally been used as conductive materials to aid in voltage application to both sides of the film. In this work, we use an electrolytic fluid solution as the electrode to enable buckling at relatively low voltages, and to enhance the rate of deformation. We show that this mechanism can be implemented as a microvalve that controls flow rate, or as a micropump that operates over a range of frequencies. A similar mechanism can be used to aid diffusion between two adjacent laminar streams and improve mixing. These low-cost micropumps, microvalves, and micromixers rely on the reversible buckling of thin plates, are easily embeddable in a microfluidic chip, and can potentially be used in variety of applications to accurately control and manipulate fluid flow in a microchannel.

Thermocryogenic buckling and stress analyses of a partially filled cryogenic tank subjected to cylindrical strip heating

NASA Technical Reports Server (NTRS)

Ko, William L.

1994-01-01

Thermocryogenic buckling and stress analyses were conducted on a horizontally oriented cryogenic tank using the finite element method. The tank is a finite-length circular cylindrical shell with its two ends capped with hemispherical shells. The tank is subjected to cylindrical strip heating in the region above the liquid-cryogen fill level and to cryogenic cooling below the fill level (i.e., under thermocryogenic loading). The effects of cryogen fill level on the buckling temperature and thermocryogenic stress field were investigated in detail. Both the buckling temperature and stress magnitudes were relatively insensitive to the cryogen fill level. The buckling temperature, however, was quite sensitive to the radius-to-thickness ratio. A mechanical stress analysis of the tank also was conducted when the tank was under: (1) cryogen liquid pressure loading; (2) internal pressure loading; and (3) tank-wall inertia loading. Deformed shapes of the cryogenic tanks under different loading conditions were shown, and high-stress domains were mapped on the tank wall for the strain-gage installations. The accuracies of solutions from different finite element models were compared.

Buckling analysis of SMA bonded sandwich structure – using FEM

NASA Astrophysics Data System (ADS)

Katariya, Pankaj V.; Das, Arijit; Panda, Subrata K.

2018-03-01

Thermal buckling strength of smart sandwich composite structure (bonded with shape memory alloy; SMA) examined numerically via a higher-order finite element model in association with marching technique. The excess geometrical distortion of the structure under the elevated environment modeled through Green’s strain function whereas the material nonlinearity counted with the help of marching method. The system responses are computed numerically by solving the generalized eigenvalue equations via a customized MATLAB code. The comprehensive behaviour of the current finite element solutions (minimum buckling load parameter) is established by solving the adequate number of numerical examples including the given input parameter. The current numerical model is extended further to check the influence of various structural parameter of the sandwich panel on the buckling temperature including the SMA effect and reported in details.

Buckling analysis of non-prismatic columns based on modified vibration modes

NASA Astrophysics Data System (ADS)

Rahai, A. R.; Kazemi, S.

2008-10-01

In this paper, a new procedure is formulated for the buckling analysis of tapered column members. The calculation of the buckling loads was carried out by using modified vibrational mode shape (MVM) and energy method. The change of stiffness within a column is characterized by introducing a tapering index. It is shown that, the changes in the vibrational mode shapes of a tapered column can be represented by considering a linear combination of various modes of uniform-section columns. As a result, by making use of these modified mode shapes (MVM) and applying the principle of stationary total potential energy, the buckling load of tapered columns can be obtained. Several numerical examples on tapered columns demonstrate the accuracy and efficiency of the proposed analytical method.

Nonlocal elasticity and shear deformation effects on thermal buckling of a CNT embedded in a viscoelastic medium

NASA Astrophysics Data System (ADS)

Zenkour, A. M.

2018-05-01

The thermal buckling analysis of carbon nanotubes embedded in a visco-Pasternak's medium is investigated. The Eringen's nonlocal elasticity theory, in conjunction with the first-order Donnell's shell theory, is used for this purpose. The surrounding medium is considered as a three-parameter viscoelastic foundation model, Winkler-Pasternak's model as well as a viscous damping coefficient. The governing equilibrium equations are obtained and solved for carbon nanotubes subjected to different thermal and mechanical loads. The effects of nonlocal parameter, radius and length of nanotube, and the three foundation parameters on the thermal buckling of the nanotube are studied. Sample critical buckling loads are reported and graphically illustrated to check the validity of the present results and to present benchmarks for future comparisons.

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.

Energy harvesting from localized dynamic transitions in post-buckled elastic beams under quasi-static loading

NASA Astrophysics Data System (ADS)

Borchani, Wassim

The deployability of structural health monitoring self-powered sensors relies on their capability to harvest energy from signals being monitored. Many of the signals required to assess the structure condition are quasi-static events which limits the levels of power that can be extracted. Several vibration-based techniques have been proposed to increase the transferred level of power and broaden the harvester operating bandwidth. However, these techniques require vibration input excitations at frequencies higher than dominant structural response frequencies which makes them inefficient and not suitable for ambient quasi-static excitations. This research proposes a novel sensing and energy harvesting technique at low frequencies using mechanical energy concentrators and triggers. These mechanisms consist of axially-loaded bilaterally-constrained beams with attached piezoelectric energy harvesters. When the quasi-static axial load reaches a certain mechanical threshold, a sudden snap-through mode-switching occurs. These transitions excite the attached piezoelectric scavengers with high-rate input accelerations, generating then electric power. The main objectives are to understand and model the post-buckling behavior of bilaterally-constrained beams, control it by tailoring geometry and material properties of the buckled elements or stacking them into system assemblies, and finally characterize the energy harvesting and sensing capability of the system under quasi-static excitations. The fundamental principle relies on the following concept. Under axial load, a straight slender beam buckles in the first buckling mode. The increased transverse deformations from a buckled shape lead to contact interaction with the lateral boundaries. The contact interaction generates transverse forces that induce the development of higher order buckling configurations. Transitions between the buckled configurations occur not only during loading, but also unloading. In this work, the post-buckling response of the bilaterally constrained beam subjected to axial loading is investigated experimentally, numerically, and theoretically. The capability of the system to generate electric energy under quasi-static excitation is also assessed experimentally. The post-buckling behavior is reproducible under cyclic loadings and independent of the input loading frequency. The static and dynamic response of the beam is theoretically studied using an energy method. The model adequately predicts the beam geometry at every loading stage, including the flattening behavior just before the snap buckling transitions, the mode transition events and the released kinetic energy as well as accelerations of the beam during transitions. The buckling transitions generate high kinetic energy and acceleration spikes. However, the location of the maximum acceleration differs from one transition to another. Tuning the parameters of the system affects dramatically the accelerations generated during snap-through transitions. However, it does not affect the number and spacing between these events. To achieve better control of the system, multiple slender beams with different geometric and material properties are stacked in parallel configurations. The system allows then to control the spacing between energy bursts and reduce the energy leakage in electronic circuits. As an application example, the mechanical energy concentrators and triggers were integrated with a piezo-floating gate events sensor. This allowed for harvesting and recording of bursts and impulses of released energy at very low frequencies. The system can be calibrated to determine the number of times the magnitude of the input signal exceeded a mechanical threshold. The mechanism allows for frequency up-conversion from the low input frequency (in the order of mHz) to the natural frequency of the piezoelectric scavenger.

Splitting methods for low Mach number Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Dutt, Pravir; Gottlieb, David

1987-01-01

Examined are some splitting techniques for low Mach number Euler flows. Shortcomings of some of the proposed methods are pointed out and an explanation for their inadequacy suggested. A symmetric splitting for both the Euler and Navier-Stokes equations is then presented which removes the stiffness of these equations when the Mach number is small. The splitting is shown to be stable.

Nonlocal theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-09-01

New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

Improved Design Formulae for Buckling of Orthotropic Plates under Combined Loading

NASA Technical Reports Server (NTRS)

Weaver, Paul M.; Nemeth, Michael P.

2008-01-01

Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane bending. The interaction formulae are the results of detailed regression analysis of buckling data obtained from a very accurate Rayleigh-Ritz method.

Comparison between Euler and quaternion parametrization in UAV dynamics

NASA Astrophysics Data System (ADS)

Alaimo, A.; Artale, V.; Milazzo, C.; Ricciardello, A.

2013-10-01

The main topic addressed in this paper is a comparison between Euler parametrization and Quaternion one in the description of the dynamics of a Unmanned Aerial Vehicle assumed as a rigid body. In details Newton Euler equations are re-written in terms of quaternions due to the singularities that the Euler angles lead. This formulation not only avoids the gimbal lock but also allows a better performance in numerical implementation thanks to the linearity of quaternion algebra. This kind of analysis, proved by some numerical results presented, has a great importance due to the applicability of quaternion to drone control. Indeed, this latter requires a time response as quick as possible, in order to be reliable.

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.

Feasibility and Biomechanics of Multilevel Arthroplasty and Combined Cervical Arthrodesis and Arthroplasty.

