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In the present article, interactions of the effects of the interfacial bond's irregularity, shear and normal tractions, and flexible edge supports on the distributions of the lateral deflections and stress of the laminated/sandwich circular plates are investigated, for the first time. To widen the applicability of the research, the layers are assumed to be functionally graded ones. A layerwise model that unlike the traditional layerwise theories, not only guarantees continuity of the transverse stress components but also takes into account the discontinuity of all of the displacement components at the imperfect or damaged bonds between layers is proposed. The governing equations are derived based on the principle of minimum potential energy and solved based on the Maclaurin transformation analytical method. Results are enhanced through a three-dimensional elasticity correction. Results reveal that while compliance of the edge restraint has a significant role on the magnitude of the global displacements, amount of the discontinuities in the displacement components at the mutual interfaces is mainly affected by both the local and global (mean) bond stiffness. Furthermore, while both the compliance of the elastic edge restraint and irregularity of the bonds increase the stress and displacement components, each combination of these parameters may specifically lead to magnifications of the stresses in a particular layer of the plate. [ABSTRACT FROM AUTHOR]

This paper is devoted to the investigation of the effects of the realistic tension–compression asymmetry and anisotropy of phase transformations of shape memory alloy wires embedded in composite sandwich plates with auxetic cores on the resulting nonlinear vibrations. A third-order zigzag description of the displacement field that takes into account the thickness variations of the flexible core and a novel three-dimensional dynamic elasticity stress and displacement correction is proposed and employed. The governing equations are extracted based on Hamilton's principle and solved using an iterative finite element procedure. A comprehensive phase transformation algorithm and a constitutive model that are capable of accurately tracking the nested hysteresis loops and sub-loops and reverse loading of the shape memory alloy are proposed, considering the tension–compression anisotropy. Interactions of the core compliance, auxeticity, and especially, the transformations anisotropy on the dynamic responses are studied numerically and three-dimensional plots are presented for distributions of the martensite volume fraction. Results show that the realistic tension–compression anisotropy of the shape memory alloy material leads to results that are quite different from those based on the assumption of the symmetry of the material properties and significantly increases the differences between the damping roles of the shape memory alloy wires of the upper and lower layers of the sandwich plate. [ABSTRACT FROM AUTHOR]

In the present paper, the shear post-buckling behavior of the FGM rectangular plates is analyzed, for the first time. Furthermore, effects of the elastic foundation on the post-buckling deformation/distortion patterns and strengths are investigated. The exact energy-based 3D theory of elasticity is implemented through incorporation of the general form of Green’s strain tensor. A fully consistent 3D Hermitian element with up to the second-order mixed derivatives continuity is utilized to satisfy continuity of the stress and distortion components at the mutual nodes of the adjacent elements. The post-buckling equilibrium paths are traced using an arc-length solution scheme in conjunction with the modified Newton–Raphson method. A comprehensive sensitivity analysis is accomplished to evaluate effects of the heterogeneity index, elastic foundation stiffness, aspect ratio, and the considered two types of practical boundary conditions on the post-buckling deformation patterns, mode jumping, and equilibrium paths. Results obtained based on post-buckling observations of properly adopted reference points reveal that mode jumping and larger distortions may occur due to increasing the post-buckling loads, the elastic foundation leads to larger number of the local deformation regions, and the buckling strengths reduce remarkably when two opposite edges are clamped. [ABSTRACT FROM AUTHOR]

Static and free vibration analyses of plates with circular holes are performed based on the three-dimensional theory of elasticity. The plates are made of a functionally graded material (FGM), and the volume fractions of the constituent materials vary continuously across the plate. The effective properties of the FGM plate are estimated by using the Mori-Tanaka homogenization method. A graded finite element method based on the Rayleigh-Ritz energy formulation is used to solve the problem. Effects of different volume fractions of the materials and hole sizes on the behavior of FGM plates under uniaxial tension are investigated. Natural frequencies of a fully clamped FGM plate with a circular cutout are derived. The results obtained are compared with available experimental data. [ABSTRACT FROM AUTHOR]

