Influence of porosity distribution on static and buckling responses of porous functionally graded plates

Abstract

Abstract This article studies the effect of porosity distribution on static and buckling response of a functionally graded (FG) porous plate with all its four edges simply supported and subjected to a transverse load. The plate’s displacement field is approximated based on an inverse hyperbolic shear deformation theory (IHSDT) involving five variables. In this theory, inplane displacements vary as an inverse hyperbolic function through the plate thickness, so account for non-linear variation of transverse shear stresses and satisfies traction free boundary conditions on the surfaces of plate without the need of any shear correction factors. The governing equations of motion are derived using the principle of virtual work, and thus, the expressions of its strain energy and work done are obtained. Effective material properties of porous plate are assumed with an additional term of porosity in the direction of thickness. Power-law is used for continuous variation of material properties along the thickness direction. In this study, five types of porosity distribution functions are considered. The effect of the porosity parameter, the power-law exponent, side-thickness ratio, and aspect ratio on the static and buckling responses of the porous FG plate is evaluated. In problem-solving, the Navier solution technique is used to obtain the exact solutions. The non-dimensional deflections and critical buckling loads of FG porous plate are thus obtained. The results are compared with available results in the literature, and good agreement is found. Moreover, the results are presented to study the effects of various parameters on the dimensionless deflections, stresses, and critical uni-axial and bi-axial buckling loads.