PubMed

Safavi-Abbasi, Sam; Reyes, Phillip M; Abjornson, Celeste; Crawford, Neil R

2016-12-01

A new experimental protocol was applied utilizing a simplified postural control model. Multiple constructs were tested nondestructively by interconnecting segmental rods to screws. To investigate how posture and distribution of segmental angles under physiological loads are affected by combined cervical arthroplasty and fusion. Previous studies of biomechanics of multilevel arthroplasty have focused on range of motion and intradiscal pressure. No previous study has investigated postural changes and segmental angle distribution. In 7 human cadaveric C3-T1 specimens, C4-C5, C5-C6, and C6-C7 disks were replaced with ProDisc-C (Synthes). Combinations of fusion (f) adjacent to arthroplasty (A) were simulated at C4-C5, C5-C6, and C6-C7, respectively: fAA, AfA, AAf, ffA, fAf, Aff, fff. C3-C4 and C7-T1 remained intact. A compressive belt apparatus simulated normal muscle cocontraction and gravitational preload; C3-C4, C4-C5, C5-C6, C6-C7, and C7-T1 motions were tracked independently. Parameters studied were segmental postural compensation, neutral buckling, and shift in sagittal plane instantaneous axis of rotation (IAR). With one or more levels unfused, the arthroplasty levels preferentially moved toward upright posture before the intact levels. Neutral buckling was greatest for 3-level arthroplasty, less for 2-level arthroplasty, and least for 1-level arthroplasty. Among the three 1-level arthroplasty groups (ffA, fAf, Aff), arthroplasty at the caudalmost level resulted in significantly greater buckling than with arthroplasty rostralmost or at mid-segment (P<0.04, analysis of variance/Holm-Sidak). Although IAR location was related to buckling, this correlation did not reach significance (P=0.112). Arthroplasty levels provide the "path of least resistance," through which the initial motion is more likely to occur. The tendency for specimens to buckle under vertical compression became greater with more arthroplasty levels. Buckling appeared more severe with arthroplasty more caudal. Buckling only moderately correlated to shifts in IAR, meaning slight malpositioning of the devices would not necessarily cause buckling.

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.

Helicity within the vortex filament model.

PubMed

Hänninen, R; Hietala, N; Salman, H

2016-11-24

Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its key attribute as a quadratic invariant. By defining a spanwise vector to the vortex through the use of a Seifert framing, we are able to introduce twist and henceforth recover the key properties of helicity. We present several examples for calculating internal twist to illustrate why the centreline helicity alone will lead to ambiguous results if a twist contribution is not introduced. Our choice of the spanwise vector can be expressed in terms of the tangential component of velocity along the filament. Since the tangential velocity does not alter the configuration of the vortex at later times, we are able to recover a similar equation for the internal twist angle to that of classical vortex tubes. Our results allow us to explain how a quasi-classical limit of helicity emerges from helicity considerations for individual superfluid vortex filaments.

Helicity within the vortex filament model

PubMed Central

Hänninen, R.; Hietala, N.; Salman, H.

2016-01-01

Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its key attribute as a quadratic invariant. By defining a spanwise vector to the vortex through the use of a Seifert framing, we are able to introduce twist and henceforth recover the key properties of helicity. We present several examples for calculating internal twist to illustrate why the centreline helicity alone will lead to ambiguous results if a twist contribution is not introduced. Our choice of the spanwise vector can be expressed in terms of the tangential component of velocity along the filament. Since the tangential velocity does not alter the configuration of the vortex at later times, we are able to recover a similar equation for the internal twist angle to that of classical vortex tubes. Our results allow us to explain how a quasi-classical limit of helicity emerges from helicity considerations for individual superfluid vortex filaments. PMID:27883029

Unsteady transonic viscous-inviscid interaction using Euler and boundary-layer equations

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar; Whitfield, Dave

1989-01-01

The Euler code is used extensively for computation of transonic unsteady aerodynamics. The boundary layer code solves the 3-D, compressible, unsteady, mean flow kinetic energy integral boundary layer equations in the direct mode. Inviscid-viscous coupling is handled using porosity boundary conditions. Some of the advantages and disadvantages of using the Euler and boundary layer equations for investigating unsteady viscous-inviscid interaction is examined.

Energy harvesting from mastication forces via a smart tooth

NASA Astrophysics Data System (ADS)

Bani-Hani, Muath; Karami, M. Amin

2016-04-01

The batteries of the current pacing devices are relatively large and occupy over 60 percent of the size of pulse generators. Therefore, they cannot be placed in the subtle areas of human body. In this paper, the mastication force and the resulting tooth pressure are converted to electricity. The pressure energy can be converted to electricity by using the piezoelectric effect. The tooth crown is used as a power autonomous pulse generator. We refer to this envisioned pulse generator as the smart tooth. The smart tooth is in the form of a dental implant. A piezoelectric vibration energy harvester is designed and modeled for this purpose. The Piezoelectric based energy harvesters investigated and analyzed in this paper initially includes a single degree of freedom piezoelectric based stack energy harvester which utilizes a harvesting circuit employing the case of a purely resistive circuit. The next step is utilizing and investigating a bimorph piezoelectric beam which is integrated/embedded in the smart tooth implant. Mastication process causes the bimorph beam to buckle or return to unbuckled condition. The transitions results in vibration of the piezoelectric beam and thus generate energy. The power estimated by the two mechanisms is in the order of hundreds of microwatts. Both scenarios of the energy harvesters are analytically modeled. The exact analytical solution of the piezoelectric beam energy harvester with Euler-Bernoulli beam assumptions is presented. The electro-mechanical coupling and the geometric nonlinearities have been included in the model for the piezoelectric beam.

Buckling Test Results and Preliminary Test and Analysis Correlation from the 8-Foot-Diameter Orthogrid-Stiffened Cylinder Test Article TA02

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Waters, W. Allen, Jr.; Haynie, Waddy T.; Thornburgh, Robert P

2017-01-01

Results from the testing of cylinder test article SBKF-P2-CYL-TA02 (referred to herein as TA02) are presented. TA02 is an 8-foot-diameter (96-inches), 78.0-inch-long, aluminum-lithium (Al-Li), orthogrid-stiffened cylindrical shell similar to those used in current state-of-the-art launch-vehicle structures and was designed to exhibit global buckling when subjected to combined compression and bending loads. The testing was conducted at the Marshall Space Flight Center (MSFC), February 3-6, 2009, in support of the Shell Buckling Knockdown Factor Project (SBKF). The test was used to verify the performance of a newly constructed buckling test facility at MSFC and to verify the test article design and analysis approach used by the SBKF researchers.

The effect of ring distortions on buckling of blunt conical shells. [Viking mission aeroshell

NASA Technical Reports Server (NTRS)

Heard, W. L., Jr.; Anderson, M. S.; Stephens, W. B.

1975-01-01

A rigorous analytical study of cones stiffened by many thin-gage, open-section rings is presented. The results are compared with data previously obtained from uniform pressure tests of the Viking mission flight aeroshell and of the Viking structural prototype aeroshells. A conventional analysis, in which the rings are modeled as discrete rigid cross sections, is shown to lead to large, unconservative strength predictions. A more sophisticated technique of modeling the rings as shell branches leads to much more realistic strength predictions and more accurately predicts the failure modes. It is also shown that if a small initial imperfection proportional to the shape of the buckling mode is assumed, the critical buckling modes from analysis and test are in agreement. However, the reduction in buckling strength from the perfect-shell predictions is small.

Finite element predictions of active buckling control of stiffened panels

NASA Astrophysics Data System (ADS)

Thompson, Danniella M.; Griffin, O. H., Jr.

1993-04-01

Materials systems and structures that can respond 'intelligently' to their environment are currently being proposed and investigated. A series of finite element analyses was performed to investigate the potential for active buckling control of two different stiffened panels by embedded shape memory alloy (SMA) rods. Changes in the predicted buckling load increased with the magnitude of the actuation level for a given structural concept. Increasing the number of actuators for a given concept yielded greater predicted increases in buckling load. Considerable control authority was generated with a small number of actuators, with greater authority demonstrated for those structural concepts where the activated SMA rods could develop greater forces and moments on the structure. Relatively simple and inexpensive analyses were performed with standard finite elements to determine such information, indicating the viability of these types of models for design purposes.

Lower bound buckling loads for design of laminate composite cylinders

NASA Astrophysics Data System (ADS)

Croll, James G. A.; Wang, Hongtao

2017-01-01

Over a period of more than 45 years, an extensive research program has allowed a series of very simple propositions, relating to the safe design of shells experiencing imperfection sensitive buckling, to be recast in the form of a series of lemmas. These are briefly summarized and their practical use is illustrated in relation to the prediction of safe lower bounds to the imperfection sensitive buckling of axially loaded, fiber reinforced polymeric, laminated cylinders. With a fundamental aspect of the approach, sometimes referred to as the reduced stiffness method, being the delineation of the various shell membrane and bending stiffness (or perhaps more appropriately energy) components contributing to the buckling resistance, the method will be shown to also provide a powerful way of making rational design decisions to optimize the use of fiber reinforcement.

Experimental Research and Method for Calculation of 'Upsetting-with-Buckling' Load at the Impression-Free (Dieless) Preforming of Workpiece

NASA Astrophysics Data System (ADS)

Kukhar, Volodymir; Artiukh, Victor; Prysiazhnyi, Andrii; Pustovgar, Andrey

2018-03-01

This paper presents the results of experimental studies of load characteristic changes during the upsetting of high billets with the upsetting ratio (height to diameter ratio) from 3.0 to 6.0, which is followed by buckling. Such pass is an effective way of preforming the workpiece for production of forgings with a bended axis or dual forming, and belongs to impression-free (dieless) operation of bulk forming. Based on the experimental data analysis, an engineering method for calculation of workpiece pre-forming load as a maximum buckling force has been developed. The analysis of the obtained data confirmed the possibility of performing of this pre-forming operation on the main forging equipment, since the load of shaping by buckling does not exceed the load of the dieforging.

The conflicting role of buckled structure in phonon transport of 2D group-IV and group-V materials.

