Efficient integration of crack singularities in the extended finite element method: Duffy-distance transformation and conformal preconditioning strategy

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

Research output: Contribution to journalArticle

12 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)559-576
Number of pages18
JournalComputer Methods in Applied Mechanics and Engineering
Volume340
DOIs
Publication statusPublished - 2018 Oct 1
Externally publishedYes

Keywords

  • Conformal preconditioning
  • Duffy transformation
  • Numerical quadrature
  • Weak singularity
  • XFEM

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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