Nouy and Clement introduced the stochastic extended finite element method to solve linear elasticity problem defined on random domain. The material properties and boundary conditions were assumed to be deterministic. In this work, we extend this framework to account for multiple independent input uncertainties, namely, material, geometry, and external force uncertainties. The stochastic field is represented using the polynomial chaos expansion. The challenge in numerical integration over multidimensional probabilistic space is addressed using the pseudo‐spectral Galerkin method. Thereafter, a sensitivity analysis based on Sobol indices using the derived stochastic extended Finite Element Method solution is presented. The efficiency and accuracy of the proposed novel framework against conventional Monte Carlo methods is elucidated in detail for a few one and two dimensional problems.

中文翻译：

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具有混合不确定性的椭圆方程组的扩展随机伪谱Galerkin有限元方法（XS‐PS‐GFEM）

Nouy和Clement引入了随机扩展有限元方法来解决在随机域上定义的线性弹性问题。假定材料特性和边界条件是确定的。在这项工作中，我们扩展了该框架以解决多个独立的输入不确定性，即材料，几何形状和外力不确定性。随机场用多项式混沌展开表示。使用伪谱Galerkin方法解决了多维概率空间上数值积分的挑战。此后，使用导出的随机扩展有限元方法解决方案，基于Sobol指数进行了灵敏度分析。