PubMed

Peng, Bo; Zhang, Dequan; Zhang, Hao; Shao, Hezhu; Ni, Gang; Zhu, Yongyuan; Zhu, Heyuan

2017-06-08

Controlling heat transport through material design is one important step toward thermal management in 2D materials. To control heat transport, a comprehensive understanding of how structure influences heat transport is required. It has been argued that a buckled structure is able to suppress heat transport by increasing the flexural phonon scattering. Using a first principles approach, we calculate the lattice thermal conductivity of 2D mono-elemental materials with a buckled structure. Somewhat counterintuitively, we find that although 2D group-V materials have a larger mass and higher buckling height than their group-IV counterparts, the calculated κ of blue phosphorene (106.6 W mK -1 ) is nearly four times higher than that of silicene (28.3 W mK -1 ), while arsenene (37.8 W mK -1 ) is more than fifteen times higher than germanene (2.4 W mK -1 ). We report for the first time that a buckled structure has three conflicting effects: (i) increasing the Debye temperature by increasing the overlap of the p z orbitals, (ii) suppressing the acoustic-optical scattering by forming an acoustic-optical gap, and (iii) increasing the flexural phonon scattering. The former two, corresponding to the harmonic phonon part, tend to enhance κ, while the last one, corresponding to the anharmonic part, suppresses it. This relationship between the buckled structure and phonon behaviour provides insight into how to control heat transport in 2D materials.

Mechanics of Unidirectional Fiber-Reinforced Composites: Buckling Modes and Failure Under Compression Along Fibers

NASA Astrophysics Data System (ADS)

Paimushin, V. N.; Kholmogorov, S. A.; Gazizullin, R. K.

2018-01-01

One-dimensional linearized problems on the possible buckling modes of an internal or peripheral layer of unidirectional multilayer composites with rectilinear fibers under compression in the fiber direction are considered. The investigations are carried out using the known Kirchhoff-Love and Timoshenko models for the layers. The binder, modeled as an elastic foundation, is described by the equations of elasticity theory, which are simplified in accordance to the model of a transversely soft layer and are integrated along the transverse coordinate considering the kinematic coupling relations for a layer and foundation layers. Exact analytical solutions of the problems formulated are found, which are used to calculate a composite made of an HSE 180 REM prepreg based on a unidirectional carbon fiber tape. The possible buckling modes of its internal and peripheral layers are identified. Calculation results are compared with experimental data obtained earlier. It is concluded that, for the composite studied, the flexural buckling of layers in the uniform axial compression of specimens along fibers is impossible — the failure mechanism is delamination with buckling of a fiber bundle according to the pure shear mode. It is realized (due to the low average transverse shear modulus) at the value of the ultimate compression stress equal to the average shear modulus. It is shown that such a shear buckling mode can be identified only on the basis of equations constructed using the Timoshenko shear model to describe the deformation process of layers.

Buckling Behavior of Compression-Loaded Composite Cylindrical Shells with Reinforced Cutouts

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Starnes, James H., Jr.

2002-01-01

Results from a numerical study of the response of thin-wall compression-loaded quasi-isotropic laminated composite cylindrical shells with reinforced and unreinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A high-fidelity nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate how a compression-loaded shell with an unreinforced cutout can exhibit a complex nonlinear response. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, the addition of reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell, as expected. However, results are presented that show how certain reinforcement configurations can actually cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved response characteristics.

Femoral neck BMD is a strong predictor of hip fracture susceptibility in elderly men and women because it detects cortical bone instability: the Rotterdam Study.

PubMed

Rivadeneira, Fernando; Zillikens, M Carola; De Laet, Chris Edh; Hofman, Albert; Uitterlinden, André G; Beck, Thomas J; Pols, Huibert Ap

2007-11-01

We studied HSA measurements in relation to hip fracture risk in 4,806 individuals (2,740 women). Hip fractures (n = 147) occurred at the same absolute levels of bone instability in both sexes. Cortical instability (propensity of thinner cortices in wide diameters to buckle) explains why hip fracture risk at different BMD levels is the same across sexes. Despite the sexual dimorphism of bone, hip fracture risk is very similar in men and women at the same absolute BMD. We aimed to elucidate the main structural properties of bone that underlie the measured BMD and that ultimately determines the risk of hip fracture in elderly men and women. This study is part of the Rotterdam Study (a large prospective population-based cohort) and included 147 incident hip fracture cases in 4,806 participants with DXA-derived hip structural analysis (mean follow-up, 8.6 yr). Indices compared in relation to fracture included neck width, cortical thickness, section modulus (an index of bending strength), and buckling ratio (an index of cortical bone instability). We used a mathematical model to calculate the hip fracture distribution by femoral neck BMD, BMC, bone area, and hip structure analysis (HSA) parameters (cortical thickness, section modulus narrow neck width, and buckling ratio) and compared it with prospective data from the Rotterdam Study. In the prospective data, hip fracture cases in both sexes had lower BMD, thinner cortices, greater bone width, lower strength, and higher instability at baseline. In fractured individuals, men had an average BMD that was 0.09 g/cm(2) higher than women (p < 0.00001), whereas no significant difference in buckling ratios was seen. Modeled fracture distribution by BMD and buckling ratio levels were in concordance to the prospective data and showed that hip fractures seem to occur at the same absolute levels of bone instability (buckling ratio) in both men and women. No significant differences were observed between the areas under the ROC curves of BMD (0.8146 in women and 0.8048 in men) and the buckling ratio (0.8161 in women and 0.7759 in men). The buckling ratio (an index of bone instability) portrays in both sexes the critical balance between cortical thickness and bone width. Our findings suggest that extreme thinning of cortices in expanded bones plays a key role on local susceptibility to fracture. Even though the buckling ratio does not offer additional predictive value, these findings improve our understanding of why low BMD is a good predictor of fragility fractures.

Buckling Load Calculations of the Isotropic Shell A-8 Using a High-Fidelity Hierarchical Approach

NASA Technical Reports Server (NTRS)

Arbocz, Johann; Starnes, James H.

2002-01-01

As a step towards developing a new design philosophy, one that moves away from the traditional empirical approach used today in design towards a science-based design technology approach, a test series of 7 isotropic shells carried out by Aristocrat and Babcock at Caltech is used. It is shown how the hierarchical approach to buckling load calculations proposed by Arbocz et al can be used to perform an approach often called 'high fidelity analysis', where the uncertainties involved in a design are simulated by refined and accurate numerical methods. The Delft Interactive Shell DEsign COde (short, DISDECO) is employed for this hierarchical analysis to provide an accurate prediction of the critical buckling load of the given shell structure. This value is used later as a reference to establish the accuracy of the Level-3 buckling load predictions. As a final step in the hierarchical analysis approach, the critical buckling load and the estimated imperfection sensitivity of the shell are verified by conducting an analysis using a sufficiently refined finite element model with one of the current generation two-dimensional shell analysis codes with the advanced capabilities needed to represent both geometric and material nonlinearities.

On the buckling of hexagonal boron nitride nanoribbons via structural mechanics

NASA Astrophysics Data System (ADS)

Giannopoulos, Georgios I.

2018-03-01

Monolayer hexagonal boron nitride nanoribbons have similar crystal structure as graphene nanoribbons, have excellent mechanical, thermal insulating and dielectric properties and additionally present chemical stability. These allotropes of boron nitride can be used in novel applications, in which graphene is not compatible, to achieve remarkable performance. The purpose of the present work is to provide theoretical estimations regarding the buckling response of hexagonal boron nitride monolayer under compressive axial loadings. For this reason, a structural mechanics method is formulated which employs the exact equilibrium atomistic structure of the specific two-dimensional nanomaterial. In order to represent the interatomic interactions appearing between boron and nitrogen atoms, the Dreiding potential model is adopted which is realized by the use of three-dimensional, two-noded, spring-like finite elements of appropriate stiffness matrices. The critical compressive loads that cause the buckling of hexagonal boron nitride nanoribbons are computed with respect to their size and chirality while some indicative buckled shapes of them are illustrated. Important conclusions arise regarding the effect of the size and chirality on the structural stability of the hexagonal boron nitride monolayers. An analytical buckling formula, which provides good fitting of the numerical outcome, is proposed.

Bending strength of delaminated aerospace composites.

PubMed

Kinawy, Moustafa; Butler, Richard; Hunt, Giles W

2012-04-28

Buckling-driven delamination is considered among the most critical failure modes in composite laminates. This paper examines the propagation of delaminations in a beam under pure bending. A pre-developed analytical model to predict the critical buckling moment of a thin sub-laminate is extended to account for propagation prediction, using mixed-mode fracture analysis. Fractography analysis is performed to distinguish between mode I and mode II contributions to the final failure of specimens. Comparison between experimental results and analysis shows agreement to within 5 per cent in static propagation moment for two different materials. It is concluded that static fracture is almost entirely driven by mode II effects. This result was unexpected because it arises from a buckling mode that opens the delamination. For this reason, and because of the excellent repeatability of the experiments, the method of testing may be a promising means of establishing the critical value of mode II fracture toughness, G(IIC), of the material. Fatigue testing on similar samples showed that buckled delamination resulted in a fatigue threshold that was over 80 per cent lower than the static propagation moment. Such an outcome highlights the significance of predicting snap-buckling moment and subsequent propagation for design purposes.

On a High-Fidelity Hierarchical Approach to Buckling Load Calculations

NASA Technical Reports Server (NTRS)

Arbocz, Johann; Starnes, James H.; Nemeth, Michael P.

