A simple refined plate theory for buckling problems of in-plane bi-directional functionally graded plates with porosity under various boundary conditions

In this article, a simple refined shear deformation theory that eliminates the use of a shear correction factor was presented for buckling analysis of in-plane bi-directional functionally graded (IBFG) porous plates under various boundary conditions. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. Material properties of IBFG are assumed to vary continuously along with two different directions simultaneously, that is, the longitudinal and transversal ones, respectively. Governing equations and boundary conditions are derived. Analytical solutions were obtained for buckling analysis of (IBFG) porous plates. Several numerical examples are presented to demonstrate the performance and effectiveness of the proposed theory. The effects of material gradations, aspect ratios, and porosity on IBFG plate responses are examined in detail as well.