Nonlinear buckling and postbuckling of FG porous variable thickness toroidal shell segments surrounded by elastic foundation subjected to compressive loads

Abstract

The paper presents an analytical approach in investigating the non-linear buckling and post-buckling behavior of functionally graded porous (FGP) variable thickness toroidal shell segments surrounded by elastic foundation under axial compressive loads. The governing equations of non-linear buckling of FGP toroidal shell segments are obtained by using Donnell shell theory in conjunction with von Kármán nonlinearity and Stein and McElman assumption. The solution in terms of displacements, the closed-form expressions of buckling load and post-buckling load-deflection relation are obtained using the Galerkin method. Three types of porosity distribution are considered. This study found that the variation of porosity distribution as well as geometrical and foundation parameters have significant effects on the non-linear buckling and post-buckling behavior of the FGP variable thickness toroidal shell segments.