Abstract
This paper presents a FEM with mesh-separation-based approximation technique that separates a standard element into three geometrically independent elements. A dual mapping scheme is introduced to couple them seamlessly and to derive the element approximation. The novel technique makes it very easy for mesh generation of problems with complex or solution-dependent, varying geometry. It offers a flexible way to construct displacement approximations and provides a unified framework for the FEM to enjoy some of the key advantages of the Hansbo and Hansbo method, the meshfree methods, the semi-analytical FEMs, and the smoothed FEM. For problems with evolving discontinuities, the method enables the devising of an efficient crack-tip adaptive mesh refinement strategy to improve the accuracy of crack-tip fields. Both the discontinuities due to intra-element cracking and the incompatibility due to hanging nodes resulted from the element refinement can be treated at the elemental level. The effectiveness and robustness of the present method are benchmarked with several numerical examples. The numerical results also demonstrate that a high precision integral scheme is critical to pass the crack patch test, and it is essential to apply local adaptive mesh refinement for low fracture energy problems.
| Original language | English |
|---|---|
| Pages (from-to) | 487-521 |
| Number of pages | 35 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 99 |
| Issue number | 7 |
| DOIs | |
| State | Published - Aug 17 2014 |
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Keywords
- Adaptive mesh refinement
- Approximation technique
- Discontinuity
- FEM
- Hanging node
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
- Numerical Analysis
Cite this
A finite element method with mesh-separation-based approximation technique and its application in modeling crack propagation with adaptive mesh refinement. / Ling, Daosheng; Bu, Lingfang; Tu, Fubin; Yang, Qingda; Chen, Yunmin.
In: International Journal for Numerical Methods in Engineering, Vol. 99, No. 7, 17.08.2014, p. 487-521.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A finite element method with mesh-separation-based approximation technique and its application in modeling crack propagation with adaptive mesh refinement
AU - Ling, Daosheng
AU - Bu, Lingfang
AU - Tu, Fubin
AU - Yang, Qingda
AU - Chen, Yunmin
PY - 2014/8/17
Y1 - 2014/8/17
N2 - This paper presents a FEM with mesh-separation-based approximation technique that separates a standard element into three geometrically independent elements. A dual mapping scheme is introduced to couple them seamlessly and to derive the element approximation. The novel technique makes it very easy for mesh generation of problems with complex or solution-dependent, varying geometry. It offers a flexible way to construct displacement approximations and provides a unified framework for the FEM to enjoy some of the key advantages of the Hansbo and Hansbo method, the meshfree methods, the semi-analytical FEMs, and the smoothed FEM. For problems with evolving discontinuities, the method enables the devising of an efficient crack-tip adaptive mesh refinement strategy to improve the accuracy of crack-tip fields. Both the discontinuities due to intra-element cracking and the incompatibility due to hanging nodes resulted from the element refinement can be treated at the elemental level. The effectiveness and robustness of the present method are benchmarked with several numerical examples. The numerical results also demonstrate that a high precision integral scheme is critical to pass the crack patch test, and it is essential to apply local adaptive mesh refinement for low fracture energy problems.
AB - This paper presents a FEM with mesh-separation-based approximation technique that separates a standard element into three geometrically independent elements. A dual mapping scheme is introduced to couple them seamlessly and to derive the element approximation. The novel technique makes it very easy for mesh generation of problems with complex or solution-dependent, varying geometry. It offers a flexible way to construct displacement approximations and provides a unified framework for the FEM to enjoy some of the key advantages of the Hansbo and Hansbo method, the meshfree methods, the semi-analytical FEMs, and the smoothed FEM. For problems with evolving discontinuities, the method enables the devising of an efficient crack-tip adaptive mesh refinement strategy to improve the accuracy of crack-tip fields. Both the discontinuities due to intra-element cracking and the incompatibility due to hanging nodes resulted from the element refinement can be treated at the elemental level. The effectiveness and robustness of the present method are benchmarked with several numerical examples. The numerical results also demonstrate that a high precision integral scheme is critical to pass the crack patch test, and it is essential to apply local adaptive mesh refinement for low fracture energy problems.
KW - Adaptive mesh refinement
KW - Approximation technique
KW - Discontinuity
KW - FEM
KW - Hanging node
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UR - http://www.scopus.com/inward/citedby.url?scp=84904278267&partnerID=8YFLogxK
U2 - 10.1002/nme.4689
DO - 10.1002/nme.4689
M3 - Article
AN - SCOPUS:84904278267
VL - 99
SP - 487
EP - 521
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 7
ER -