Details
| Original language | English |
|---|---|
| Pages (from-to) | 559-576 |
| Number of pages | 18 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 340 |
| Publication status | Published - 2 Jun 2018 |
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.
Keywords
- Conformal preconditioning, Duffy transformation, Numerical quadrature, Weak singularity, XFEM
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 340, 02.06.2018, p. 559-576.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Efficient integration of crack singularities in the extended finite element method
T2 - Duffy-distance transformation and conformal preconditioning strategy
AU - Lv, Jia He
AU - Jiao, Yu Yong
AU - Wriggers, Peter
AU - Rabczuk, Timon
AU - Feng, Xia Ting
AU - Tan, Fei
N1 - Funding information: The authors acknowledge the financial support from the National Natural Science Foundation of China (Nos. 51621006 , 51509240 , 41731284 and 11672360 ).
PY - 2018/6/2
Y1 - 2018/6/2
N2 - 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.
AB - 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.
KW - Conformal preconditioning
KW - Duffy transformation
KW - Numerical quadrature
KW - Weak singularity
KW - XFEM
UR - http://www.scopus.com/inward/record.url?scp=85049085032&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2018.05.028
DO - 10.1016/j.cma.2018.05.028
M3 - Article
AN - SCOPUS:85049085032
VL - 340
SP - 559
EP - 576
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -