A variational approach for analytical buckling solution of moderately thick microplate using strain gradient theory incorporating two-variable refined plate theory: a benchmark study

In this paper, two-variable refined plate theory and strain gradient theory (SGT) are adopted and termed (TV-SGT) for buckling analysis of moderately thick microplate. The TV-SGT embraces both shear and micro-effects simultaneously and, therefore, does not need the shear correction factor. Notably, the governing equations and new boundary conditions are derived using variational approach. Moreover, the boundary conditions are generalized for complicated problems. The constitutive equations are solved analytically as a benchmark problem for simply supported thick moderately microplate. The accuracy and simplicity of utilizing this theory for investigating stability analysis of thick microplate are assessed, and the critical buckling load of the microplate for uniaxial and biaxial loadings is studied. The impacts of thickness, length scale parameters and dimensions on the non-dimensionalized critical buckling load of the microplate are investigated. Consequently, increasing thickness leads to the rising gap between TV-SGT and classical theory results. Therefore, classical plate theory is ruled out in analysing of the moderately thick microplate, whereas TV-SGT is well defined to analyse the moderately thick microplate.