Buckling Analysis of Functionally Graded Sandwich Plates Resting on an Elastic Foundation and Subjected to a Nonuniform Loading

A buckling analysis of functionally graded plates of a complex form resting on an elastic foundation and subjected to an in-plane nonuniform loading is performed by the R-functions method for the first time. The mathematical formulation of the problem is presented within the framework of the classical laminate plate theory. The plates considered consist of three layers. The middle layer (core) is ceramic or metal, a face layers are fabricated of functionally graded materials (FGMs). The power-law distribution of volume fraction of constituents is used to compute the effective material properties of FGM layers. The approach proposed and the software developed consider the heterogeneous subcritical state of the plates. First, the problem of in-plane elasticity problem is solved, and then the stability problem is considered. To solve both the problems, the Ritz method combined with the R-functions theory is used. The method proposed and the software developed are verified by comparing the buckling loads of square plates subjected to a nonuniform loading. The critical loads for sandwich FG plates of a complex geometry in a nonuniform edge compression are calculated. The effects of boundary conditions, the scheme of layer arrangement, and the type of FGM on the critical load are studied.