2001-01-01

As a step towards developing a new design philosophy, one that moves away from the traditional empirical approach used today in design towards a science-based design technology approach, a recent test series of 5 composite shells carried out by Waters at NASA Langley Research Center is used. It is shown how the hierarchical approach to buckling load calculations proposed by Arbocz et al can be used to perform an approach often called "high fidelity analysis", where the uncertainties involved in a design are simulated by refined and accurate numerical methods. The Delft Interactive Shell DEsign COde (short, DISDECO) is employed for this hierarchical analysis to provide an accurate prediction of the critical buckling load of the given shell structure. This value is used later as a reference to establish the accuracy of the Level-3 buckling load predictions. As a final step in the hierarchical analysis approach, the critical buckling load and the estimated imperfection sensitivity of the shell are verified by conducting an analysis using a sufficiently refined finite element model with one of the current generation two-dimensional shell analysis codes with the advanced capabilities needed to represent both geometric and material nonlinearities.

Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels

NASA Technical Reports Server (NTRS)

Stein, M.; Housner, J. D.

1978-01-01

A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

Investigation on imperfection sensitivity of composite cylindrical shells using the nonlinearity reduction technique and the polynomial chaos method

NASA Astrophysics Data System (ADS)

Liang, Ke; Sun, Qin; Liu, Xiaoran

2018-05-01

The theoretical buckling load of a perfect cylinder must be reduced by a knock-down factor to account for structural imperfections. The EU project DESICOS proposed a new robust design for imperfection-sensitive composite cylindrical shells using the combination of deterministic and stochastic simulations, however the high computational complexity seriously affects its wider application in aerospace structures design. In this paper, the nonlinearity reduction technique and the polynomial chaos method are implemented into the robust design process, to significantly lower computational costs. The modified Newton-type Koiter-Newton approach which largely reduces the number of degrees of freedom in the nonlinear finite element model, serves as the nonlinear buckling solver to trace the equilibrium paths of geometrically nonlinear structures efficiently. The non-intrusive polynomial chaos method provides the buckling load with an approximate chaos response surface with respect to imperfections and uses buckling solver codes as black boxes. A fast large-sample study can be applied using the approximate chaos response surface to achieve probability characteristics of buckling loads. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with an unstiffened CFRP cylinder.

Buckling Design Studies of Inverted, Oblate Bulkheads for a Propellant Tank

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S., III; Bowman, Lynn M.

2002-01-01

An investigation of the deformation and buckling characteristics of a composite, oblate bulkhead that has an inverted geometry and is subjected to pressure-only loading is presented for three bulkhead geometries and thicknesses. The effects of a stiffening support ring at the bulkhead to cylinder interface are also evaluated. Buckling analyses conducted using the axisymmetric shell code BOSOR4 are discussed for several bulkhead configurations. These results are analytically verified using results from the Structural Analysis of General Shells (STAGS) code for a selected bulkhead configuration. The buckling characterization of an inverted, oblate bulkhead requires careful attention as small changes in bulkhead parameters can have a significant effect on the critical buckling load. Comparison of BOSOR4 and STAGS results provided a very good correlation between the two analysis methods. In addition, the analysis code BOSOR4 was found to be an efficient sizing tool that is useful during the preliminary design stage of a practical shell structure. Together, these two aspects should give the design engineer confidence in sizing these stability critical structures. Additional characterization is warranted, especially for a composite tank structure, since only one bulkhead configuration was examined closely.

A Numerical Study on the Effect of Facesheet-Core Disbonds on the Buckling Load of Curved Honeycomb Sandwich Panels

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Myers, David E.; Bednarcyk, Brett A.; Krivanek, Thomas M.

2015-01-01

A numerical study on the effect of facesheet-core disbonds on the post-buckling response of curved honeycomb sandwich panels is presented herein. This work was conducted as part of the development of a damage tolerance approach for the next-generation Space Launch System heavy lift vehicle payload fairing. As such, the study utilized full-scale fairing barrel segments as the structure of interest. The panels were composed of carbon fiber reinforced polymer facesheets and aluminum honeycomb core. The panels were analyzed numerically using the finite element method. Facesheet and core nodes in a predetermined circular region were detached to simulate a disbond induced via low-speed impact between the outer mold line facesheet and honeycomb core. Surface-to-surface contact in the disbonded region was invoked to prevent interpenetration of the facesheet and core elements. The diameter of this disbonded region was varied and the effect of the size of the disbond on the post-buckling response was observed. A significant change in the slope of the edge load-deflection response was used to determine the onset of global buckling and corresponding buckling load.

Euler solutions for an unbladed jet engine configuration

NASA Technical Reports Server (NTRS)

Stewart, Mark E. M.

1991-01-01

A Euler solution for an axisymmetric jet engine configuration without blade effects is presented. The Euler equations are solved on a multiblock grid which covers a domain including the inlet, bypass duct, core passage, nozzle, and the far field surrounding the engine. The simulation is verified by considering five theoretical properties of the solution. The solution demonstrates both multiblock grid generation techniques and a foundation for a full jet engine throughflow calculation.

A minimum entropy principle in the gas dynamics equations

NASA Technical Reports Server (NTRS)

Tadmor, E.

1986-01-01

Let u(x bar,t) be a weak solution of the Euler equations, governing the inviscid polytropic gas dynamics; in addition, u(x bar, t) is assumed to respect the usual entropy conditions connected with the conservative Euler equations. We show that such entropy solutions of the gas dynamics equations satisfy a minimum entropy principle, namely, that the spatial minimum of their specific entropy, (Ess inf s(u(x,t)))/x, is an increasing function of time. This principle equally applies to discrete approximations of the Euler equations such as the Godunov-type and Lax-Friedrichs schemes. Our derivation of this minimum principle makes use of the fact that there is a family of generalized entrophy functions connected with the conservative Euler equations.

Buckling Of Shells Of Revolution /BOSOR/ with various wall constructions

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Bushnell, D.; Sobel, L. H.

1969-01-01

Computer program, using numerical integration and finite difference techniques, solves almost any buckling problem for shells exhibiting orthotropic behavior. Stability analyses can be performed with reasonable accuracy and without unduly restrictive approximations.

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

NASA Technical Reports Server (NTRS)

Seide, Paul; Stowell, Elbridge Z

1950-01-01

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

Masquerading Orbital Abscess Following Attempted Hydrogel Scleral Buckle Removal: Diagnostic Value of Orbital Magnetic Resonance Spectroscopy.

PubMed

Pakdel, Farzad; Hadizadeh, Homayoun; Pirmarzdashty, Niloofar; Kiavash, Victoria

2015-01-01

A 59-year-old patient developed acute proptosis, peri-orbital swelling and restriction of ocular movements 2 days after attempted scleral buckle removal. Initial clinical and orbital MRI findings were suggestive for orbital cellulitis and orbital abscess. Empiric intravenous antibiotics were not effective. Proton magnetic resonance spectroscopy (MRS) revealed a distinctive composition and helped rule out suppurative and neoplastic processes. The patient recovered soon after removing clear liquefied and tiny particles of the hydrogel buckle by an effective peristaltic technique.

Buckling behavior of composite cylinders subjected to compressive loading

NASA Technical Reports Server (NTRS)

Carri, R. L.

1973-01-01

Room temperature compressive buckling strengths of eight cylinders, four boron-epoxy and four boron-epoxy reinforced-titanium, with diameter to thickness ratios ranging between 40 and 67 are determined experimentally and compared with analytical predictions. Numerical buckling strengths are presented for Donnell's, Flugge's and Sanders' shell theories for anisotropic and orthotropic material cases. Comparison of analytical predictions with experimental results indicates good agreement and the recommended correlation factor suggested in the literature is applicable for design. For the cylinders tested, the correlation between experiment and theory ranged from 0.73 to 0.97.

Elastocapillary snapping

NASA Astrophysics Data System (ADS)

Antkowiak, Arnaud; Fargette, Aurelie; Neukirch, Sebastien

2010-11-01

An elastica buckled in the form of an arch is subjected to a transverse force. Above a critical load value, the buckling mode is switched and the elastica takes the form of a reversed arch. This is the well-known snap-through phenomenon which has been extensively studied in solid mechanics. Here, we revisit this phenomenon and show that capillary forces may promote snapping of a buckled polymer strip. We report detailed experiments of this new paradigm for elasto-capillary interactions, and the obtained results are in close agreement with a simple elastic stability theory.

Stretchable Fiber Supercapacitors with High Volumetric Performance Based on Buckled MnO2 /Oxidized Carbon Nanotube Fiber Electrodes.

PubMed

Li, Mingyang; Zu, Mei; Yu, Jinshan; Cheng, Haifeng; Li, Qingwen

2017-03-01

A stretchable fiber supercapacitor (SC) based on buckled MnO 2 /oxidized carbon nanotube (CNT) fiber electrode is fabricated by a simple prestraining-then-buckling method. The prepared stretchable fiber SC has a specific volumetric capacitance up to 409.4 F cm -3 , which is 33 times that of the pristine CNT fiber based SC, and shows the outstanding stability and repeatability in performance as a stretchable SC. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

NASTRAN buckling study of a linear induction motor reaction rail

NASA Technical Reports Server (NTRS)

Williams, J. G.

1973-01-01

NASTRAN was used to study problems associated with the installation of a linear induction motor reaction rail test track. Specific problems studied include determination of the critical axial compressive buckling stress and establishment of the lateral stiffness of the reaction rail under combined loads. NASTRAN results were compared with experimentally obtained values and satisfactory agreement was obtained. The reaction rail was found to buckle at an axial compressive stress of 11,400 pounds per square inch. The results of this investigation were used to select procedures for installation of the reaction rail.

The origin of Korotkoff sounds and the accuracy of auscultatory blood pressure measurements.

