3D energy-based finite element elasticity approach for shear postbuckling analysis of functionally graded plates on elastic foundations

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.