Buckling analysis of functionally graded microplates incorporating nonlocal strain gradient theory and surface energy effects

The purpose of this work is to present a buckling analysis of functionally graded (FG) microplates by combining nonlocal strain gradient theory (NSGT) with the higher-order shear deformation plate theories (HSDPTs). The microplate is assumed to be composed of a combination of ceramic and metal materials, and the material properties are assumed to vary continuously in the thickness direction based on a simple power law. The equilibrium equations and the boundary conditions are derived using the principle of minimum potential energy. Analytical solutions are determined for the critical buckling loads of the rectangular FG microplates with different boundary conditions. The results obtained have been verified by comparison with existing findings in the literature. Furthermore, some numerical illustrations are provided to investigate the effects of nonlocal parameters, the material length scale parameter, shear deformation, aspect ratios, the power-law index, and the surface energy on the buckling response of the rectangular FG microplates.