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  4. Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping
 
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2019
Journal Article
Titel

Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping

Abstract
In this study, the extended finite element method (XFEM) is applied to the two-dimensional Laplace equation with an internal discontinuity. The real part of a complex velocity potential from potential flow theory is used to repre- sent the enrichment function in this technique. The Joukowski mapping, which maps a circle to a line, is mainly used to obtain a solution around an airfoil in two-dimensional potential flow; here, we extend that solution to model magnetic flux around an internal crack. The effectiveness of the proposed method is veri- fied using numerical examples of single and multiple cracks. The L 2 error norm is used to evaluate the accuracy of the proposed method in comparison with XFEM using previously proposed enrichment functions (Heaviside and analyt- ical f orms for a single crack tip). The proposed method gives better results than those of the existing XFEM in the case of a coarse mesh.
Author(s)
Nakasumi, Shogo
Advanced Manufacturing Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba East, 1-2-1 Namiki, Tsukuba 305-8564, Japan
Schweitzer, Marc Alexander
Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI
Zeitschrift
International journal for numerical methods in engineering
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DOI
10.1002/nme.6039
Language
English
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Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI
Tags
  • Efficient modeling

  • Laplace problem

  • XFEM

  • elliptic

  • extended finite element method

  • finite element methods

  • inverse problem

  • partial differential equations

  • partition-of-unity

  • potential flow

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