Buckling analysis of functionally graded plates using the finite difference method and first-order shear deformation theory

Abstract

Background/Aim: This study develops and verifies a finite-difference formulation for the linear buckling analysis of rectangular power-law functionally graded material (P-FGM) plates, based on first-order shear deformation theory (FSDT). The aim is to provide an accurate, computationally efficient numerical approach for predicting the critical buckling loads of P-FGM plates under various loading and support conditions. Methods: Material properties were assumed to vary continuously throughout the plate thickness according to a power-law distribution between ceramic and metallic constituents. The governing equilibrium and stability equations were derived using an energy-based variational formulation and discretised using second-order central finite differences, resulting in a generalised eigenvalue problem. The numerical formulation was verified through mesh refinement, experimental order of convergence and Richardson extrapolation. A parametric study investigated the effects of the material gradient index, loading configuration, aspect ratio, thickness ratio and boundary conditions. Results: The formulation exhibited second-order spatial convergence, with discretisation errors below 0.1% for refined meshes. The numerical predictions showed excellent agreement with the benchmark solutions reported in the literature. Ceramic-rich distributions increased the critical buckling load, whereas metallic-rich distributions reduced structural stability. Biaxial compression decreased the critical buckling load compared to uniaxial compression, while clamped boundary conditions produced the greatest buckling resistance. Conclusion: The verified, FSDT-based, finite-difference formulation provides accurate, robust and computationally efficient predictions of the linear buckling behaviour of rectangular P-FGM plates. It offers a reliable and straightforward alternative for stability analysis.