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Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping
Author(s) -
Nakasumi Shogo,
Schweitzer Marc Alexander
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6039
Subject(s) - heaviside step function , extended finite element method , classification of discontinuities , discontinuity (linguistics) , laplace transform , finite element method , mathematical analysis , airfoil , laplace's equation , mathematics , algorithm , geometry , structural engineering , engineering , boundary value problem
Summary 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 represent 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 verified 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 analytical forms for a single crack tip). The proposed method gives better results than those of the existing XFEM in the case of a coarse mesh.