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.
出处
《西北工业大学学报》
EI
CAS
CSCD
北大核心
2013年第3期413-416,共4页
Journal of Northwestern Polytechnical University
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
computational efficiency
convergence of numerical methods
crack propagation
finite element method
Monte-Carlo methods
stochastic models
Neumann expansion
stochasticlly extended finite element method
作者简介
杜永恩（1986-），西北工业大学博士研究生，主要从事航空结构损伤容限及可靠性研究。
