Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 340, Issue -, Pages 559-576Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2018.05.028
Keywords
Weak singularity; Duffy transformation; Conformal preconditioning; XFEM; Numerical quadrature
Funding
- National Natural Science Foundation of China [51621006, 51509240, 41731284, 11672360]
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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. (C) 2018 Elsevier B.Y. All rights reserved.
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