Instability analysis of moderately thick porous micro-plate via two-variable strain gradient theory

In this study, the buckling analysis of moderately thick porous micro-plate is investigated to predict instability of the micro-plate using strain gradient theory and two-variable refined plate theory termed two-variable strain gradient theory (TV-SGT). The governing equations and new boundary conditions are achieved. Also, the Navier solution technique is utilized to obtain analytical solutions for the simply supported moderately thick porous rectangular micro-plates. The non-dimensionalized critical buckling load of moderately thick porous micro-plate for uniaxial and biaxial buckling loadings is obtained, and the results of the uniaxial loading show a larger threshold compared to the biaxial loading. The effects of thickness, length scale parameters, porosity, and the variation of material property through the thickness on the non-dimensionalized critical buckling load of thick porous micro-plate are investigated. Increasing thickness reflects a large difference between two-variable strain gradient theory (TV-SGT) and classical theory results. Moreover, increasing thickness affects the non-dimensionalized critical buckling load, significantly. Notably, increasing porosity presents a distinguished influence on the non-dimensionalized critical buckling load of the thick porous micro-plate.