Buckling instabilities of thick elastic plates subjected to in-plane stresses

Abstract

Buckling instabilities of a simply supported thick elastic plate subjected to in-plane stresses are studied. Taking into account the effects of shear deformations and thickness changes, buckling loads and buckling displacement modes of thick plates are obtained. Buckling of thick plates can occur in the (x α, x 3)-planes involving either in-plane or out-of-plane mode shapes with arbitrary integer numbers r and s of wavelengths. The same asymptotic buckling load appears at higher displacement modes with wrinkling instabilities for the in-plane and out-of-plane problems. Based on the power series expansion of displacement components, a set of fundamental equations of a two-dimensional higher-order plate theory is derived through the principle of virtual displacements. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a thick plate. The convergence properties of the buckling loads for the in-plane and out-of-plane problems of a simply supported square plate are examined in detail. It is noticed that the present approximate theories can predict the buckling loads of an extremely thick plate more accurately compared to other refined theories and classical plate theory.