A simple refined plate theory for the analysis of bending, buckling and free vibration of functionally graded porous plates reinforced by graphene platelets

Abstract

This paper presents a simple refined plate theory (S-RPT) which contains only three unknown variables in the displacement field for bending and buckling analysis and only one unknown variable in the displacement field for free vibration analysis. Unlike other simplified plate theories, S-RPT in its simplification (1) takes into account the Poisson’s ratio variation along the thickness direction (2) takes into account the full coupling of in-plane and transverse displacements. These features make S-RPT applicable to the analysis of bending, buckling, and free vibration of functionally graded porous plates reinforced with graphene platelets (FGP–GPLs). Some simplified plate theories already available in the literature can be regarded as special cases of S-RPT. The S-RPT is first used in isotropic and metal–ceramic functionally graded plates to verify its accuracy. Then, the effect of pore distribution, GPLs distribution, porosity coefficient, aspect ratio, thickness ratio, and GPLs weight fraction on the bending, buckling, and free vibration behaviors are investigated based on S-RPT.