基于Neumann展开的Monte-Carlo随机扩展有限元法  

Stochastically Extended Finite Element Method Based on Neumann Expansion

作　　者：杜永恩[1] 王生楠[1] 闫晓中[1] 

机构地区：[1]西北工业大学航空学院,陕西西安710072

出　　处：《西北工业大学学报》2013年第3期413-416,共4页Journal of Northwestern Polytechnical University

摘　　要：基于Neumann级数展开的Monte-Carlo随机有限元在涉及几何构形存在随机性的问题时,需要对网格进行重新划分,需要极大的计算量。为解决该问题,提高运算效率,提出一种新的计算裂纹问题的随机方法。该方法结合了扩展有限元法与随机有限元法的优点,通过对扩展有限元控制方程进行Neumann展开,可方便地处理几何构形的随机性,不需重新划分网格。该方法具有计算量小,计算效率高的优点,并能保持较高的计算精度。利用矩阵级数理论讨论了该方法的收敛性。最后通过数值算例验证了该方法的有效性。The introduction of the full paper discusses relevant matters and then proposes the method mentioned in the title.Sections 1 and 2 present the stochastically extended finite element method based on Neumann expansions;this method is the main and core result of our research.Section 1 introduces the extended finite element method as applied to crack propagation.Section 2 presents the method mentioned in the title.The Neumann expansion of the control equation of extended finite element method is employed in this method so as to deal with the randomness of geometric configuration conveniently without remeshing.Convergence of this method is discussed using the matrix theory in section 3.The validity and efficiency of this method are verified with numerical examples in section 4.The calculation results,presented in Fig 2,and their analysis show that this method has the advantage of high computational efficiency;also it maintains excellent computation accuracy.

关 键 词：计算效率 数值方法收敛性 裂纹扩展 有限元法 MONTE-CARLO法 随机模型 Neumann展开 随机扩展有限元法 

分 类 号：TU451[建筑科学—岩土工程] TU311[建筑科学—土工工程]