期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 86, 期 4-5, 页码 637-666出版社
WILEY
DOI: 10.1002/nme.3156
关键词
smoothed finite element method; boundary integration; eXtended finite element method; strain smoothing; linear elastic fracture mechanics
资金
- Royal Academy of Engineering and of the Leverhulme Trust
- EPSRC [EP/G042705/1]
- British Council under UK-France Alliance Grant for Bordas and Dal Pont
- Overseas Research Students Awards Scheme
- Faculty of Engineering, University of Glasgow
- School of Engineering (Cardiff University)
- EPSRC [EP/G042705/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/G042705/1] Funding Source: researchfish
By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). Copyright (C) 2011 John Wiley & Sons, Ltd.
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