Efficient modeling of internal cracks for Laplace problem by XFEM using Joukowski mapping. (8th March 2019)

• Record Type: Journal Article
• Authors: Nakasumi, Shogo; Schweitzer, Marc Alexander
• Is Part Of: International journal for numerical methods in engineering. Volume 119:Number 1(2019)
• Page Start: 1
• Page End: 17
• Publication Date: 2019-03-08
• Subjects: elliptic -- extended finite element method -- finite element methods -- inverse problem -- partial differential equations -- partition‐of‐unity -- potential flow; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6039
• Languages: English
• ISSNs: 0029-5981

Abstract

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.