Buckling analysis of functionally graded sandwich thin plates using a meshfree Hermite Radial Point Interpolation Method

This paper introduces an innovative mesh-free computational approach for simulating problems with geometric nonlinearity, focusing on the buckling analysis of thin plates. Addressing significant deformations, the study formulates governing partial differential equations based on Kirchhoff's plate theory and discretizes them using the Galerkin method. To tackle the complexities of this problem, which demands higher-order continuity in shape functions and accommodates both Dirichlet and Neumann boundary conditions, the research extends the Hermite-type point interpolation method (HPIM). Despite HPIM's effectiveness, occasional singularities in the moment matrix require enhancement. This work proposes an improved Hermite-type point interpolation method augmented by radial basis functions (Hermite-RPIM) to ensure a well-conditioned moment matrix. The efficacy of the proposed method is validated through detailed numerical examples, including buckling and post-buckling analysis of sandwich functionally graded material (FGM) plates under various loadings, boundary conditions, and material types. These examples highlight the robustness, reliability, and computational efficiency of the enhanced Hermite-RPIM, establishing its potential as a valuable tool for analyzing geometrically nonlinear problems, especially in thin plate buckling analysis.