Static analysis of functionally graded plates with a porous middle layer based on higher order shear deformation theory with linear/quadratic transverse displacement

In this article, we present an analytical solution for an imperfect functionally graded plate based on higher order shear deformation theory with cubic variation of in-plane displacements according to thickness and linear/quadratic transverse displacement. The developed solution is used to analyze the static responses of a plate with a porous layer to mechanical loading. Two porosity types and their influences on material properties, displacement, and stress behaviors are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using power-law distribution idealization in terms of the volume fractions of constituents. The computed results are presented to illustrate the accuracy of the proposed solutions based on comparisons to previously reported analytical and numerical solutions in the literature. We also analyzed the effects of different volume fractions and thicknesses of porous layers on the mechanical loading and mechanical behavior of the imperfect functionally graded plate.