Abstract

In this article, the semianalytical method based on the Galerkin technique and fourth-order Runge-Kutta method is utilized to investigate the static and dynamic postbuckling analysis of internal/external spiral stiffened functionally graded (ISSFG/ESSFG) cylindrical shells, respectively. The simply supported SSFG shell subjected to an axial compression is resting on a nonlinear elastic foundation (EF) which is including the Pasternak and Winkler foundation parameters augmented by a softening/hardening cubic nonlinearity. The material constitutes of both the stiffeners and the shells that are continuously changed along the thickness. The discretized motion equation is extracted utilizing the Galerkin method regarding to the Donnel’s shells theory and nonlinear strain-displacement von Kármán. To obtain the responses of dynamic postbuckling (DPB) analysis, the fourth-order Runge-Kutta method is utilized. To validate the results, comparisons are made with the available solutions for both static postbuckling (SPB) and DPB analysis of stiffened homogeneous and functionally graded cylindrical shells. The influences of various material and geometrical parameters with the inclusion of the supporting nonlinear EF on the SPB and DPB behavior of imperfect ISSFG/ESSFG cylindrical shells are presented. As one of the most interesting results, for the ISSFG cylindrical shells with the stiffeners angle $\theta =\beta ={60}^{°}$ and ESSFG cylindrical shells with the stiffeners angle $\theta ={30}^{°},\mathrm{ }\beta ={60}^{°},$ the buckling load-bearing capacity is the most.

摘要

本文采用基于 Galerkin 技术和四阶 Runge-Kutta 方法的半解析方法分别研究了内/外螺旋加劲功能梯度 (ISSFG/ESSFG) 圆柱壳的静态和动态后屈曲分析。受轴向压缩的简支 SSFG 壳位于非线性弹性基础 (EF) 上，该基础包括通过软化/硬化三次非线性增强的 Pasternak 和 Winkler 基础参数。材料由沿厚度连续变化的加强件和外壳组成。利用有关Donnel壳理论和非线性应变-位移von Kármán的Galerkin方法提取离散运动方程。为了获得动态后屈曲 (DPB) 分析的响应，使用了四阶龙格-库塔法。为了验证结果，我们与现有解决方案进行了比较，用于加劲均质和功能梯度圆柱壳的静态后屈曲 (SPB) 和 DPB 分析。介绍了包括支持非线性 EF 在内的各种材料和几何参数对不完美 ISSFG/ESSFG 圆柱壳的 SPB 和 DPB 行为的影响。作为最有趣的结果之一，对于具有加强角的 ISSFG 圆柱壳 介绍了包括支持非线性 EF 在内的各种材料和几何参数对不完美 ISSFG/ESSFG 圆柱壳的 SPB 和 DPB 行为的影响。作为最有趣的结果之一，对于具有加强角的 ISSFG 圆柱壳 介绍了包括支持非线性 EF 在内的各种材料和几何参数对不完美 ISSFG/ESSFG 圆柱壳的 SPB 和 DPB 行为的影响。作为最有趣的结果之一，对于具有加强角的 ISSFG 圆柱壳$\theta =\beta ={60}^{°}$和带有加劲肋角的 ESSFG 圆柱壳$\theta ={30}^{°},\mathrm{ }\beta ={60}^{°},$屈曲承载力最大。