Longitudinally varying the material properties may be an adequate optimization solution when there are restrictions in varying cross sections of the load carrying elements but leads to distorted and variable length buckling and post-buckling deformation waves. In the present paper, uniaxial and biaxial post-buckling behaviors of the longitudinally graded plates are investigated. Neither post-buckling nor even buckling of the longitudinally graded plates have been studied so far. Moreover, effects of the elastic foundation that significantly alter the post-buckling deformations and strength of the plate, are studied. Due to occurrence of large deformations in the post-buckling region, the exact 3D elasticity theory is employed here instead of the approximate plate theories. Furthermore, the full form of Green’s strain tensor is adopted. To establish a stress field that is continuous at the mutual nodes of the adjacent elements, a C 1 -continuous 3D Hermitian element is employed to discretize the plate. The nonlinear post-buckling equilibrium equations are solved by Crisfield–Ramm arc-length method in conjunction with the modified Newton–Raphson technique. Results show that heterogeneity of the material properties may lead to abrupt deflection decreases or even reversals and the elastic foundation leads to increases in both the buckling strength and number of the deformation waves. [ABSTRACT FROM AUTHOR]

By using a three-dimensional (3D) space-frame-like model, a molecular mechanics (MM) approach is proposed for determination of the buckling loads, effective Young's modulus and Poisson's ratio of the nanosheets, using a proper unit cell. The governing equations are derived based on the 3D kinematics of deformations and the principle of minimum total potential energy. The unit-cell-based results are employed for the space-frame-like finite element model of the nanosheet. The nonlinear MM equations are solved by representing bonds of the boron nitride nanosheet (BNNS) by beam elements to extract the local characteristics. These properties are employed in modelling of the nanosheet, as a space-frame-like finite element structure. The force field constants are chosen according to the Morse, AMBER, UFF and DREIDING models to determine the buckling strength, and effective Poisson's ratio and in-plane rigidity of the whole graphene and BNNSs. Silicon Carbide nanosheets are analysed based on different force constants. These results are concordant with the results available in the literature. The comparisons reveal that the DREIDING force field usually gives the most accurate predictions. [ABSTRACT FROM AUTHOR]

In the present paper, a complicated and general problem of a functionally graded porous variable thickness circular plate subjected to non-axisymmetric and non-uniform shear and normal tractions and a magnetic actuation, and supported by a non-uniform Kerr elastic foundation is analyzed. Although such a combination of complexities may rarely be observed in the practical applications, the developed solution may identically be employed for many practical problems, as special cases. The governing equations are derived based on the three-dimensional theory of elasticity instead of using the approximate plate theories. The solution is proposed based on the differential quadrature and state space vector techniques in the radial and thickness directions, respectively. A comprehensive parametric study is presented to evaluate effects of the material, loading, boundary, and elastic foundation specifications on the resulting displacement, stress, Lorentz force, electromagnetic stress, and magnetic perturbation quantities. [ABSTRACT FROM AUTHOR]

While the 3D elasticity and the available local and zigzag theories encounter inaccuracies for very thin plates, results of the global theories become unreliable for thick plates with severe transverse variations in the material properties. In the present research, a quadratic finite element global–local sandwich plate theory with elasticity correction (stress recovery) is proposed for static stress and displacement analysis of sandwich plates with orthotropic face sheets and single or dual cores. Since the transverse shear stresses are derived based on the three-dimensional theory of elasticity, the continuity condition of the transverse shear stresses is satisfied at the interfaces between the layers, a priori. The presented theory not only leads to higher accuracies in comparison to the available high-order zigzag theories in some cases (especially, for soft or dual cores) but also it is computationally more economic. Results show that the results of the available zigzag and global–local theories may encounter inaccuracy problems not only for huge numbers of the sub-layers, but also for small numbers of the orthotropic layers. [ABSTRACT FROM AUTHOR]

