Efficient integration of crack singularities in the extended finite element method
Duffy-distance transformation and conformal preconditioning strategy
- verfasst von
- 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.
- Organisationseinheit(en)
-
Institut für Kontinuumsmechanik
- Externe Organisation(en)
-
China University of Geosciences (CUG)
Bauhaus-Universität Weimar
Universität Nordostchinas (NEU)
- Typ
- Artikel
- Journal
- Computer Methods in Applied Mechanics and Engineering
- Band
- 340
- Seiten
- 559-576
- Anzahl der Seiten
- 18
- ISSN
- 0045-7825
- Publikationsdatum
- 01.10.2018
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Numerische Mechanik, Werkstoffmechanik, Maschinenbau, Allgemeine Physik und Astronomie, Angewandte Informatik
- Elektronische Version(en)
-
https://doi.org/10.1016/j.cma.2018.05.028 (Zugang:
Geschlossen)
