Buckling of rectangular FSDT plates resting on orthotropic foundation by mixed FEM

Abstract

This study presents a mixed type finite element procedure for the linear buckling analysis of moderately thick plates lying on orthotropic elastic foundation. Kinematical expressions are due to the Mindlin plate theory and von Karman strains. The force intensity exerted by orthotropic foundation on the plate is reflected according to the Pasternak model. Material directions of the foundation coincides with the global axes of the plate. The first variation of the systems nonlinear functional is obtained by following the Hellinger-Reissner principle. This expression is linearized according to the incremental formulation, thus the system and geometric matrices of the problem are obtained. Finite element equations are constructed by discretizing the plate domain with four noded isoparametric quadrilateral elements. After a static condensation procedure, force and couple type field variables are removed from the equations in order to reduce the problem into the solution of a standard Eigen-value system. Firstly, a convergence and comparison study is presented to verify the formulation and numerical procedure. The effects of foundation and plate parameters on the critical buckling loads are investigated.