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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]

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]

Post-buckling behavior of the auxetic (with negative Poisson ratio) structures has not been investigated so far, especially for structures fabricated from heterogeneous materials. In the present research, effects of auxeticity of the materials on uniaxial and biaxial post-buckling behaviors of the FGM plates are investigated using the exact three-dimensional theory of elasticity, instead of the approximate plate theories. Furthermore, influence of the Winkler-type elastic foundation on the post-buckling responses of the plate is investigated. In this regard, a full compatible C 1 -continuous 3D Hermitian element that in contrast to the conventional elements, satisfies the stress continuity condition at the mutual nodes of the adjacent elements, is employed to solve the governing equations of the post-buckling. The full Green’s strain tensor is employed instead of using the approximate von Karman strain–displacement expressions to enable tracing behavior of the plate for quite large deformations. The governing system of equations is solved by a condensation-based incremental under-relaxation Newton–Raphson procedure, due to sensitivity and high numerical compliance of the resulting highly non-linear finite element system of equations. Furthermore, new criteria are proposed for tracing the post-buckling behavior. Results reveal that the elastic foundation significantly affects the post-buckling mechanism and deformation pattern and post-buckling behavior of the plate is enhanced drastically by more negative Poisson’s ratios. [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]

Impact analysis of plates with either elastic foundations or partially supported edges has not been accomplished, even for the homogeneous isotropic plates. In the present paper, eccentric low-velocity impact analysis of a functionally graded plate with fully/partially supported edges and a Winkler-type elastic foundation is performed. In contrast to the available researches, stiffness of the underneath layers is also taken into account in determination of the apparent stiffness of the contact region, employing Mori–Tanaka micromechanics-based model instead of the traditional rule of mixtures. The governing equations are derived based on the principle of minimum total potential energy and the first-order shear-deformation plate theory. Some of the included novelties are: modification of the contact law, incorporation of effects of the elastic foundation, considering the material heterogeneity and partially supporting the edges, and proposing various semi-analytical and (Galerkin-type) numerical solutions. Numerical time integration schemes are used to trace time variations of the responses. A sensitivity analysis is performed to investigate influences of the specifications of the plate and the indenter, the eccentricity, and the supporting length ratio on time histories of the indentation and contact force. [ABSTRACT FROM AUTHOR]

Based on the three-dimensional theory of elasticity, a comprehensive stress analysis is performed for the rotating bidirectional functionally graded thick axisymmetric circular/annular plates, for the first time. The plate may be subjected to arbitrary distributions of the transverse load and various mixed (Dirichlet-type and Neumann-type) edge conditions. Furthermore, the circular plate may be supported by a nonuniform elastic foundation or a rigid substrate. In contrast to the very limited works presented for the rotating functionally graded circular plates so far, the transverse flexibility and the transverse stress components are considered and studied in the present research. Since finite element and boundary element techniques, due to their integral natures, cannot adequately trace abrupt changes of the quantities, a second-order point collocation method with forward–backward schemes is adopted to solve the system of the governing and boundary conditions. Effects of the distributions of the various material properties (Poisson’s ratio, Young’s modulus, and mass density), angular velocity, foundation compliance, and edge conditions are evaluated. Results reveal that radially graded or transversely graded material properties significantly affect distribution and magnitude and location of the extrema of the stress components and the lateral deflections and orientation of the general neutral surface of the plate. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, bending and stress analyses of two-directional functionally graded (FG) annular plates resting on non-uniform two-parameter Winkler-Pasternak foundations and subjected to normal and in-plane-shear tractions is investigated using the exact three-dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two-directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material properties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction: linear, parabolic, and sinusoidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters (e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions) is carried out. The results are reported for the first time and are discussed in detail. [Copyright &y& Elsevier]

Three-dimensional bending and stress analyses of the rotating two-directional functionally graded annular/circular plates or disks have not been accomplished so far. This task is performed in the present paper, employing a finite element formulation with a C1- continuity. Therefore, both transversely graded and radially-graded plates may be analyzed as special cases of the present research. Distribution of the transverse loads as well as coefficients of the elastic foundation may be non-uniform. Mixed stress-based and displacement-based edge conditions are considered to cover many practical applications. Compatible Hermitian elements are employed to develop a consistent formulation and avoid jumps in the stress components at the elements interfaces. In contrast to the very limited works presented for the rotating functionally graded circular plates so far, the transverse flexibility and the transverse stress components are also considered in the present research. Finally, influences of the material properties distribution, angular speed, geometric parameters, and the elastic foundation on distributions of the stress and displacement components are investigated for a variety of edge and boundary conditions and some design criteria are extracted. [ABSTRACT FROM AUTHOR]

Abstract: Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin''s plate theory. The complex modulus approach in combination with the elastic–viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties. [Copyright &y& Elsevier]