Only simple tractions and material properties have been considered in derivation of the available shear correction factors, e.g., they have been developed for homogeneous isotropic plates and/or assuming that no shear tractions are imposed on the top or bottom surfaces of the plate. In the present research, the more general case of an annular functionally graded plate subjected to both normal and shear non-uniform tractions and/or resting on a non-uniform Winkler–Pasternak elastic foundation is considered. Instead of using approximate numerical methods, the solutions are derived using the analytical Taylor׳s transformation method. Instead of using the traditional constitutive-equation-based approach, the most accurate equilibrium-equation-based 3D elasticity approach is used. To enhance modeling of variations of the material properties, Mori–Tanka micromechanical-based model is chosen instead of the traditional rule of mixtures. The proposed analytical correction factor and the resulting elasticity-based formulation are evaluated for both the modal and the stress analyses. Results reveal that the resulting accuracies are comparable to those of the elasticity theory. [ABSTRACT FROM AUTHOR]

Abstract: Three-dimensional buckling analysis of the functionally graded plates has not been investigated under non-uniform in-plane compressive loads so far. The only available work in this field has been performed based on the first-order shear deformation theory, employing the simple rule of mixtures. In the present paper, a non-linear three-dimensional energy-based elasticity analysis is developed for buckling investigation of functionally graded plates subjected to non-uniform in-plane compressions. The comparative studies performed in the present paper reveal that the rule of mixtures is generally inappropriate for determination of the effective material properties. For this reason, a micromechanics-based model is used instead. In contrast to the common displacement-based numerical or semi-analytical elasticity analyses (with C 0-continuity), present formulations are C 2-continuous due to using the proposed 3D cubic B-spline element. Buckling analysis is accomplished through a two-step procedure wherein the prebuckling stresses are determined first. A non-linear weighted-residuals-based finite element solution is used. The buckling load associated with each of the adopted 8 types of the load distribution patterns is detected based on a generalized geometric stiffness concept. Various and comprehensive parametric studies are accomplished and various boundary conditions are considered to extract more precise conclusions. [Copyright &y& Elsevier]

Abstract: In the present paper, a global–local theory with three-dimensional elasticity correction is developed for stress and deformation analysis of the multilayered and sandwich plates. The governing equations are derived based on the principle of minimum potential energy. The coupled governing equations are solved based on a finite element procedure uses the second-order Lagrangian elements and a Galerkin-type formulation. Results of this theory are accurate for both thin and thick plates. The transverse shear stresses are extracted based on the three-dimensional theory of elasticity. Thus, the continuity of the interlaminar transverse shear stresses is satisfied a priori. The proposed finite element formulation is implemented using MATLAB software. Results revealed that, while the accuracy of the present theory is comparable to that of the three-dimensional theory of elasticity and sometimes (e.g., when a very soft core is used) is higher than the high-order zigzag theories, the presented solution approach is computationally more economic. Finally, a comprehensive parametric study including evaluating the influences of the lamination scheme, number of layers, plate aspect ratio, side-to-thickness ratio, and material properties variations on the in-plane stresses, transverse shear stresses, and displacement components is performed. [Copyright &y& Elsevier]

Abstract: In the present paper, shear buckling analysis of the orthotropic heterogeneous FGM plates is investigated for the first time. Moreover, influence of the Winkler-type elastic foundation is considered. The material properties are assumed to have in-plane orthotropy and transverse heterogeneity. The most accurate approach, i.e., the three-dimensional elasticity is employed instead of using the approximate plate theories. In contrast to all of the available displacement-based buckling analyses that have employed C0-continuous commercial finite element codes or semi-analytical methods, present formulations are C2-continuous due to using the proposed 3D cubic B-spline element. Results are derived based on principle of minimum potential energy and a non-linear finite element procedure utilizing a Galerkin-type 3D cubic B-spline solution algorithm. Buckling loads are detected based on a generalized geometric stiffness concept. In this regard, effects of both the prebuckling and buckling states are considered. To present a better imagination and more detailed discussions, details of the buckling mode shapes and the foundation interaction are discussed for plates with simply-supported edges. In addition, the more practical free and clamped edge conditions are also considered. [Copyright &y& Elsevier]

