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A series of Duffy-distance transformation for integrating 2D and 3D vertex singularities

文献类型：期刊论文

作者Lv, Jia-He2,3,4; Jiao, Yu-Yong2; Feng, Xia-Ting1,3; Wriggers, Peter4; Zhuang, Xiao-Ying4; Rabczuk, Timon5
刊名INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
出版日期2019-04-06
卷号118期号:1页码:38-60
关键词distance transformation Duffy transformation near singularity numerical quadrature vertex singularity
ISSN号0029-5981
DOI10.1002/nme.6016
英文摘要With the development of the generalized/extended finite element method for fracture problems, the accurate and efficient integration of singular enrichment functions has been an open issue, especially for the 3D case. In this paper, we reveal the near singularities caused by distorted integral patch/cell shape numerically and theoretically during the implementation of generalized Duffy transformation, and the Duffy-distance transformation is developed step by step for the 2D and 3D vertex singularities. Meanwhile, the 3D conformal preconditioning strategy is constructed to eliminate the near singularity caused by element shape distortion during the iso-parametric transformation, which enables the Duffy-distance transformation to be applicable for arbitrary shaped tetrahedral elements. As a result, the near singularities can be fully or partly canceled depending on the order of singularity. The implementation of the proposed scheme in existing codes is straightforward. Numerous numerical examples for arbitrary shaped triangles and tetrahedrons are presented to demonstrate its robustness and efficiency, along with comparisons to the generalized Duffy transformation.
资助项目National Natural Science Foundation of China[51621006] ; National Natural Science Foundation of China[51509240] ; National Natural Science Foundation of China[41731284] ; National Natural Science Foundation of China[11672360] ; State Key Research Development Program of China[2016YFC0600707]
WOS研究方向Engineering ; Mathematics
语种英语
WOS记录号WOS:000460346700003
出版者WILEY
源URL[http://202.127.146.157/handle/2RYDP1HH/7524]  
专题中国科学院武汉植物园
通讯作者Jiao, Yu-Yong
作者单位1.Northeastern Univ, Sch Resources & Civil Engn, Minist Educ Safe Min Deep Met Mines, Key Lab, Shenyang, Liaoning, Peoples R China
2.China Univ Geosci, Fac Engn, Wuhan 430074, Hubei, Peoples R China
3.Chinese Acad Sci, Inst Rock & Soil Mech, State Key Lab Geomech & Geotech Engn, Wuhan, Hubei, Peoples R China
4.Leibniz Univ Hannover, Inst Continuum Mech, Hannover, Germany
5.Bauhaus Univ Weimar, Inst Struct Mech, Weimar, Germany
推荐引用方式
GB/T 7714		 Lv, Jia-He,Jiao, Yu-Yong,Feng, Xia-Ting,et al. A series of Duffy-distance transformation for integrating 2D and 3D vertex singularities[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,2019,118(1):38-60.
APA Lv, Jia-He,Jiao, Yu-Yong,Feng, Xia-Ting,Wriggers, Peter,Zhuang, Xiao-Ying,&Rabczuk, Timon.(2019).A series of Duffy-distance transformation for integrating 2D and 3D vertex singularities.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,118(1),38-60.
MLA Lv, Jia-He,et al."A series of Duffy-distance transformation for integrating 2D and 3D vertex singularities".INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 118.1(2019):38-60.

入库方式： OAI收割

来源：武汉植物园

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