论文标题
一种基于样本的随机有限元方法，用于结构可靠性分析
A sample-based stochastic finite element method for structural reliability analysis
论文作者
论文摘要
本文通过随机有限元方法（SFEM）提出了一种用于结构可靠性分析的新方法。新型基于样本的SFEM首先用于同时计算所有空间点的结构随机响应，该响应将随机响应与随机可变系数的一系列确定性响应的组合结合在一起，并通过迭代算法求解相应的随机有限元方程。基于SFEM获得的随机响应，可以在无需任何困难的情况下计算由随机响应和可靠性分析中遇到的多维积分所描述的极限状态函数，并计算出所有空间点的故障概率一次。所提出的方法可以应用于高维的随机问题，并且可以在没有昂贵的计算成本的情况下避开高维可靠性分析中遇到的最具挑战性的问题之一。与蒙特卡洛模拟相比，给出了三个实际示例，包括大规模和高维可靠性分析，以证明所提出方法的准确性和效率。
This paper presents a new methodology for structural reliability analysis via stochastic finite element method (SFEM). A novel sample-based SFEM is firstly used to compute structural stochastic responses of all spatial points at the same time, which decouples the stochastic response into a combination of a series of deterministic responses with random variable coefficients, and solves corresponding stochastic finite element equation through an iterative algorithm. Based on the stochastic response obtained by the SFEM, the limit state function described by the stochastic response and the multidimensional integral encountered in reliability analysis can be computed without any difficulties, and failure probabilities of all spatial points are calculated once time. The proposed method can be applied to high-dimensional stochastic problems, and one of the most challenging issues encountered in high-dimensional reliability analysis, known as Curse of Dimensionality, can be circumvented without expensive computational costs. Three practical examples, including large-scale and high-dimensional reliability analysis, are given to demonstrate the accuracy and efficiency of the proposed method in comparison to the Monte Carlo simulation.