PubMed

Babbs, Charles F

2015-12-01

This study explores the hypothesis that the sharper, high frequency Korotkoff sounds come from resonant motion of the arterial wall, which begins after the artery transitions from a buckled state to an expanding state. The motions of one mass, two nonlinear springs, and one damper, driven by transmural pressure under the cuff, are used to model and compute the Korotkoff sounds according to principles of classical Newtonian physics. The natural resonance of this spring-mass-damper system provides a concise, yet rigorous, explanation for the origin of Korotkoff sounds. Fundamentally, wall stretching in expansion requires more force than wall bending in buckling. At cuff pressures between systolic and diastolic arterial pressure, audible vibrations (> 40 Hz) occur during early expansion of the artery wall beyond its zero pressure radius after the outward moving mass of tissue experiences sudden deceleration, caused by the discontinuity in stiffness between bucked and expanded states. The idealized spring-mass-damper model faithfully reproduces the time-domain waveforms of actual Korotkoff sounds in humans. Appearance of arterial sounds occurs at or just above the level of systolic pressure. Disappearance of arterial sounds occurs at or just above the level of diastolic pressure. Muffling of the sounds is explained by increased resistance of the artery to collapse, caused by downstream venous engorgement. A simple analytical model can define the physical origin of Korotkoff sounds, suggesting improved mechanical or electronic filters for their selective detection and confirming the disappearance of the Korotkoff sounds as the optimal diastolic end point. Copyright © 2015 American Society of Hypertension. Published by Elsevier Inc. All rights reserved.

Buckling Test Results from the 8-Foot-Diameter Orthogrid-Stiffened Cylinder Test Article TA01. [Test Dates: 19-21 November 2008

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Waters, W. Allen, Jr.; Haynie, Waddy T.

2015-01-01

Results from the testing of cylinder test article SBKF-P2-CYLTA01 (referred to herein as TA01) are presented. The testing was conducted at the Marshall Space Flight Center (MSFC), November 19?21, 2008, in support of the Shell Buckling Knockdown Factor (SBKF) Project.i The test was used to verify the performance of a newly constructed buckling test facility at MSFC and to verify the test article design and analysis approach used by the SBKF project researchers. TA01 is an 8-foot-diameter (96-inches), 78.0-inch long, aluminum-lithium (Al-Li), orthogrid-stiffened cylindrical shell similar to those used in current state-of-the-art launch vehicle structures and was designed to exhibit global buckling when subjected to compression loads. Five different load sequences were applied to TA01 during testing and included four sub-critical load sequences, i.e., loading conditions that did not cause buckling or material failure, and one final load sequence to buckling and collapse. The sub-critical load sequences consisted of either uniform axial compression loading or combined axial compression and bending and the final load sequence subjected TA01 to uniform axial compression. Traditional displacement transducers and strain gages were used to monitor the test article response at nearly 300 locations and an advanced digital image correlation system was used to obtain low-speed and high-speed full-field displacement measurements of the outer surface of the test article. Overall, the test facility and test article performed as designed. In particular, the test facility successfully applied all desired load combinations to the test article and was able to test safely into the postbuckling range of loading, and the test article failed by global buckling. In addition, the test results correlated well with initial pretest predictions.

Implementation of Fiber Optic Sensing System on Sandwich Composite Cylinder Buckling Test

NASA Technical Reports Server (NTRS)

Pena, Francisco; Richards, W. Lance; Parker, Allen R.; Piazza, Anthony; Schultz, Marc R.; Rudd, Michelle T.; Gardner, Nathaniel W.; Hilburger, Mark W.

2018-01-01

The National Aeronautics and Space Administration (NASA) Engineering and Safety Center Shell Buckling Knockdown Factor Project is a multicenter project tasked with developing new analysis-based shell buckling design guidelines and design factors (i.e., knockdown factors) through high-fidelity buckling simulations and advanced test technologies. To validate these new buckling knockdown factors for future launch vehicles, the Shell Buckling Knockdown Factor Project is carrying out structural testing on a series of large-scale metallic and composite cylindrical shells at the NASA Marshall Space Flight Center (Marshall Space Flight Center, Alabama). A fiber optic sensor system was used to measure strain on a large-scale sandwich composite cylinder that was tested under multiple axial compressive loads up to more than 850,000 lb, and equivalent bending loads over 22 million in-lb. During the structural testing of the composite cylinder, strain data were collected from optical cables containing distributed fiber Bragg gratings using a custom fiber optic sensor system interrogator developed at the NASA Armstrong Flight Research Center. A total of 16 fiber-optic strands, each containing nearly 1,000 fiber Bragg gratings, measuring strain, were installed on the inner and outer cylinder surfaces to monitor the test article global structural response through high-density real-time and post test strain measurements. The distributed sensing system provided evidence of local epoxy failure at the attachment-ring-to-barrel interface that would not have been detected with conventional instrumentation. Results from the fiber optic sensor system were used to further refine and validate structural models for buckling of the large-scale composite structures. This paper discusses the techniques employed for real-time structural monitoring of the composite cylinder for structural load introduction and distributed bending-strain measurements over a large section of the cylinder by utilizing unique sensing capabilities of fiber optic sensors.

Kinematic constraints on buckling a lithospheric-scale orocline during Pangea assembly: a geologic synthesis

NASA Astrophysics Data System (ADS)

Weil, Arlo; Gutiérrez-Alonso, Gabriel; Johnston, Stephen; Pastor Galán, Daniel

2013-04-01

The Paleozoic Variscan orogeny was a large-scale collisional event involving amalgamation of multiple continents and micro-continents. Existing data, suggests oroclinal buckling of an originally near-linear convergent margin during the last stages of Variscan deformation in the late Paleozoic. Closure of the Rheic Ocean resulted in E-W shortening (present-day coordinates) in the Carboniferous, producing a near linear N-S trending, east-verging belt. Subsequent N-S shortening near the Carb-Permian boundary resulted in oroclinal buckling. This late-stage orogenic event remains an enigmatic part of final Pangea amalgamation. The present-day arc curvature of the Variscan has inspired many tectonic models, with little agreement between them. While there is general consensus that two separate phases of deformation occurred, various models consider that curvature was caused by: dextral transpression around a Gondwana indentor; strike-slip wrench tectonics; or a change in tectonic transport direction due to changing stress fields. More recent models explain the curvature as an orocline, with potentially two opposite-facing bends, caused by secondary rotations. Deciphering the kinematic history of curved orogens is difficult, and requires establishment of two deformation phases: an initial compressive phase that forms a relatively linear belt, and a second phase that causes vertical-axis rotation of the orogenic limbs. Historically the most robust technique to accurately quantify vertical axis-rotation in curved orogens is paleomagnetic analysis, but recently other types of data, including fracture, geochemical, petrologic, paleo-current and calcite twin data, have been used to corroborate secondary buckling. A review of existing and new Variscan data from Iberia is presented that argues for secondary buckling of an originally linear orogenic system. Together, these data constrain oroclinal buckling of the Cantabrian Orocline to have occurred in about 10 Ma during the latest Carboniferous, which agrees well with recent geodynamical models and structural data that relate oroclinal buckling with lithospheric delamination in the Variscan.

Kinematic constraints on buckling a lithospheric-scale orocline along the northern margin of Gondwana: A geologic synthesis

NASA Astrophysics Data System (ADS)

Weil, A. Brandon; Gutiérrez-Alonso, G.; Johnston, S. T.; Pastor-Galán, D.

2013-01-01

The Paleozoic Variscan orogeny was a large-scale collisional event involving amalgamation of multiple continents and micro-continents. Existing data, suggests oroclinal buckling of an originally near-linear convergent margin during the last stages of Variscan deformation in the late Paleozoic. Closure of the Rheic Ocean resulted in E-W shortening (present-day coordinates) in the Carboniferous, producing a near linear N-S trending, east-verging belt. Subsequent N-S shortening near the Carb-Permian boundary resulted in oroclinal buckling. This late-stage orogenic event remains an enigmatic part of final Pangea amalgamation. The present-day arc curvature of the Variscan has inspired many tectonic models, with little agreement between them. While there is general consensus that two separate phases of deformation occurred, various models consider that curvature was caused by: dextral transpression around a Gondwana indentor; strike-slip wrench tectonics; or a change in tectonic transport direction due to changing stress fields. More recent models explain the curvature as an orocline, with potentially two opposite-facing bends, caused by secondary rotations. Deciphering the kinematic history of curved orogens is difficult, and requires establishment of two deformation phases: an initial compressive phase that forms a relatively linear belt, and a second phase that causes vertical-axis rotation of the orogenic limbs. Historically the most robust technique to accurately quantify vertical axis-rotation in curved orogens is paleomagnetic analysis, but recently other types of data, including fracture, geochemical, petrologic, paleo-current and calcite twin data, have been used to corroborate secondary buckling. A review of existing and new Variscan data from Iberia is presented that argues for secondary buckling of an originally linear orogenic system. Together, these data constrain oroclinal buckling of the Cantabrian Orocline to have occurred in about 10 Ma during the latest Carboniferous, which agrees well with recent geodynamical models and structural data that relate oroclinal buckling with lithospheric delamination in the Variscan.

Extended hamiltonian formalism and Lorentz-violating lagrangians

NASA Astrophysics Data System (ADS)

Colladay, Don

2017-09-01

A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

On Electron-Positron Pair Production by a Spatially Inhomogeneous Electric Field

NASA Astrophysics Data System (ADS)

Chervyakov, A.; Kleinert, H.

