Abstract In this article, a semi-analytical and analytical method for the nonlinear static and dynamic thermal buckling behavior of imperfect multilayer FG cylindrical shells with an FG porous core in the thermal environment is investigated. The structure is embedded within a generalized nonlinear elastic foundation which is composed of a two-parameter Winkler-Pasternak foundation augmented by a nonlinear cubic stiffness. Two types of multilayer FG cylindrical shells with an FG porosity core distribution consist of a uniform porosity distribution and a non-uniform porosity distribution core are considered. Using the Galerkin method with regard to the von Kármán equations, the discretized motion equation is obtained. The fourth-order Runge-Kutta method is utilized to obtain the nonlinear dynamic thermal buckling responses. The effects of various geometrical characteristics, material parameters, and elastic foundation coefficients are investigated on the nonlinear static thermal buckling and dynamic thermal buckling behavior of the multilayer FG system with an FG porous core. The results show that the various types of porosity core, imperfection and the elastic foundation parameters have strongly effect on the thermal buckling behaviors of the multilayer FG cylindrical shells with an FG porous core.

中文翻译：

---

非线性弹性基础上具有 FG 多孔芯的不完美多层 FG 圆柱壳的非线性静态和动态热屈曲分析

摘要 在本文中，研究了热环境中具有 FG 多孔芯的不完美多层 FG 圆柱壳的非线性静态和动态热屈曲行为的半解析和解析方法。该结构嵌入在广义非线性弹性基础中，该基础由非线性三次刚度增强的双参数 Winkler-Pasternak 基础组成。考虑了具有 FG 孔隙率核分布的两种类型的多层 FG 圆柱壳，包括均匀孔隙率分布和非均匀孔隙率分布核。对von Kármán方程使用Galerkin方法，得到离散化的运动方程。四阶Runge-Kutta方法用于获得非线性动态热屈曲响应。研究了各种几何特性、材料参数和弹性基础系数对具有 FG 多孔芯的多层 FG 系统的非线性静态热屈曲和动态热屈曲行为的影响。结果表明，不同类型的孔隙率核、缺陷和弹性基础参数对含 FG 多孔核的多层 FG 圆柱壳的热屈曲行为有很大影响。