Abstract We present in this paper a novel and efficient computational approach in terms of triangular extended stochastic finite element method (T-XSFEM) for simulation of random void problems. The present T-XSFEM is further enhanced by local mesh refinement with the aid of variable-node elements to couple/link different mesh-scales, increasing the efficiency of the developed approach and saving the computational cost. The degrees of freedom are approximated with a truncated generalized polynomial chaos (GPC). The present work depends on the extension of extended finite element method (XFEM) to the stochastic context, containing implicit expression of voids through the random level set functions. A new partition technique is defined to divide the random domain for integration by using a priori knowledge of the void shape function, which can further reduce the computational time. To show the effectiveness and accuracy of the developed approach, numerical experiments are studied and computed results are compared with existing reference solutions.

中文翻译：

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通过局部网格细化增强的扩展随机有限元方法用于随机空隙分析

摘要 我们在本文中提出了一种新的、有效的计算方法，即三角形扩展随机有限元法 (T-XSFEM) 用于模拟随机空洞问题。目前的 T-XSFEM 通过局部网格细化进一步增强，借助可变节点元素耦合/链接不同的网格尺度，提高了所开发方法的效率并节省了计算成本。自由度近似于截断广义多项式混沌 (GPC)。目前的工作取决于扩展有限元方法 (XFEM) 到随机上下文的扩展，包含通过随机水平集函数隐式表达的空隙。定义了一种新的划分技术，通过使用空隙形状函数的先验知识来划分随机域以进行积分，这可以进一步减少计算时间。为了显示所开发方法的有效性和准确性，研究了数值实验并将计算结果与现有参考解决方案进行了比较。