Abstract: Present paper is devoted to stress and deformation analysis of functionally graded annular sandwich plates subjected to non-uniform normal and/or shear tractions. In spite of its wide applications, analytical stress analysis of plates under shear or combinations of normal and shear tractions has not been performed so far, especially for the sandwich plates. Furthermore, it is the first time that a power solution is developed for the annular functionally graded sandwich plates. The governing equations are derived based on principle of minimum potential energy and a double superposition zigzag theory. The transverse shear stresses are determined based on the three-dimensional theory of elasticity. The resulting governing equations may cover symmetric and asymmetric layups, various boundary conditions, and arbitrary non-uniform tractions on the top and bottom face sheets. The obtained results are verified by comparing them with results of the three-dimensional theory of elasticity. While the present approach is accurate, it is computationally more economic than the three-dimensional elasticity approach. Finally, a parametric study including evaluating effects of various parameters on the stress and displacement distributions of the annular sandwich FGM plates is accomplished. [Copyright &y& Elsevier]

Free vibration of functionally graded annular sandwich plates resting on Winkler-type elastic foundations is investigated based on a zigzag global-local plate theory and a finite Taylor's transform whose center is located at the outer edge. Material properties of each layer may be graded in the transverse direction according to a power law. It is the first time that a global-local theory is combined with a layerwise analytical solution for analysis of the annular functionally graded sandwich plates. Various edge conditions are considered for the inner and outer edges. A parametric study including evaluating effects of the material properties distributions of the core and face sheets, symmetric and asymmetric layups, thickness to radius ratio of the plate, inner to outer radius ratio, coefficient of the elastic foundation, and the edge conditions on vibration behavior of the annular plate is carried out. Accuracy of the employed sandwich plate theory and the presented analytical solution are verified by comparing present results with those of the three-dimensional theory of elasticity extracted from ABAQUS software. [ABSTRACT FROM AUTHOR]

Abstract: In the present research, transient and forced dynamic responses of annular sandwich plates with functionally graded face sheets or cores are investigated by an analytical zigzag-elasticity approach, for the first time. The time-dependent partial differential governing equations are obtained based on principle of minimum total potential energy and solved through replacing the spatial derivatives by means of a series solution whose center is located at the outer radius of the plate and discretizing the time domain by the fourth-order Runge–Kutta numerical time integration scheme. The interlaminar continuity condition of the transverse shear stresses is satisfied a priori. The zigzag plate theory serves as a predictor approach and the three-dimensional theory of elasticity as a corrector technique. Since for the subject under investigation exact elasticity solutions do not exist, accuracy and efficiency of the proposed modeling and solution procedures are verified by comparing present results with high-fidelity finite element solutions obtained using the ABAQUS commercial code. Results reveal that using functionally graded face sheets or cores with transition variations of the material properties may lead to very smooth through-thickness stress distributions and removing the interlaminar jumps in the transverse distribution of the radial stresses. Consequently, some of the failure modes may be prevented at the interfaces between the layers. [Copyright &y& Elsevier]

Abstract: Buckling of the orthotropic FGM plates has not been investigated so far. In the present paper, a highly accurate nonlinear three-dimensional energy-based finite element elasticity formulation is developed for buckling investigation of anisotropic functionally graded plates with arbitrary orthotropy directions. The material properties are assumed to have in-plane orthotropy and transverse heterogeneity. The formulation and results cover uniaxial compression and compression and tension–compression biaxial loading conditions. The governing equations are developed based on the principle of minimum total potential energy and solved based on finite element orthogonal integral equations. To achieve most accurate results, a full compatible Hermitian element with 168 degrees of freedom, which satisfies continuity of the strain and stress components at the mutual edges and nodes of the element a priori, is employed. A variety of loading combinations, orthotropy directions, and aspect ratios is considered and discussed in the results section to draw practical conclusions. Results reveal that when the external loads are exerted in the principal directions of the materials, higher strengths may be achieved. [Copyright &y& Elsevier]