2018-05-01

A detailed analysis of electron-positron pair creation induced by a spatially non-uniform and static electric field from vacuum is presented. A typical example is provided by the Sauter potential. For this potential, we derive the analytic expressions for vacuum decay and pair production rate accounted for the entire range of spatial variations. In the limit of a sharp step, we recover the divergent result due to the singular electric field at the origin. The limit of a constant field reproduces the classical result of Euler, Heisenberg and Schwinger, if the latter is properly averaged over the width of a spatial variation. The pair production by the Sauter potential is described for different regimes from weak to strong fields. For all these regimes, the locally constant-field rate is shown to be the upper limit.

Process and outcome evaluation: the Buckle Up America initiatives

DOT National Transportation Integrated Search

2001-07-01

Buckle Up America (BUA) was a national initiative announced January 1997 directing the Department of Transportation (DOT) to prepare a plan to increase seat belt usage nationwide. In response, the DOT's National Highway Traffic Safety Administration ...

Analysis of Thermal Track Buckling in the Lateral Plane

DOT National Transportation Integrated Search

1976-09-01

The post-buckling equilibrium states are determined analytically. To obtain a consistent formulation of the problem, use is made of the principle of virtual displacements and the variational calculus for variable matching points. The obtained formula...

Track buckling prevention : theory, safety concepts, and applications

DOT National Transportation Integrated Search

2013-03-31

This report is a part of the John A. Volpe National Transportation Systems Centers Track Stability Research Program for the Federal Railroad Administration on thermal buckling of continuous welded rail (CWR) track and its prevention. Presented in ...

Buckling of thin walled composite cylindrical shell filled with solid propellant

NASA Astrophysics Data System (ADS)

Dash, A. P.; Velmurugan, R.; Prasad, M. S. R.

2017-12-01

This paper investigates the buckling of thin walled composite cylindrical tubes that are partially filled with solid propellant equivalent elastic filler. Experimental investigation is conducted on thin composite tubes made out of S2-glass epoxy, which is made by using filament winding technique. The composite tubes are filled with elastic filler having similar mechanical properties as that of a typical solid propellant used in rocket motors. The tubes are tested for their buckling strength against the external pressure in the presence of the filler. Experimental data confirms the enhancement of external pressure carrying capacity of the composite tubes by up to three times as that of empty tubes for a volumetric loading fraction (VLF) of 0.9. Furthermore, the finite element based geometric nonlinearity analysis predicts the buckling behaviour of the partially filled composite tubes close to the experimental results.

A first-principles study on second-order ferroelectric phase transition in two-dimensional puckered group V materials

NASA Astrophysics Data System (ADS)

Lee, Sang-Hoon; Jhi, Seung-Hoon

We study two-dimensional group V materials (P, As, Sb, and Bi) in puckered honeycomb structure using first-principles calculations. Two factors, the degree of puckering and buckling characterize not only the atomic structure but also the electronic structure and its topological phase. By analyzing the lone-pair character of constituent elements and the softening of the phonon mode, we clarify the origin of the buckling. We show that the phonon softening leads the second-order type structural phase transition from a flat to a buckled configuration. The inversion symmetry breaking associated with the structural transition induces the spontaneous polarization in these homogenous materials. Our calculations suggest that external strains or n-type doping are effective methods to control the degree of buckling. We find that the ferroelectric and non-trivial topological phase can coexist in puckered Bi when tensile strains are applied.

Surface buckling of black phosphorus: Determination, origin, and influence on electronic structure

NASA Astrophysics Data System (ADS)

Dai, Zhongwei; Jin, Wencan; Yu, Jie-Xiang; Grady, Maxwell; Sadowski, Jerzy T.; Kim, Young Duck; Hone, James; Dadap, Jerry I.; Zang, Jiadong; Osgood, Richard M.; Pohl, Karsten

2017-12-01

The surface structure of black phosphorus materials is determined using surface-sensitive dynamical microspot low energy electron diffraction (μ LEED ) analysis using a high spatial resolution low energy electron microscopy (LEEM) system. Samples of (i) crystalline cleaved black phosphorus (BP) at 300 K and (ii) exfoliated few-layer phosphorene (FLP) of about 10 nm thickness which were annealed at 573 K in vacuum were studied. In both samples, a significant surface buckling of 0.22 Å and 0.30 Å, respectively, is measured, which is one order of magnitude larger than previously reported. As direct evidence for large buckling, we observe a set of (for the flat surface forbidden) diffraction spots. Using first-principles calculations, we find that the presence of surface vacancies is responsible for the surface buckling in both BP and FLP, and is related to the intrinsic hole doping of phosphoresce materials previously reported.

Buckling of Aluminium Sheet Components

NASA Astrophysics Data System (ADS)

Hegadekatte, Vishwanath; Shi, Yihai; Nardini, Dubravko

Wrinkling is one of the major defects in sheet metal forming processes. It may become a serious obstacle to implementing the forming process and assembling the parts, and may also play a significant role in the wear of the tool. Wrinkling is essentially a local buckling phenomenon that results from compressive stresses (compressive instability) e.g., in the hoop direction for axi-symmetric systems such as beverage cans. Modern beverage can is a highly engineered product with a complex geometry. Therefore in order to understand wrinkling in such a complex system, we have started by studying wrinkling with the Yoshida buckling test. Further, we have studied the buckling of ideal and dented beverage cans under axial loading by laboratory testing. We have modelled the laboratory tests and also the imperfection sensitivity of the two systems using finite element method and the predictions are in qualitative agreement with experimental data.

Improving Strength of Postbuckled Panels Through Stitching

NASA Technical Reports Server (NTRS)

Jegley, Dawn C.

2007-01-01

The behavior of blade-stiffened graphite-epoxy panels with impact damage is examined to determine the effect of adding through-the-thickness stitches in the stiffener flange-to-skin interface. The influence of stitches is evaluated by examining buckling and failure for panels with failure loads up to 3.5 times greater than buckling loads. Analytical and experimental results from four configurations of panel specimens are presented. For each configuration, two panels were manufactured with skin and flanges held together with through-the-thickness stitches introduced prior to resin infusion and curing and one panel was manufactured with no stitches holding the flange to the skin. No mechanical fasteners were used for the assembly of any of these panels. Panels with and without low-speed impact damage were loaded to failure in compression. Buckling and failure modes are discussed. Stitching had little effect on buckling loads but increased the failure loads of impact-damaged panels by up to 30%.

Fabrication and evaluation of cold/formed/weldbrazed beta-titanium skin-stiffened compression panels

NASA Technical Reports Server (NTRS)

Royster, D. M.; Bales, T. T.; Davis, R. C.; Wiant, H. R.

1983-01-01

The room temperature and elevated temperature buckling behavior of cold formed beta titanium hat shaped stiffeners joined by weld brazing to alpha-beta titanium skins was determined. A preliminary set of single stiffener compression panels were used to develop a data base for material and panel properties. These panels were tested at room temperature and 316 C (600 F). A final set of multistiffener compression panels were fabricated for room temperature tests by the process developed in making the single stiffener panels. The overall geometrical dimensions for the multistiffener panels were determined by the structural sizing computer code PASCO. The data presented from the panel tests include load shortening curves, local buckling strengths, and failure loads. Experimental buckling loads are compared with the buckling loads predicted by the PASCO code. Material property data obtained from tests of ASTM standard dogbone specimens are also presented.

Optimal Design of Grid-Stiffened Panels and Shells With Variable Curvature

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.; Jaunky, Navin

2001-01-01

A design strategy for optimal design of composite grid-stiffened structures with variable curvature subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. Stiffening configuration is herein defined as a design variable that indicates the combination of axial, transverse and diagonal stiffeners in the stiffened panel. The design optimization process is adapted to identify the lightest-weight stiffening configuration and stiffener spacing for grid-stiffened composite panels given the overall panel dimensions. in-plane design loads, material properties. and boundary conditions of the grid-stiffened panel or shell.

Buckling instability in amorphous carbon films

NASA Astrophysics Data System (ADS)

Zhu, X. D.; Narumi, K.; Naramoto, H.

2007-06-01

In this paper, we report the buckling instability in amorphous carbon films on mirror-polished sapphire (0001) wafers deposited by ion beam assisted deposition at various growth temperatures. For the films deposited at 150 °C, many interesting stress relief patterns are found, which include networks, blisters, sinusoidal patterns with π-shape, and highly ordered sinusoidal waves on a large scale. Starting at irregular buckling in the centre, the latter propagate towards the outer buckling region. The maximum length of these ordered patterns reaches 396 µm with a height of ~500 nm and a wavelength of ~8.2 µm. However, the length decreases dramatically to 70 µm as the deposition temperature is increased to 550 °C. The delamination of the film appears instead of sinusoidal waves with a further increase of the deposition temperature. This experimental observation is correlated with the theoretic work of Crosby (1999 Phys. Rev. E 59 R2542).

Effect of corrosion on the buckling capacity of tubular members

NASA Astrophysics Data System (ADS)

Øyasæter, F. H.; Aeran, A.; Siriwardane, S. C.; Mikkelsen, O.

2017-12-01

Offshore installations are subjected to harsh marine environment and often have damages from corrosion. Several experimental and numerical studies were performed in the past to estimate buckling capacity of corroded tubular members. However, these studies were either based on limited experimental tests or numerical analyses of few cases resulting in semi-empirical relations. Also, there are no guidelines and recommendations in the currently available design standards. To fulfil this research gap, a new formula is proposed to estimate the residual strength of tubular members considering corrosion and initial geometrical imperfections. The proposed formula is verified with results from finite element analyses performed on several members and for varying corrosion patch parameters. The members are selected to represent the most relevant Eurocode buckling curve for tubular members. It is concluded that corrosion reduces the buckling capacity significantly and the proposed formula can be easily applied by practicing engineers without performing detailed numerical analyses.

