The Effect of Porosity on Elastic Stability of Toroidal Shell Segments Made of Saturated Porous Functionally Graded Materials

Abstract

This research deals with the stability analysis of shallow segments of the toroidal shell made of saturated porous functionally graded (FG) material. The nonhomogeneous material properties of porous shell are assumed to be functionally graded as a function of the thickness and porosity parameters. The porous toroidal shell segments with positive and negative Gaussian curvatures and nonuniform distributed porosity are considered. The nonlinear equilibrium equations of the porous shell are derived via the total potential energy of the system. The governing equations are obtained on the basis of classical thin shell theory and the assumptions of Biot's poroelasticity theory. The equations are a set of the coupled partial differential equations. The analytical method including the Airy stress function is used to solve the stability equations of porous shell under mechanical loads in three cases. Porous toroidal shell segments subjected to lateral pressure, axial compression, and hydrostatic pressure loads are analytically analyzed. Closed-form solutions are expressed for the elastic buckling behavior of the convex and concave porous toroidal shell segments. The effects of porosity distribution and geometrical parameters of the shell on the critical buckling loads of porous toroidal shell segments are studied.