This paper deals with the nonlinear large deflection torsional buckling of functionally graded carbon nanotube (CNT) orthogonally reinforced composite cylindrical shells surrounded by Pasternak’s elastic foundations with the thermal effect. The shell is made by two layers where the polymeric matrix is reinforced by the CNTs in longitudinal and circumferential directions for outer and inner layers, respectively. The stability equation system is obtained by combining the Donnell’s shell theory, von Kármán nonlinearity terms, the circumferential condition in average sense and three-state solution form of deflection. The critical torsional buckling load, postbuckling load-deflection and the load-end shortening expressions are obtained by applying the Galerkin procedure. The effects of temperature change, foundation parameters, geometrical properties and CNT distribution law on the nonlinear behavior of cylindrical shell are numerically predicted. Especially, the effect of orthogonal reinforcement in comparison with longitudinal and circumferential reinforcement on the torsional buckling behavior of shells is observed.

中文翻译：

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功能梯度碳纳米管正交增强复合圆柱壳在热环境中的非线性扭转屈曲

本文研究了功能梯度碳纳米管（CNT）正交增强复合圆柱壳的非线性大挠度扭转屈曲，该圆柱壳被帕斯捷尔纳克弹性基础包围，具有热效应。外壳由两层制成，其中聚合物基体在外层和内层的纵向和圆周方向上分别由 CNT 增强。结合Donnell壳理论、von Kármán非线性项、平均意义上的圆周条件和挠度的三态解形式得到稳定性方程组。临界扭转屈曲载荷、后屈曲载荷挠度和载荷端缩短表达式是通过应用 Galerkin 程序获得的。温度变化的影响，基础参数，对圆柱壳非线性行为的几何特性和碳纳米管分布规律进行了数值预测。特别是，观察了正交钢筋与纵向和周向钢筋相比对壳的扭转屈曲行为的影响。