Details
| Original language | English |
|---|---|
| Pages (from-to) | 38-60 |
| Number of pages | 23 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 118 |
| Issue number | 1 |
| Early online date | 5 Mar 2019 |
| Publication status | Published - 6 Apr 2019 |
Abstract
With the development of the generalized/extended finite element method for fracture problems, the accurate and efficient integration of singular enrichment functions has been an open issue, especially for the 3D case. In this paper, we reveal the near singularities caused by distorted integral patch/cell shape numerically and theoretically during the implementation of generalized Duffy transformation, and the Duffy-distance transformation is developed step by step for the 2D and 3D vertex singularities. Meanwhile, the 3D conformal preconditioning strategy is constructed to eliminate the near singularity caused by element shape distortion during the iso-parametric transformation, which enables the Duffy-distance transformation to be applicable for arbitrary shaped tetrahedral elements. As a result, the near singularities can be fully or partly canceled depending on the order of singularity. The implementation of the proposed scheme in existing codes is straightforward. Numerous numerical examples for arbitrary shaped triangles and tetrahedrons are presented to demonstrate its robustness and efficiency, along with comparisons to the generalized Duffy transformation.
Keywords
- distance transformation, Duffy transformation, near singularity, numerical quadrature, vertex singularity
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 118, No. 1, 06.04.2019, p. 38-60.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A series of Duffy-distance transformation for integrating 2D and 3D vertex singularities
AU - Lv, Jia He
AU - Jiao, Yu Yong
AU - Feng, Xia Ting
AU - Wriggers, Peter
AU - Zhuang, Xiao Ying
AU - Rabczuk, Timon
N1 - Funding information: The authors acknowledge the financial support from the National Natural Science Foundation of China (grants 51621006, 51509240, 41731284, and 11672360) and the State Key Research Development Program of China (grant 2016YFC0600707).
PY - 2019/4/6
Y1 - 2019/4/6
N2 - With the development of the generalized/extended finite element method for fracture problems, the accurate and efficient integration of singular enrichment functions has been an open issue, especially for the 3D case. In this paper, we reveal the near singularities caused by distorted integral patch/cell shape numerically and theoretically during the implementation of generalized Duffy transformation, and the Duffy-distance transformation is developed step by step for the 2D and 3D vertex singularities. Meanwhile, the 3D conformal preconditioning strategy is constructed to eliminate the near singularity caused by element shape distortion during the iso-parametric transformation, which enables the Duffy-distance transformation to be applicable for arbitrary shaped tetrahedral elements. As a result, the near singularities can be fully or partly canceled depending on the order of singularity. The implementation of the proposed scheme in existing codes is straightforward. Numerous numerical examples for arbitrary shaped triangles and tetrahedrons are presented to demonstrate its robustness and efficiency, along with comparisons to the generalized Duffy transformation.
AB - With the development of the generalized/extended finite element method for fracture problems, the accurate and efficient integration of singular enrichment functions has been an open issue, especially for the 3D case. In this paper, we reveal the near singularities caused by distorted integral patch/cell shape numerically and theoretically during the implementation of generalized Duffy transformation, and the Duffy-distance transformation is developed step by step for the 2D and 3D vertex singularities. Meanwhile, the 3D conformal preconditioning strategy is constructed to eliminate the near singularity caused by element shape distortion during the iso-parametric transformation, which enables the Duffy-distance transformation to be applicable for arbitrary shaped tetrahedral elements. As a result, the near singularities can be fully or partly canceled depending on the order of singularity. The implementation of the proposed scheme in existing codes is straightforward. Numerous numerical examples for arbitrary shaped triangles and tetrahedrons are presented to demonstrate its robustness and efficiency, along with comparisons to the generalized Duffy transformation.
KW - distance transformation
KW - Duffy transformation
KW - near singularity
KW - numerical quadrature
KW - vertex singularity
UR - http://www.scopus.com/inward/record.url?scp=85060240256&partnerID=8YFLogxK
U2 - 10.1002/nme.6016
DO - 10.1002/nme.6016
M3 - Article
AN - SCOPUS:85060240256
VL - 118
SP - 38
EP - 60
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 1
ER -