Efficient integration of crack singularities in the extended finite element method

Duffy-distance transformation and conformal preconditioning strategy

authored by
Jia He Lv, Yu Yong Jiao, Peter Wriggers, Timon Rabczuk, Xia Ting Feng, Fei Tan
Abstract

For integrals with various orders of vertex singularity encountered in the generalized/extended finite element method, three difficulties should be concerned as: (a) the singularity with respect to local distance r; (b) the near singularity caused by ill-shaped patches; (c) the near singularity during the iso-parametric transformation. In this paper, based on the Duffy transformation, the near singularities caused by ill-shaped patches and element shape distortion are revealed theoretically and numerically, a Duffy-distance transformation is constructed to damp out the near singularity caused by ill-shaped patches, and a conformal preconditioning strategy is developed to fully eliminate the near singularity caused by element shape distortion. Extensive numerical examples, including crack-tip elements with distorted shape, are given to validate the efficiency and robustness of the presented scheme in this paper.

Organisation(s)
Institute of Continuum Mechanics
External Organisation(s)
China University of Geosciences
Bauhaus-Universität Weimar
Northeastern University, Shenyang (NEU)
Type
Article
Journal
Computer Methods in Applied Mechanics and Engineering
Volume
340
Pages
559-576
No. of pages
18
ISSN
0045-7825
Publication date
02.06.2018
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s)
https://doi.org/10.1016/j.cma.2018.05.028 (Access: Closed)
 

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