A mesh-free Hermite-type approach for buckling analysis of functionally graded polygonal thin plates

Abstract

This work aims to establish a developed Meshless process which uses the point interpolation and the Hermite-type point interpolation methods for instability analysis of functionally graded material (FGM) thin polygonal plates. The structure’s material characteristics should gradually change according to the thickness direction. The minimization principle is used to obtain the governing nonlinear static equilibrium differential equations and related boundary conditions. To obtain the discrete weak form, point interpolation method (PIM) is used to approximate membrane components, while Hermite-type point interpolation method (HtPIM) ones are used for flexural components. The critical buckling loads and the associated eigenmodes are obtained by transforming the resulting equations into an eigenvalues problem. To evaluate the validity and effectiveness of the presented methodology, several examples concerning specimens of FGM rectangular and polygonal plates of various geometric planar shapes (L, T and C) subjected to uniaxial and biaxial in-plan loads are studied. The outcomes are contrasted with those of the finite element approach and with some data from the literature. Based on the analysis of the comparative study, the proposed methodology presents a very good agreement with the validated and previously published numerical results.