Buckling of paramagnetic chains in soft gels

NASA Astrophysics Data System (ADS)

Huang, Shilin; Pessot, Giorgio; Cremer, Peet; Weeber, Rudolf; Holm, Christian; Nowak, Johannes; Odenbach, Stefan; Menzel, Andreas M.; Auernhammer, Günter K.

We study the magneto-elastic coupling behavior of paramagnetic chains in soft polymer gels exposed to external magnetic fields. To this end, a laser scanning confocal microscope is used to observe the morphology of the paramagnetic chains together with the deformation field of the surrounding gel network. The paramagnetic chains in soft polymer gels show rich morphological shape changes under oblique magnetic fields, in particular a pronounced buckling deformation. The details of the resulting morphological shapes depend on the length of the chain, the strength of the external magnetic field, and the modulus of the gel. Based on the observation that the magnetic chains are strongly coupled to the surrounding polymer network, a simplified model is developed to describe their buckling behavior. A coarse-grained molecular dynamics simulation model featuring an increased matrix stiffness on the surfaces of the particles leads to morphologies in agreement with the experimentally observed buckling effects.

Large-deflection theory for end compression of long rectangular plates rigidly clamped along two edges

NASA Technical Reports Server (NTRS)

Levy, Samuel; Krupen, Philip

1943-01-01

The von Karman equations for flat plates are solved beyond the buckling load up to edge strains equal to eight time the buckling strain, for the extreme case of rigid clamping along the edges parallel to the load. Deflections, bending stresses, and membrane stresses are given as a function of end compressive load. The theoretical values of effective width are compared with the values derived for simple support along the edges parallel to the load. The increases in effective width due to rigid clamping drops from about 20 percent near the buckling strain to about 8 percent at an edge strain equal to eight times the buckling strain. Experimental values of effective width in the elastic range reported in NACA Technical Note No. 684 are between the theoretical curves for the extremes of simple support and rigid clamping.

Effect of load eccentricity on the buckling of thin-walled laminated C-columns

NASA Astrophysics Data System (ADS)

Wysmulski, Pawel; Teter, Andrzej; Debski, Hubert

2018-01-01

The study investigates the behaviour of short, thin-walled laminated C-columns under eccentric compression. The tested columns are simple-supported. The effect of load inaccuracy on the critical and post-critical (local buckling) states is examined. A numerical analysis by the finite element method and experimental tests on a test stand are performed. The samples were produced from a carbon-epoxy prepreg by the autoclave technique. The experimental tests rest on the assumption that compressive loads are 1.5 higher than the theoretical critical force. Numerical modelling is performed using the commercial software package ABAQUS®. The critical load is determined by solving an eigen problem using the Subspace algorithm. The experimental critical loads are determined based on post-buckling paths. The numerical and experimental results show high agreement, thus demonstrating a significant effect of load inaccuracy on the critical load corresponding to the column's local buckling.

Surface buckling of black phosphorus: Determination, origin, and influence on electronic structure

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

Dai, Zhongwei; Jin, Wencan; Yu, Jie-Xiang

The surface structure of black phosphorus materials is determined using surface-sensitive dynamical microspot low energy electron diffraction ( μ LEED ) analysis using a high spatial resolution low energy electron microscopy (LEEM) system. Samples of (i) crystalline cleaved black phosphorus (BP) at 300 K and (ii) exfoliated few-layer phosphorene (FLP) of about 10 nm thickness which were annealed at 573 K in vacuum were studied. In both samples, a significant surface buckling of 0.22 Å and 0.30 Å, respectively, is measured, which is one order of magnitude larger than previously reported. As direct evidence for large buckling, we observe amore » set of (for the flat surface forbidden) diffraction spots. Using first-principles calculations, we find that the presence of surface vacancies is responsible for the surface buckling in both BP and FLP, and is related to the intrinsic hole doping of phosphoresce materials previously reported.« less

Surface buckling of black phosphorus: Determination, origin, and influence on electronic structure

DOE PAGES

Dai, Zhongwei; Jin, Wencan; Yu, Jie-Xiang; ...

2017-12-29

The surface structure of black phosphorus materials is determined using surface-sensitive dynamical microspot low energy electron diffraction ( μ LEED ) analysis using a high spatial resolution low energy electron microscopy (LEEM) system. Samples of (i) crystalline cleaved black phosphorus (BP) at 300 K and (ii) exfoliated few-layer phosphorene (FLP) of about 10 nm thickness which were annealed at 573 K in vacuum were studied. In both samples, a significant surface buckling of 0.22 Å and 0.30 Å, respectively, is measured, which is one order of magnitude larger than previously reported. As direct evidence for large buckling, we observe amore » set of (for the flat surface forbidden) diffraction spots. Using first-principles calculations, we find that the presence of surface vacancies is responsible for the surface buckling in both BP and FLP, and is related to the intrinsic hole doping of phosphoresce materials previously reported.« less

Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Nemeth, Michael P.; Starnes, James H., Jr.

2004-01-01

An analysis-based approach .for developing shell-buckling design criteria for laminated-composite cylindrical shells that accurately accounts for the effects of initial geometric imperfections is presented. With this approach, measured initial geometric imperfection data from six graphite-epoxy shells are used to determine a manufacturing-process-specific imperfection signature for these shells. This imperfection signature is then used as input into nonlinear finite-element analyses. The imperfection signature represents a "first-approximation" mean imperfection shape that is suitable for developing preliminary-design data. Comparisons of test data and analytical results obtained by using several different imperfection shapes are presented for selected shells. Overall, the results indicate that the analysis-based approach presented for developing reliable preliminary-design criteria has the potential to provide improved, less conservative buckling-load estimates, and to reduce the weight and cost of developing buckling-resistant shell structures.

Lateral-Torsional Buckling Instability Caused by Individuals Walking on Wood Composite I-Joists

NASA Astrophysics Data System (ADS)

Villasenor Aguilar, Jose Maria

Recent research has shown that a significant number of the falls from elevation occur when laborers are working on unfinished structures. Workers walking on wood I-joists on roofs and floors are prone to fall hazards. Wood I-joists have been replacing dimension lumber for many floor systems and a substantial number of roof systems in light-frame construction. Wood I-joists are designed to resist axial stresses on the flanges and shear stresses on the web while minimizing material used. However, wood I-joists have poor resistance to applied lateral and torsional loads and are susceptible to lateral-torsional buckling instability. Workers walking on unbraced or partially braced wood I-joists can induce axial and lateral forces as well as twist. Experimental testing demonstrated that workers cause lateral-torsional buckling instability in wood I-joists. However, no research was found related to the lateral-torsional buckling instability induced by individuals walking on the wood I-joists. Furthermore, no research was found considering the effects of the supported end conditions and partial bracing in the lateral-torsional buckling instability of wood I-joists. The goal of this research was to derive mathematical models to predict the dynamic lateral-torsional buckling instability of wood composite I-joists loaded by individuals walking considering different supported end conditions and bracing system configurations. The dynamic lateral-torsional buckling instability was analyzed by linearly combining the static lateral-torsional buckling instability with the lateral bending motion of the wood Ijoists. Mathematical models were derived to calculate the static critical loads for the simply supported end condition and four wood I-joist hanger supported end conditions. Additionally, mathematical models were derived to calculate the dynamic maximum lateral displacements and positions of the individual walking on the wood Ijoists for the same five different supported end conditions. Three different lean-on bracing systems were investigated, non-bracing, one-bracing, and two-bracing systems. Mathematical models were derived to calculate the amount of constraint due to the lean-on bracing system. The derived mathematical models were validated by comparison to data from testing for all supported end conditions and bracing systems. The predicted critical loads using the static buckling theoretical models for the non-bracing system and the static buckling theoretical models combined with the bracing theoretical models for the simply and hanger supported end conditions agreed well with the critical loads obtained from testing for the two wood I-joist sizes investigated. The predicted maximum lateral displacements and individual positions using the bending motion theoretical models for the simply and hanger supported end conditions agreed well with the corresponding maximum lateral displacements and individual positions obtained from testing for both wood I-joist sizes. Results showed that; a) the supported end condition influenced the critical loads, maximum lateral displacements and individual positions, b) the bracing system increased the critical loads and reduced the maximum lateral displacements, c) the critical load increased as the load position displaced away from the wood I-joist mid-span, d) the critical load reduced as the initial lateral displacement of the wood I-joist increased and e) the wood I-joist mid-span was the critical point in the dynamic lateral-torsional buckling instability.

Analysis and Tests of Reinforced Carbon-Epoxy/Foam-Core Sandwich Panels with Cutouts

NASA Technical Reports Server (NTRS)

Baker, Donald J.; Rogers, Charles

1996-01-01

The results of a study of a low-cost structurally efficient minimum-gage shear-panel design that can be used in light helicopters are presented. The shear-panel design is based on an integrally stiffened syntactic-foam stabilized-skin with an all-bias-ply tape construction for stabilized-skin concept with an all-bias-ply tape construction for the skins. This sandwich concept is an economical way to increase the panel bending stiffness weight penalty. The panels considered in the study were designed to be buckling resistant up to 100 lbs/in. of shear load and to have an ultimate strength of 300 lbs/in. The panel concept uses unidirectional carbon-epoxy tape on a syntactic adhesive as a stiffener that is co-cured with the skin and is an effective concept for improving panel buckling strength. The panel concept also uses pultruded carbon-epoxy rods embedded in a syntactic adhesive and over-wrapped with a bias-ply carbon-epoxy tape to form a reinforcing beam which is an effective method for redistributing load around rectangular cutout. The buckling strength of the reinforced panels is 83 to 90 percent of the predicted buckling strength based on a linear buckling analysis. The maximum experimental deflection exceeds the maximum deflection predicted by a nonlinear analysis by approximately one panel thickness. The failure strength of the reinforced panels was two and a half to seven times of the buckling strength. This efficient shear-panel design concept exceeds the required ultimate strength requirement of 300 lbs/in by more than 100 percent.

