Hermite-type PIM approach for buckling analysis of L-shaped FGM thin plates

Abstract

This work intends to elaborate a Meshfree approach of a thin plate made by a mixture of a ceramic metal Functionally Graded Material (FGM), which utilises meshless methods PIM and HPIM for the nonlinear buckling analysis. The Classical Plate Theory (CPT) is utilised here to introduce the plate kinematics. The nonlinear static equilibrium differential equations of the plate and related boundary conditions are laid through the Stationary Potential Energy principle. The in-plane displacements, the transverse displacement and its derivatives are estimated successively by PIM method and HPIM in order to find the discrete weak form. By transforming the obtained equations to an eigenvalue problem, one can get the critical loads resulting from buckling and the associated mode shapes. Examples of L-shaped FGM plates subjected to biaxial in-plan loadings are explored to demonstrate the correctness of the proposed approach. This is done by comparing the obtained results with those calculated using FEM and some published data in the literature.