Three-dimensional biaxial post-buckling analysis of heterogeneous auxetic rectangular plates on elastic foundations by new criteria

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 C1-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.