This paper presents an analytical investigation on buckling and post-buckling of shear deformable sandwich toroidal shell segments with functionally graded core and homogeneous face sheets. The effective material properties of core layer are graded in the thickness direction according to a simple power law distribution in terms of volume fraction index. The shells are surrounded by an elastic foundation and subjected to axial compressive or thermal loads. Reddy's third-order shear deformation shell theory (TSDT) is used to established formulations. A new solution using Galerkin method for solving a governing system of four-partial differential equations is carried out to obtain closed-form expressions of buckling stresses and post-buckling curves. Two cases of bowed-out and bowed-in sandwich toroidal shells are considered. Effects of material, geometric parameters and elastic foundation on stability behavior of the shells is analyzed in detail. The difference between bucking stresses basing on TSDT and those basing on classical shell theory (CST) is also clearly shown in this study.

本文对具有功能梯度型芯和均质面板的剪切可变形夹心环形壳段的屈曲和后屈曲进行了分析研究。根据体积分数指数，根据简单的幂律分布，将芯层的有效材料特性沿厚度方向分级。壳体被弹性基础包围，并承受轴向压缩或热负荷。Reddy的三阶剪切变形壳理论（TSDT）用于建立公式。为了解决屈曲应力和屈曲后曲线的闭合形式，采用Galerkin方法求解了四部分微分方程的控制系统。考虑了弓形和弓形夹心环形壳的两种情况。材料的影响 详细分析了壳的几何参数和弹性特性。这项研究也清楚地表明了基于TSDT的屈曲应力与基于经典壳理论（CST）的屈曲应力之间的差异。