In this paper, semi-analytical and analytical methods for the nonlinear static and dynamic buckling analyses of imperfect functionally graded porous (FGP) cylindrical shells subjected to axial compression are presented. The structure is embedded within a generalized nonlinear elastic foundation, treated as a two-parameter Winkler–Pasternak foundation augmented by a nonlinear cubic stiffness. The material property of the shell changes continuously through the thickness. Two types of FGP distributions, i.e. uniform porosity distribution (UPD) and nonuniform porosity distribution (NPD), are considered. By applying the Galerkin’s method to the von Kármán equations, the buckling of the shells was solved. The fourth-order Runge–Kutta method is utilized to obtain the responses of nonlinear dynamic buckling (NDB). The results obtained for some special cases are compared with those available elsewhere. The effects of various geometrical properties, material parameters and elastic foundation coefficients are investigated on the nonlinear static buckling (NSB) and dynamic buckling (DB) analyses of the shells. It was shown that various types of porosity, imperfection and the elastic foundation parameters have a strong effect on the buckling behaviors of the FGP cylindrical shells.

中文翻译：

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轴压下非线性弹性地基上不完美FGP圆柱壳的非线性静态和动态屈曲分析

本文介绍了受轴向压缩的不完全功能梯度多孔 (FGP) 圆柱壳的非线性静态和动态屈曲分析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，被视为由非线性立方刚度增强的双参数 Winkler-Pasternak 基础。壳的材料特性随着厚度不断变化。考虑了两种类型的FGP分布，即均匀孔隙率分布（UPD）和非均匀孔隙率分布（NPD）。通过将 Galerkin 方法应用于 von Kármán 方程，求解了壳的屈曲。四阶龙格-库塔方法用于获得非线性动态屈曲 (NDB) 的响应。将某些特殊情况下获得的结果与其他地方的结果进行比较。研究了各种几何特性、材料参数和弹性地基系数对壳的非线性静态屈曲 (NSB) 和动态屈曲 (DB) 分析的影响。结果表明，各种类型的孔隙率、缺陷和弹性基础参数对 FGP 圆柱壳的屈曲行为有很大的影响。