Abstract

An analytical investigation on nonlinear stability of porous functionally graded spherical caps and circular plates under uniform external pressure and elevated temperature, respectively, is presented in this article. Porosities are evenly and unevenly distributed within the structures and the effective properties of functionally graded material (FGM) are determined according to a modified rule of mixture. Governing equations are established within the framework of classical theory taking into account geometrically nonlinear terms, initial geometric imperfection, and interactive pressure from nonlinear three-parameter elastic foundation. Both temperature dependence of material properties and tangential elasticity of edge constraint are included. Approximate analytical solutions are assumed to satisfy clamped condition of boundary edge and Galerkin method is applied to derive load-deflection relations from which buckling loads and postbuckling paths are determined. Numerical results indicate that porosities have deteriorative and beneficial influences on load-carrying capacity of structures under external pressure and elevated temperature, respectively. Furthermore, the snap-through buckling response of pressurized FGM spherical cap can be alleviated and even eliminated by virtue of elastic foundations with suitable stiffness parameters.

摘要

本文介绍了多孔功能梯度球盖和圆板分别在均匀外压和高温下的非线性稳定性的分析研究。孔隙率在结构内均匀和不均匀分布，功能梯度材料（FGM）的有效性能根据混合的修改规则确定。控制方程是在经典理论框架内建立的，考虑了几何非线性项、初始几何缺陷和非线性三参数弹性地基的相互作用压力。包括材料特性的温度依赖性和边缘约束的切向弹性。假设近似解析解满足边界边缘的夹紧条件，并应用伽辽金方法导出载荷-挠度关系，由此确定屈曲载荷和后屈曲路径。数值结果表明，孔隙率对结构在外压和高温下的承载能力分别具有不利和有益的影响。此外，借助具有合适刚度参数的弹性基础，可以减轻甚至消除加压FGM球冠的突然屈曲响应。数值结果表明，孔隙率对结构在外压和高温下的承载能力分别具有不利和有益的影响。此外，借助具有合适刚度参数的弹性基础，可以减轻甚至消除加压FGM球冠的突然屈曲响应。数值结果表明，孔隙率对结构在外压和高温下的承载能力分别具有不利和有益的影响。此外，借助具有合适刚度参数的弹性基础，可以减轻甚至消除加压FGM球冠的突然屈曲响应。