Details
| Original language | English |
|---|---|
| Pages (from-to) | 72-85 |
| Number of pages | 14 |
| Journal | Engineering Analysis with Boundary Elements |
| Volume | 115 |
| Publication status | Published - 14 Apr 2020 |
Abstract
In this paper, an adaptive mesh refinement, namely polytree is presented to increase the resolution of polygonal meshes. Conforming to elements with hanging nodes from the process of generating polytree meshes by commonly using polygonal basic functions is inaccurate because their derivatives are singular in the vicinity of these nodes. Scaled boundary finite element method (SBFEM) is an excellent candidate to overcome such shortcomings. For crack simulations by using extended finite element method (XFEM), enrichment functions of discontinuous and asymptotic fields which get involved with high gradients are necessary to be solved by local mesh refinements. The idea of coupling XFEM with SBFEM is thus designed as an effective numerical technique to solve the negative effects of hanging nodes in adaptive mesh scheme and to raise the computational capability of XFEM in modeling crack problems over polygonal meshes. In addition, a modification of enriched nodes around the crack tip and a treatment of blending elements are introduced to improve the accuracy of XFEM analysis. Several numerical examples are examined to prove the computational efficiency of the present method for modeling crack problems in comparison with the uncoupled counterpart and previous published results.
Keywords
- Coupled numerical method, Fracture, Polytree, SBFEM, XFEM
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Engineering(all)
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Engineering Analysis with Boundary Elements, Vol. 115, 14.04.2020, p. 72-85.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A polytree-based adaptive scheme for modeling linear fracture mechanics using a coupled XFEM–SBFEM approach
AU - Huynh, Hai D.
AU - Zhuang, Xiaoying
AU - Nguyen-Xuan, H.
PY - 2020/4/14
Y1 - 2020/4/14
N2 - In this paper, an adaptive mesh refinement, namely polytree is presented to increase the resolution of polygonal meshes. Conforming to elements with hanging nodes from the process of generating polytree meshes by commonly using polygonal basic functions is inaccurate because their derivatives are singular in the vicinity of these nodes. Scaled boundary finite element method (SBFEM) is an excellent candidate to overcome such shortcomings. For crack simulations by using extended finite element method (XFEM), enrichment functions of discontinuous and asymptotic fields which get involved with high gradients are necessary to be solved by local mesh refinements. The idea of coupling XFEM with SBFEM is thus designed as an effective numerical technique to solve the negative effects of hanging nodes in adaptive mesh scheme and to raise the computational capability of XFEM in modeling crack problems over polygonal meshes. In addition, a modification of enriched nodes around the crack tip and a treatment of blending elements are introduced to improve the accuracy of XFEM analysis. Several numerical examples are examined to prove the computational efficiency of the present method for modeling crack problems in comparison with the uncoupled counterpart and previous published results.
AB - In this paper, an adaptive mesh refinement, namely polytree is presented to increase the resolution of polygonal meshes. Conforming to elements with hanging nodes from the process of generating polytree meshes by commonly using polygonal basic functions is inaccurate because their derivatives are singular in the vicinity of these nodes. Scaled boundary finite element method (SBFEM) is an excellent candidate to overcome such shortcomings. For crack simulations by using extended finite element method (XFEM), enrichment functions of discontinuous and asymptotic fields which get involved with high gradients are necessary to be solved by local mesh refinements. The idea of coupling XFEM with SBFEM is thus designed as an effective numerical technique to solve the negative effects of hanging nodes in adaptive mesh scheme and to raise the computational capability of XFEM in modeling crack problems over polygonal meshes. In addition, a modification of enriched nodes around the crack tip and a treatment of blending elements are introduced to improve the accuracy of XFEM analysis. Several numerical examples are examined to prove the computational efficiency of the present method for modeling crack problems in comparison with the uncoupled counterpart and previous published results.
KW - Coupled numerical method
KW - Fracture
KW - Polytree
KW - SBFEM
KW - XFEM
UR - http://www.scopus.com/inward/record.url?scp=85082107560&partnerID=8YFLogxK
U2 - 10.1016/j.enganabound.2019.11.001
DO - 10.1016/j.enganabound.2019.11.001
M3 - Article
AN - SCOPUS:85082107560
VL - 115
SP - 72
EP - 85
JO - Engineering Analysis with Boundary Elements
JF - Engineering Analysis with Boundary Elements
SN - 0955-7997
ER -