This paper presents a new stochastic finite element method for computing structural stochastic responses of linear problems. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of deterministic responses with random variable coefficients. A dedicated iterative algorithm is proposed to compute the deterministic responses and corresponding random variable coefficients one by one. The algorithm computes the deterministic responses and corresponding random variable coefficients in their individual spaces and is insensitive to stochastic dimensions, thus it can be applied to high-dimensional stochastic problems without extra difficulties. More importantly, the deterministic responses can be computed efficiently by use of existing finite element method (FEM) solvers, thus the proposed method can be easy to embed into existing FEM structural analysis software. Three practical examples, including low-dimensional and high-dimensional stochastic problems, are given to demonstrate the accuracy and effectiveness of the proposed method.

本文提出了一种新的随机有限元方法，用于计算线性问题的结构随机响应。该方法提供了随机响应的新​​扩展，并将随机响应解耦为一系列具有随机变量系数的确定性响应的组合。提出了一种专用的迭代算法来逐一计算确定性响应和相应的随机变量系数。该算法在各自的空间中计算确定性响应和相应的随机变量系数，并且对随机维度不敏感，因此可以应用于高维随机问题，没有额外的困难。更重要的是，可以通过使用现有的有限元方法（FEM）求解器来高效地计算确定性响应，因此该方法可以轻松地嵌入到现有的FEM结构分析软件中。给出了三个实际的例子，包括低维和高维随机问题，以证明该方法的准确性和有效性。