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.

在这项研究中，研究了中等厚度多孔微板的屈曲分析，以使用应变梯度理论和称为双变量应变梯度理论 (TV-SGT) 的双变量细化板理论来预测微板的不稳定性。实现了控制方程和新的边界条件。此外，还利用 Navier 求解技术获得了简单支撑的中等厚度多孔矩形微板的解析解。获得了单轴和双轴屈曲载荷下中等厚度多孔微板的无量纲化临界屈曲载荷，单轴加载的结果显示出比双轴加载更大的阈值。厚度、长度尺度参数、孔隙率、研究了厚多孔微板无量纲临界屈曲载荷下材料性能随厚度的变化。增加厚度反映了双变量应变梯度理论 (TV-SGT) 和经典理论结果之间的巨大差异。此外，增加厚度会显着影响无量纲化临界屈曲载荷。值得注意的是，增加孔隙率对厚多孔微板的无量纲临界屈曲载荷产生显着影响。