Finite cell method is known as a combination of finite element method and fictitious domain approach in order to reduce the difficulties associated with mesh generation so that it can successfully handle complex geometries. This study proposes a stochastic extension of finite cell method, as a novel computational framework, for uncertainty quantification of structures. For this purpose, stochastic finite cell method (SFCM) is developed as a new efficient method, including the features of finite cell method, for computational stochastic mechanics considering complicated geometries arising from computer-aided design (CAD). Firstly, finite cell method is formulated for solving the Fredholm integral equation of the second kind used for Karhunen-Loève expansion in order to decompose the random field within a physical domain having arbitrary boundaries. Then, the SFCM is formulated based on Karhunen-Loève and polynomial chaos expansions for the stochastic analysis. Several numerical examples consisting of benchmark problems are provided to demonstrate the efficiency, accuracy and capability of the proposed SFCM.

有限元方法被称为有限元方法和虚拟域方法的组合，目的是减少与网格生成相关的困难，以便它可以成功处理复杂的几何形状。这项研究提出了一种有限元方法的随机扩展，作为一种新颖的计算框架，用于结构的不确定性量化。为此，随机有限元法（SFCM）被开发为一种新的有效方法，包括有限元方法的特征，用于考虑计算机辅助设计（CAD）产生的复杂几何形状的计算随机力学。首先，为了解决Karhunen-Loève展开所用的第二类Fredholm积分方程，提出了有限元方法，以分解具有任意边界的物理域中的随机场。然后，基于Karhunen-Loève和多项式混沌展开式来建立SFCM，以进行随机分析。提供了一些由基准问题组成的数值示例，以证明所提出的SFCM的效率，准确性和功能。