A COMPLEX VARIABLE MESHLESS MANIFOLD METHOD FOR FRACTURE PROBLEMS

被引：64
作者：
Gao, Hongfen [1 ,2 ]
Cheng, Yumin [1 ]
机构：
[1] Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China
[2] Jinan Inst Railway Technol, Jinan 250104, Shandong, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS | 2010年 / 7卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Complex variable meshless manifold method; finite cover theory; complex variable moving least-squares approximation; crack; stress intensity factor; PARTITION;
D O I：
10.1142/S0219876210002064
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
Based on the complex variable moving least-squares (CVMLS) approximation and the finite cover theory, the complex variable meshless manifold method (CVMMM) for fracture problems is presented in this paper. The CVMMM employs two cover systems which are the mathematical cover system and the physical cover system. The shape function in the CVMMM is derived with the CVMLS approximation and the finite cover theory. The finite cover theory is used to model cracks which lead to interior discontinuous displacements. At the tip of a crack of a problem, we use the analytical solution near the tip of a crack to extend the trial function of the CVMMM, then the corresponding approximation function is obtained. From the minimum potential energy principle, the corresponding formulae of the CVMMM for fracture problems are presented. Some numerical examples are presented to demonstrate the method in this paper.
引用
收藏
页码：55 / 81
页数：27
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