Details
| Original language | English |
|---|---|
| Article number | 112908 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 363 |
| Publication status | Published - 19 Feb 2020 |
Abstract
With the development of PU-based numerical methods for crack problems, the evaluation of various orders of vertex/edge singularity has been one of the most critical issues, which restrains the computational efficiency of PU-based methods, especially for 3D crack problems. In this paper, based on the conventional Duffy transformation, a general algorithm for numerical integration of three-dimensional crack singularities is proposed for the vertex/edge singularity problems, which takes the integration cell shape into full consideration. Besides, the corresponding 3D conformal preconditioning strategy is constructed to fully eliminate the shape influence of tetrahedron elements. Extensive numerical examples, including ill-shaped integration cells and crack-front tetrahedron elements with parallel/nonparallel crack front, are given to validate the feasibility and accuracy of the proposed method. As a result, for each crack-front element, several hundreds of Gauss points are sufficient to achieve the precision of 10−6 for both kernels 1∕r and 1∕r, in sharp contrast with around ten thousands of Gauss points using the conventional Duffy transformation.
Keywords
- Distance transformation, Duffy transformation, Numerical quadrature, PU-based numerical methods, Singular integrals
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 363, 112908, 19.02.2020.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A general algorithm for numerical integration of three-dimensional crack singularities in PU-based numerical methods
AU - Lv, Jia He
AU - Jiao, Yu Yong
AU - Rabczuk, Timon
AU - Zhuang, Xiaoying
AU - Feng, Xia Ting
AU - Tan, Fei
N1 - Funding information: The authors acknowledge the financial support from the National Natural Science Foundation of China (Nos. 51979253 , 41731284 , 41920104007 , 11672360 , 51621006 and 51879245 ).
PY - 2020/2/19
Y1 - 2020/2/19
N2 - With the development of PU-based numerical methods for crack problems, the evaluation of various orders of vertex/edge singularity has been one of the most critical issues, which restrains the computational efficiency of PU-based methods, especially for 3D crack problems. In this paper, based on the conventional Duffy transformation, a general algorithm for numerical integration of three-dimensional crack singularities is proposed for the vertex/edge singularity problems, which takes the integration cell shape into full consideration. Besides, the corresponding 3D conformal preconditioning strategy is constructed to fully eliminate the shape influence of tetrahedron elements. Extensive numerical examples, including ill-shaped integration cells and crack-front tetrahedron elements with parallel/nonparallel crack front, are given to validate the feasibility and accuracy of the proposed method. As a result, for each crack-front element, several hundreds of Gauss points are sufficient to achieve the precision of 10−6 for both kernels 1∕r and 1∕r, in sharp contrast with around ten thousands of Gauss points using the conventional Duffy transformation.
AB - With the development of PU-based numerical methods for crack problems, the evaluation of various orders of vertex/edge singularity has been one of the most critical issues, which restrains the computational efficiency of PU-based methods, especially for 3D crack problems. In this paper, based on the conventional Duffy transformation, a general algorithm for numerical integration of three-dimensional crack singularities is proposed for the vertex/edge singularity problems, which takes the integration cell shape into full consideration. Besides, the corresponding 3D conformal preconditioning strategy is constructed to fully eliminate the shape influence of tetrahedron elements. Extensive numerical examples, including ill-shaped integration cells and crack-front tetrahedron elements with parallel/nonparallel crack front, are given to validate the feasibility and accuracy of the proposed method. As a result, for each crack-front element, several hundreds of Gauss points are sufficient to achieve the precision of 10−6 for both kernels 1∕r and 1∕r, in sharp contrast with around ten thousands of Gauss points using the conventional Duffy transformation.
KW - Distance transformation
KW - Duffy transformation
KW - Numerical quadrature
KW - PU-based numerical methods
KW - Singular integrals
UR - http://www.scopus.com/inward/record.url?scp=85079558017&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2020.112908
DO - 10.1016/j.cma.2020.112908
M3 - Article
AN - SCOPUS:85079558017
VL - 363
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 112908
ER -