The present study proposes a new stochastic finite element method. The Karhunen–Loéve expansion is utilized to discretize the stochastic field, while the point estimate method is applied for calculating the random response of the structure. Two illustrative examples, including finite element models with one-dimensional and two-dimensional stochastic fields, are investigated to demonstrate the accuracy and efficiency of the proposed method. Furthermore, two classical finite element analysis methods are used to validate the results. It is proved that the proposed method can model both the one-dimensional and the two-dimensional stochastic finite element problems accurately and efficiently.

本研究提出了一种新的随机有限元方法。Karhunen-Loéve展开用于离散随机场，而点估计方法则用于计算结构的随机响应。研究了两个说明性示例，包括具有一维和二维随机场的有限元模型，以证明该方法的准确性和效率。此外，使用两种经典的有限元分析方法来验证结果。实践证明，该方法可以准确，高效地对一维和二维随机有限元问题进行建模。