Buckling of Rectangular Functionally Graded Material Plates under Various Edge Conditions

Abstract

In the present paper, the buckling problem of rectangular functionally graded (FG) plate with arbitrary edge supports is investigated. The present analysis is based on the classical plate theory (CPT) and large deformation is assumed for deriving stability equations. The plate is subjected to bi-axial compression loading. Mechanical properties of FG plate are assumed to vary continuously along the thickness of the plate according to different volume of fraction functions of constituents. These functions are assumed to have power law distributions. The displacement function is assumed to have the form of double Fourier series, of which derivatives are legitimized using Stokes' transformation method. The advantage of using this method is the capability of considering effect of any possible combination of boundary conditions on the buckling loads. The out-plane displacement distribution is assumed using Fourier Sinus Series. This results in a general eigenvalue problem which can be used for evaluating the buckling load under different edge conditions, plate aspect ratios and various volume fraction functions. For generality of problem, plate is elastically restrained using some rotational and translational springs at four edges. Some numerical examples are presented and compared the to numerical results of finite element method using ABAQUS and other researchers' results to validate the proposed method. It has been shown that there is good agreement between them