Postbuckling responses of porous FGM spherical caps and circular plates including edge constraints and nonlinear three-parameter elastic foundations

Abstract

An analytical investigation on nonlinear stability of porous functionally graded spherical caps and circular plates under uniform external pressure and elevated temperature, respectively, is presented in this article. Porosities are evenly and unevenly distributed within the structures and the effective properties of functionally graded material (FGM) are determined according to a modified rule of mixture. Governing equations are established within the framework of classical theory taking into account geometrically nonlinear terms, initial geometric imperfection, and interactive pressure from nonlinear three-parameter elastic foundation. Both temperature dependence of material properties and tangential elasticity of edge constraint are included. Approximate analytical solutions are assumed to satisfy clamped condition of boundary edge and Galerkin method is applied to derive load-deflection relations from which buckling loads and postbuckling paths are determined. Numerical results indicate that porosities have deteriorative and beneficial influences on load-carrying capacity of structures under external pressure and elevated temperature, respectively. Furthermore, the snap-through buckling response of pressurized FGM spherical cap can be alleviated and even eliminated by virtue of elastic foundations with suitable stiffness parameters.