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.

本文提出了一种分析方法，用于研究功能性梯度多孔（FGP）变厚度环形壳段在轴向压缩载荷下被弹性基础包围的非线性屈曲和后屈曲行为。利用Donnell壳理论结合vonKármán非线性和Stein和McElman假设，获得了FGP环形壳分段的非线性屈曲控制方程。使用Galerkin方法获得了位移，屈曲载荷的闭合形式和屈曲后载荷-挠度关系的解。考虑了三种类型的孔隙度分布。