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A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics

  • This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement intoThis paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.show moreshow less

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Metadaten
Document Type:Article
Author: N. Vu-Bac, Hung Nguyen-Xuan, Lei Chen, C.K. Lee, Goangseup Zi, Xiaoying Zhuang, G.R. Liu, Timon RabczukORCiDGND
DOI (Cite-Link):https://doi.org/10.1155/2013/978026Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170426-31676Cite-Link
Parent Title (English):Journal of Applied Mathematics
Language:English
Date of Publication (online):2017/04/26
Year of first Publication:2013
Release Date:2017/04/26
Publishing Institution:Bauhaus-Universität Weimar
Institutes:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
GND Keyword:Finite-Elemente-Methode; Steifigkeit; Bruchmechanik; Riss
Dewey Decimal Classification:600 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
54 Informatik / 54.80 Angewandte Informatik
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)