Stable Tearing and Buckling Responses of Unstiffened Aluminum Shells with Long Cracks

NASA Technical Reports Server (NTRS)

Starnes, James H., Jr.; Rose, Cheryl A.

1999-01-01

The results of an analytical and experimental study of the nonlinear response of thin, unstiffened, aluminum cylindrical shells with a long longitudinal crack are presented. The shells are analyzed with a nonlinear shell analysis code that accurately accounts for global and local structural response phenomena. Results are presented for internal pressure and for axial compression loads. The effect of initial crack length on the initiation of stable crack growth and unstable crack growth in typical shells subjected to internal pressure loads is predicted using geometrically nonlinear elastic-plastic finite element analyses and the crack-tip-opening angle (CTOA) fracture criterion. The results of these analyses and of the experiments indicate that the pressure required to initiate stable crack growth and unstable crack growth in a shell subjected to internal pressure loads decreases as the initial crack length increases. The effects of crack length on the prebuckling, buckling and postbuckling responses of typical shells subjected to axial compression loads are also described. For this loading condition, the crack length was not allowed to increase as the load was increased. The results of the analyses and of the experiments indicate that the initial buckling load and collapse load for a shell subjected to axial compression loads decrease as the initial crack length increases. Initial buckling causes general instability or collapse of a shell for shorter initial crack lengths. Initial buckling is a stable local response mode for longer initial crack lengths. This stable local buckling response is followed by a stable postbuckling response, which is followed by general or overall instability of the shell.

Stable Tearing and Buckling Responses of Unstiffened Aluminum Shells with Long Cracks

NASA Technical Reports Server (NTRS)

Starnes, James H., Jr.; Rose, Cheryl A.

1998-01-01

The results of an analytical and experimental study of the nonlinear response of thin, unstiffened, aluminum cylindrical shells with a long longitudinal crack are presented. The shells are analyzed with a nonlinear shell analysis code that accurately accounts for global and local structural response phenomena. Results are presented for internal pressure and for axial compression loads. The effect of initial crack length on the initiation of stable crack growth and unstable crack growth in typical shells subjected to internal pressure loads is predicted using geometrically nonlinear elastic-plastic finite element analyses and the crack-tip-opening angle (CTOA) fracture criterion. The results of these analyses and of the experiments indicate that the pressure required to initiate stable crack growth and unstable crack growth in a shell subjected to internal pressure loads decreases as the initial crack length increases. The effects of crack length on the prebuckling, buckling and postbuckling responses of typical shells subjected to axial compression loads are also described. For this loading condition, the crack length was not allowed to increase as the load was increased. The results of the analyses and of the experiments indicate that the initial buckling load and collapse load for a shell subjected to axial compression loads decrease as the initial crack length increases. Initial buckling causes general instability or collapse of a shell for shorter initial crack lengths. Initial buckling is a stable local response mode for longer initial crack lengths. This stable local buckling response is followed by a stable postbuckling response, which is followed by general or overall instability of the shell.

Parametric Analysis and Safety Concepts of CWR Track Buckling.

DOT National Transportation Integrated Search

1993-12-01

The report presents a comprehensive study of continuous welded rail (CWR) track buckling strength as influenced by the range of all key parameters such as the lateral, torsional and longitudinal resistance, vehicle loads, etc. The parametric study pr...

Wood tie track resistance characterization and correlations study

DOT National Transportation Integrated Search

1995-01-01

The work presented here is part of a major program to evaluate lateral buckling of continuous welded rail (CWR) tracks. The program to develop the technical information to support safety guidelines and specifications for track buckling prevention is ...

Thermal Buckling of Straight Tracks : Fundamentals, Analyses, and Preventive Measures

DOT National Transportation Integrated Search

1978-09-01

This report, written mainly for the practicing railroad engineer, explains the phenomenon of thermal buckling of straight tracks, shows how to analyze it, and describes measures for preventing it. Following an introductory discussion of track bucklin...

CFD analysis of multiphase blood flow within aorta and its thoracic branches of patient with coarctation of aorta using multiphase Euler - Euler approach

NASA Astrophysics Data System (ADS)

Ostrowski, Z.; Melka, B.; Adamczyk, W.; Rojczyk, M.; Golda, A.; Nowak, A. J.

2016-09-01

In the research a numerical Computational Fluid Dynamics (CFD) model of the pulsatile blood flow was created and analyzed. A real geometry of aorta and its thoracic branches of 8-year old patient diagnosed with a congenital heart defect - coarctation of aorta was used. The inlet boundary condition were implemented as the User Define Function according to measured values of volumetric blood flow. The blood flow was treated as multiphase: plasma, set as the primary fluid phase, was dominant with volume fraction of 0.585 and morphological elements of blood were treated in Euler-Euler approach as dispersed phases (with 90% Red Blood Cells and White Blood Cells as remaining solid volume fraction).

Euler polynomials and identities for non-commutative operators

NASA Astrophysics Data System (ADS)

De Angelis, Valerio; Vignat, Christophe

2015-12-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

The stability of cassette walls in compression

NASA Astrophysics Data System (ADS)

Voutay, Pierre-Arnaud

Much research into the behaviour of cold formed steel columns in the last decade has focused on channel sections undergoing local, distortional and overall buckling. Light gauge steel cassette sections are a particular form of channel section which offers an alternative form of load-bearing wall assembly for use in low-rise steel framed construction. Cassette wall sections possess wide and slender flanges so that, by including intermediate stiffeners in these wide flanges, a significant increase in the ultimate load capacity may be achieved. However, the introduction of intermediate stiffeners also increases the number of buckling modes (stiffener buckling) and, therefore complicates the behaviour and increases the risk of interactive buckling between these modes. The work undertaken in this thesis aims to clarify the behaviour of wide flanges in compression with and without intermediate stiffeners. In this research, the distortional mode of web and narrow flange buckling was inhibited by connecting the narrow flanges of the cassettes together at suitable intervals. "Generalised Beam Theory" (GBT), which allows the individual buckling modes to be considered individually and in predetermined combinations, provides a particularly good tool with which to analyse and understand the buckling behaviour of cassette sections with and without intermediate stiffeners. "Generalised Beam Theory" (GBT) is used throughout this work to determine the elastic buckling stress of the sections studied (simply supported stiffened plates, as well as cassette sections). Since the economic design of cold-formed steel sections requires the consideration of post- buckling behaviour, elastic buckling values are not directly comparable with design code values which are usually based on the concept of effective width. Therefore, finite element analysis with both material and geometric nonlinearity has also been carried out in order to obtain the ultimate strength in the critical mode or mode combination. Firstly the results of experimental test are analysed and their behaviour reproduced numerically. This serves to explain the test results and verify the numerical model. Confidence in modelling non-linear instability phenomena with the finite element method is acquired. Secondly, an initial parametric study was undertaken on the behaviour of cassette sections with and without intermediate stiffeners. This study considers the effect of the length and overall buckling on the behaviour of cassette sections, the effect of load eccentricity and the effect of the rotational restraint given by the web to the stiffened wide flange. A second parametric study including 96 specimens was undertaken next. This study considered the effect of the number (up to three intermediate stiffeners) and sizes of intermediate stiffeners on slender flanges with a slenderness ratio between 150 ≤ w/t ≤ 600. A wide range of geometries was studied covering single and interactive buckling modes. Comparison of the ultimate strength obtained from finite element analysis with the ultimate strength obtained using the effective width approach of modem design codes such as Eurocode 3 part 1.3 (1996) and NAS (North American specification (2001)) was then possible. By integrating the stress distribution over the length of the specimen, the stiffened wide flange can be isolated from the rest of the section (webs and narrow flanges). Design procedures tor plate elements incorporating one or two intermediate stiffeners under compressive load are given in Eurocode 3; Part 1.3. However, cassette sections, which have wider and more slender flanges than typical sheeting and decking, are increasingly being used in practical construction. For such cases, the design procedures in Eurocode 3 are less well founded. An improvement of the Eurocode 3 procedure dealing with intermediate stiffeners is proposed and validated for one, two or three stiffeners. Throughout the work, simple expressions suitable for design calculations are presented. Modern design codes as well as Direct Strength Method are evaluated in the light of findings of this work and wherever possible suggestions for improvements are made.

Transonic flow analysis for rotors. Part 3: Three-dimensional, quasi-steady, Euler calculation

NASA Technical Reports Server (NTRS)

Chang, I-Chung

1990-01-01

A new method is presented for calculating the quasi-steady transonic flow over a lifting or non-lifting rotor blade in both hover and forward flight by using Euler equations. The approach is to solve Euler equations in a rotor-fixed frame of reference using a finite volume method. A computer program was developed and was then verified by comparison with wind-tunnel data. In all cases considered, good agreement was found with published experimental data.

Computation of transonic viscous-inviscid interacting flow

NASA Technical Reports Server (NTRS)

Whitfield, D. L.; Thomas, J. L.; Jameson, A.; Schmidt, W.

1983-01-01

Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points. Previously announced in STAR N83-17829

Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations

NASA Technical Reports Server (NTRS)

Darmofal, David L.

1998-01-01

An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.