In this paper, for the first time, two-term deflection is suggested for nonlinear analysis of shear deformable cylindrical shells and, to the authors’ knowledge, a first investigation on thermal nonlinear buckling behavior of functionally graded material (FGM) cylindrical shells including porosities is presented. Material properties are assumed to be temperature dependent, volume fractions of constituents are graded in the thickness direction according to a power law, and effective properties of porous FGM are estimated according to a modified rule of mixture. Porosities are evenly or unevenly distributed within the shell. Mathematical formulations are based on a first-order shear deformation theory taking into account geometrical nonlinearity and elasticity of in-plane restraints of edges. Two-term deflection and a multiterm stress function are assumed to satisfy simply supported boundary conditions. The Galerkin method and an iteration procedure are employed to evaluate critical buckling temperatures and trace temperature-deflection paths in the postbuckling region. The two-term solution of deflection is a significant suggestion for nonlinear buckling analysis of shear deformable cylindrical shells in general and thermal postbuckling analysis of porous FGM cylindrical shells in particular. This two-term solution includes inherent uniform deflection at the prebuckling state and overcomes mathematically tremendous difficulty in using three-term deflection for shear deformable cylindrical shells. Besides this innovative approach, the obtained results are of great interest for many engineering applications. Unlike the case of mechanical loads, porosities have beneficial influences on the stability of thermally loaded FGM cylindrical shells.

在本文中，首次提出了对挠性可变形圆柱壳进行非线性分析的两项挠度，并且据作者所知，首次对功能梯度材料（FGM）圆柱壳的热非线性屈曲行为（包括孔隙）进行了研究。被呈现。假定材料特性与温度有关，根据幂定律在厚度方向上对组分的体积分数进行分级，并根据混合物的修正规则估算多孔FGM的有效特性。孔隙均匀或不均匀地分布在壳体内。数学公式基于一阶剪切变形理论，考虑了几何非线性和边缘平面约束的弹性。假设两个挠度和一个多重应力函数满足简单支持的边界条件。采用Galerkin方法和迭代程序来评估临界屈曲温度和后屈曲区域中的痕量温度偏转路径。挠度的两个问题解决方案对于一般剪切可变形圆柱壳的非线性屈曲分析，尤其是多孔FGM圆柱壳的热后屈曲分析，是一个重要的建议。该二项解决方案包括在预屈曲状态下固有的均匀挠度，并克服了在数学上将三项挠度用于可剪切变形的圆柱壳的巨大困难。除了这种创新的方法外，获得的结果还对许多工程应用非常感兴趣。