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An isogeometric‐meshfree coupling approach for analysis of cracks
Author(s) -
NguyenThanh Nhon,
Huang Jiazhao,
Zhou Kun
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5713
Subject(s) - meshfree methods , discretization , moving least squares , isogeometric analysis , diffuse element method , mathematics , finite element method , basis function , robustness (evolution) , mathematical analysis , mathematical optimization , computer science , structural engineering , extended finite element method , engineering , biochemistry , spectral element method , chemistry , gene
Summary This paper presents a new concurrent simulation approach to couple isogeometric analysis (IGA) with the meshfree method for studying of crack problems. In the present method, the overall physical domain is divided into 2 subdomains that are formulated with the IGA and meshfree method, respectively. In the meshfree subdomain, the moving least squares shape function is adopted for the discretization of the area around crack tips, and the IGA subdomain is adopted in the remaining area. Meanwhile, the interface region between the 2 subdomains is represented by coupled shape functions. The resulting shape function, which comprises both IGA and meshfree shape functions, satisfies the consistency condition, thus ensuring convergence of the method. Moreover, the meshfree shape functions augmented with the enriched basis functions to predict the singular stress fields near a crack tip are presented. The proposed approach is also applied to simulate the crack propagation under a mixed‐mode condition. Several numerical examples are studied to demonstrate the use and robustness of the proposed method.