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

Kazuki Shibanuma, Tomoaki Utsunomiya, Shuji Aihara

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)551-581
Number of pages31
JournalInternational Journal for Numerical Methods in Engineering
Volume97
Issue number8
DOIs
Publication statusPublished - Feb 24 2014
Externally publishedYes

Fingerprint

Partition of Unity
Fracture mechanics
Fracture Mechanics
Approximation
Remeshing
Cracks
Crack
Mesh
Numerical Results
Knowledge

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

Cite this

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abstract = "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.",
author = "Kazuki Shibanuma and Tomoaki Utsunomiya and Shuji Aihara",
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AU - Shibanuma, Kazuki

AU - Utsunomiya, Tomoaki

AU - Aihara, Shuji

PY - 2014/2/24

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N2 - 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.

AB - 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.

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