Buckling analysis of thick plates on biparametric elastic foundation: a MAEM solution

The meshless analog equation method, a purely meshless method, is applied to the buckling analysis of moderately thick plates described by Mindlin's theory and resting on two-parameter elastic foundation (Pasternak type). The method is based on the concept of the analog equation, which converts the three governing second-order partial differential equations (PDEs) in terms of the three plate displacements (transverse displacement and two rotations) into three substitute equations, the analog equations. The analog equations constitute a set of three uncoupled Poisson's equations under fictitious sources, which are approximated by multi-quadric radial basis functions (MQ-RBFs) series. This enables the direct integration of the analog equations and allows the representation of the sought solution by new RBFs series. These RBFs approximate accurately not only the displacements but also their derivatives involved in the governing equations. Then, inserting the approximate solution in the original PDEs and in the associated boundary conditions (BCs) and collocating at mesh-free nodal points, a generalized eigenvalue problem is obtained, which allows the evaluation of the buckling load and the buckling modes. The studied examples demonstrate the efficiency of the presented method that is its ability to solve accurately and in a straightforward way difficult engineering problems.