This paper develops an efficient reliability analysis method for composite structures with high-dimensional uncertain variables. The concept and mathematical definition of the approximate design point (ADP) and the approximate important direction (AID) are introduced. A fast calculation ADP/AID formula is proposed. A numerical line sampling (LS) strategy is devised, which is further combined with ADP/AID to form a novel reliability method, named AID-LS. An equivalent criterion is introduced to address the problems with the non-normal random variables. A stochastic mechanical model of composite structures with geometrical nonlinearity is established based on first-order shear deformation theory and implemented with finite element analysis (FEA). Numerical examples are given to demonstrate the validity of the proposed method. The results show that the proposed method can significantly reduce the number of FEA samples in the reliability analysis of composite structures.

本文针对具有高维不确定变量的复合结构开发了一种有效的可靠性分析方法。介绍了近似设计点（ADP）和近似重要方向（AID）的概念和数学定义。提出了一种快速计算的ADP/AID公式。设计了一种数值线采样 (LS) 策略，该策略进一步与 ADP/AID 相结合，形成一种新的可靠性方法，称为 AID-LS。引入了等效标准来解决非正态随机变量的问题。基于一阶剪切变形理论建立了具有几何非线性的复合结构随机力学模型，并通过有限元分析（FEA）实现。给出了数值例子来证明所提出方法的有效性。