Abstract: In the present paper, a three-dimensional elasticity approach is employed to investigate buckling of heterogeneous functionally graded plates under biaxial compression, shear, tension-compression, and shear-compression load conditions. In this regard, a formulation that employs a full compatible three-dimensional Hermitian element with 168 degrees of freedom and guarantees continuity of the strain and stress components is used. It is known that all of the available famous commercial finite element softwares and the proposed series solutions satisfy continuity conditions of the displacement rather than the stress components. Buckling occurrence is detected based on checking both the instability onset and equilibrium criteria. Results are extracted based on a Galerkin-type orthogonality. Therefore, they are more accurate than those obtained based on the traditional Ritz method. The presented three-dimensional finite element analysis and the extracted results are quite new. A vast variety of results including results of biaxial compression, compression-tension, shear, and shear-compression load cases is considered and discussed in detail. [Copyright &y& Elsevier]

On the basis of the three-dimensional theory of elasticity, a graded finite element method capable of modeling static and dynamic behaviors of elliptical plates made of functionally graded materials (FGMs) subjected to uniform pressure is developed. In the present paper, two different material properties distributions are considered. For the dynamic analysis, the effective through-the-thickness continuous material properties distribution of the FGM (which is assumed to be composed of ceramic and metallic constituents) is determined based on Mori-Tanaka homogenization technique. The three-dimensional graded finite element formulation is derived based on the principle of minimum potential energy and Rayleigh Ritz method. To solve the time-dependent equations, Newmark's direct integration method is employed. To present the efficiency of the present work, several numerical examples are included. Since similar results are not available in the literature, results of the present formulations are verified by comparing them with available ones of a homogenous elliptical plate. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, a consistent power series solution is proposed for dynamic behaviors analysis of circular sandwich plates with functionally graded face sheets/cores, for the first time. The proposed solution is a combination of the finite Taylor’s transform and the fourth-order Runge–Kutta procedure. The extension-bending coupling and the higher-order inertias are considered in the present research. The formulation guarantees continuity of the transverse stress components at the interfaces between layers. Another novelty is proposing a zigzag formulation whose results are corrected on the basis of the dynamic three-dimensional theory of elasticity. An interesting discussion for defining explicit/implicit layerwise shear correction factors is also presented. Furthermore, results reveal that using functionally graded face sheets or cores with transition variations of the material properties may lead to very smooth through-the-thickness stress distributions. Consequently, some of the failure modes may be prevented at the interfaces between the layers. [Copyright &y& Elsevier]

Abstract: In the present paper, characteristics of low/medium velocity impact responses of thin nanocomposite plates impacted by rigid spherical indenters are investigated. The plates may either have lateral deflections or resting on rigid substrates. It is obvious that for thin plates with transverse mobility subjected to impact with rigid indenters, the actual indentation value is much less than that predicted by the traditional Hertz-type laws. A modified contact law that takes into account effects of the plate thickness and boundary conditions is employed in the present research. The variational iteration method is employed to develop a closed form semi-analytical solution. In comparison with the available numerical solution procedures, convergence of the present solution scheme is much higher and the solution algorithm converges unconditionally. Therefore, novelties may be found in the treated subject, modeling procedure, and solution algorithm. Comparisons made with results of the available numerical procedures, reveal the efficiency and accuracy of the presented solution algorithm. [Copyright &y& Elsevier]

