Nonlinear thermal buckling analyses of functionally graded plates by a mesh-free radial point interpolation method

Abstract

This study intends to analyze nonlinear buckling behavior of functionally graded (FG) plates under thermal loading by a mesh-free method. The buckling formulation is derived based on the higher-order shear deformation plate theory in which the von Kármán large deflection assumption is employed. An improved mesh-free radial point interpolation method (RPIM) which incorporates the normalized radial basis function capable of building the shape functions without any fitting parameters is presented and utilized to scrutinize the buckling responses. The nonlinear equations are solved by the modified Newton–Raphson iterative technique. Verification of the improved RPIM is implemented by simulating several numerical examples available in the literature and comparing the outcomes with the analytical results. Detailed parametric studies demonstrate that the improved mesh-free RPIM can effectively predict the thermal buckling responses of FG plates, and the volume fraction, plate length-to-thickness ratio, aspect ratio, boundary condition have considerable effects on the critical buckling temperatures of FG plates subjected to various types of temperature variations through the thickness.