Size-Dependent Elastic Buckling of Two-Variable Refined Microplates Embedded in Elastic Medium

Abstract

This study applies a two-variable refined shear deformation theory (TVRSDT) and a modified couple stress theory (MCST) to develop a size-dependent elastic buckling model for microplates under combined axial compression and in-plane shear and resting on Winkler–Pasternak foundation. Our model incorporates two transverse displacement variables and one material length scale parameter (MLSP); it satisfies the zero-traction boundary conditions on the top and bottom surfaces of microplates, thereby circumventing the use of a shear correction factor. The equations of motion are determined via the Euler–Lagrange equation. A closed-form buckling solution is presented for microplates with four edges simply supported. To handle the nonsimply supported microplates, a thirty-two-degree-of-freedom (32-DOF) four-node differential quadrature (DQ) finite element with [Formula: see text]-continuity is proposed. The corresponding element matrices are obtained using the minimum potential energy principle. Comparison studies are conducted to exhibit the validity of the derived formulations. Finally, the present buckling model is employed for predicting the elastic buckling behaviors of microplates embedded in an elastic medium. The effects of in-plane loading patterns, boundary conditions, aspect ratio, length-to-thickness ratio, MLSP and elastic medium parameters on the buckling load and buckling mode are elucidated.