An explicit application of partition of unity approach to XFEM approximation for precise reproduction of<i>a priori</i>knowledge of solution

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  • Kazuki Shibanuma
    Department of Systems Innovation; The University of Tokyo; Tokyo Japan
  • Tomoaki Utsunomiya
    Department of Civil and Earth Resources Engineering; Kyoto University; Kyoto Japan
  • Shuji Aihara
    Department of Systems Innovation; The University of Tokyo; Tokyo Japan

書誌事項

タイトル別名
  • EXPLICIT APPLICATION OF PU APPROACH TO XFEM APPROXIMATION
公開日
2013-11-04
権利情報
  • http://doi.wiley.com/10.1002/tdm_license_1.1
DOI
  • 10.1002/nme.4593
公開者
Wiley

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説明

SUMMARY The application of the XFEM to fracture mechanics is effective, because a crack can be modeled independently from the meshes and a complex remeshing procedure can be avoided. However, the classical XFEM has an essential problem in the approximation of partially enriched elements, that is, blending elements, which causes a lack of accuracy. For the weighted XFEM, although the numerical results show the effective improvements, it was found that the issue of blending elements still remains upon detailed examination. In the present paper, the PU-XFEM is formulated as an explicit application of the partition of unity (PU) approach to the XFEM, in order to precisely reproduce a priori knowledge of the solution by enrichment. The PU-XFEM is applied to two-dimensional linear fracture mechanics, and its effectiveness is verified. It is consequently found out that the PU-XFEM precisely reproduces a priori knowledge of the solution and is therefore effective to completely solve the problem of the blending elements. Copyright © 2013 John Wiley & Sons, Ltd.

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