Abstract: The available semi-analytical solutions for bending and stress analysis of the composite/sandwich plates have mainly been proposed for rectangular plates with specific material properties and edge conditions. In the present paper, axisymmetric bending and stress analysis of circular functionally graded sandwich plates subjected to transversely distributed loads is performed. The governing equations are derived based on an elasticity-equilibrium-based (rather than the traditional constitutive-equations-based) zigzag theory. Therefore, both ideas of using the local variations of the displacement field and satisfying a priori the continuity conditions of the transverse stresses at the layer interfaces for predicting the global and local responses of the sandwich circular plates are employed, for the first time. The resulting governing equations are then solved by a semi-analytical Maclaurin-type power-series solution. Each layer of the plate may be made of functionally graded materials. The transverse shear and normal stresses are determined based on the three-dimensional theory of elasticity. Comparisons made with results of a numerical finite element code (ABAQUS software) reveal that even for thick sandwich plates with soft cores, accuracy of results of the present formulation is comparable with that of the three-dimensional theory of elasticity. [Copyright &y& Elsevier]

In the present paper, the differential transformation method is employed to develop a semi-analytical solution for free vibration and modal stress analyses of two-dimensional functionally graded circular plates resting on two-parameter elastic foundations. Simultaneous variations of the material properties in the radial and transverse directions are described by a general function. Some comprehensive sensitivity analyses are performed, and the natural frequencies and the modal stresses are extracted for free, simply supported, and clamped boundary conditions and different combinations of the geometric, material, and foundation parameters. Therefore, very complex combinations of the material properties, boundary conditions, and parameters of the elastic foundation are considered in the present semi-analytical solution approach. Thus, many novelties are included in the present research. Comparisons made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. Moreover, the paper treats some interesting problems, for the first time. [ABSTRACT FROM AUTHOR]

Discusses a study which applied the three-dimensional theory of elasticity in curvilinear coordinates to investigate the dynamic buckling of an imperfect orthotropic circular cylindrical shell under mechanical loads and thermal loads. Formulation of the problem; Equations of motion; Numerical solution and buckling criteria; Conclusions.

In this study, effects of the presence of vacancy defects in a hexagonal nanosheet on Young's modulus, effective Poisson's ratio, buckling loads and buckling modes, regardless of its constituent atoms, have been studied. Explicit expressions are proposed in order to define these characteristics considering a defect distribution term as a modifying parameter. Molecular structural mechanics concepts and FEM simulation are utilized in order to obtain these expressions and results. Different sizes and shapes of defects as well as random distribution of vacancies have been considered. The results for perfect Boron Nitride, Silicon Carbide and graphene nanosheet as well as defected Boron Nitride nanosheets are in a good agreement with those available in literature. Linear degradation behavior of Young's modulus and linear increase of effective Poisson's ratio in terms of defects distribution are observed in obtained results. A second order behavior is also observed in decreasing buckling load in terms of increasing vacancy distribution. Moreover, buckling mode characteristics due to the percentage of defects distribution has been investigated. [ABSTRACT FROM AUTHOR]

Abstract: This study deals with the dynamic analysis of a continuous SMA hybrid composite beam subjected to impulse load, taking into account the instantaneous phase transformation at any time and also material nonlinearity effects, for every point along the beam for the first time. Due to the phase transformation, the equations of motion are coupled with the phase transformation’s kinetic equations of SMA wires which make the problem more complicated. The one-dimensional constitutive equation of SMA proposed by Brinson is employed to model the pseudoelastic behavior of SMA wires. A transient finite element along with an iterative incremental method is employed to investigate the dynamic response of pseudoelastic SMA hybrid composite beam and also full SMA beam. The Newmark time integration method is used in solving the dynamic finite element equations. Results show the efficiency of the proposed model and the relevant solution algorithm. Furthermore, damped response of SMA hybrid composite beam and full SMA beam is observed, which is due to the hysteresis behavior of SMAs. In the case of full SMA beam, the phase transformation is considered for every point along the length and also through the thickness of the beam. A result shows that the through-the-thickness variation of the stress is nonlinear due to the material nonlinearity. Finally, several numerical examples upon the effect of amplitude of the loading, different boundary conditions and thermal loading have been analyzed. [Copyright &y& Elsevier]