The postbuckling and geometrically nonlinear behaviors of imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shells under axial compression are investigated in this paper. For the first time, a new type of instability named “snap-backward” with the presence of three limit points on the equilibrium path is proposed. A novel formulation based on non-uniform rational B-Spline (NURBS) basis functions and the first-order shear deformation shell theory (FSDT) using the von Karman assumption and considering the initial deformation of the shells is presented. In addition, the advantage of NURBS in modeling exactly geometries of shells is exploited. In numerical implementation, the discrete nonlinear equation system is iteratively solved by a modified Riks method. The rule of mixture is used to estimate the effective material properties of FG-CNTRC shells. Some benchmark problems are solved to verify the high reliability of the proposed formulation. Effects of geometrical imperfection, CNTs distribution, volume fraction, CNTs orientation, thickness, radius of shell on the postbuckling and geometrically nonlinear behaviors of FG-CNTRC shells are rigorously investigated. Especially, some new and complex load-deflection curves of imperfect FG-CNTRC shells under axial compression are first provided that could be useful for future references.

研究了不完全功能梯度的碳纳米管增强复合材料（FG-CNTRC）壳在轴向压缩下的后屈曲和几何非线性行为。首次提出了一种新型的不稳定性，称为“向后捕捉”，在平衡路径上存在三个极限点。提出了一种基于非均匀有理B样条（NURBS）基函数和一阶剪切变形壳理论（FSDT）的新公式，该理论使用von Karman假设并考虑了壳的初始变形。此外，还利用了NURBS在精确建模壳的几何形状方面的优势。在数值实现中，离散非线性方程组通过改进的Riks方法迭代求解。混合规则用于估计FG-CNTRC壳的有效材料性能。解决了一些基准问题，以验证所提出配方的高可靠性。严格研究了几何缺陷，碳纳米管的分布，体积分数，碳纳米管的取向，厚度，壳的半径对FG-CNTRC壳的后屈曲和几何非线性行为的影响。特别是，首先提供了不完整的FG-CNTRC壳体在轴向压缩下的一些新的和复杂的载荷-挠度曲线，这些曲线可能对将来的参考很有用。严格研究了FG-CNTRC壳在屈曲后的半径和几何非线性行为。特别是，首先提供了不完整的FG-CNTRC壳体在轴向压缩下的一些新的和复杂的载荷-挠度曲线，这些曲线可能对将来的参考很有用。严格研究了FG-CNTRC壳在屈曲后的半径和几何非线性行为。特别是，首先提供了不完整的FG-CNTRC壳体在轴向压缩下的一些新的和复杂的载荷-挠度曲线，这些曲线可能对将来的参考很有用。