Reference : On the performance of strain smoothing for quadratic and enriched finite element appr...

	Document type :	Scientific journals : Article
	Discipline(s) :	Engineering, computing & technology : Multidisciplinary, general & others
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/12113

Title :	On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)
Language :	English
Author, co-author :	Bordas, Stéphane [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
	Natarajan, S. [Cardiff School of Engineering Theoretical, Applied and Computational Mechanics, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, United Kingdom]
	Kerfriden, P. [Cardiff School of Engineering Theoretical, Applied and Computational Mechanics, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, United Kingdom, Theoretical Applied and Computational Mechanics, Leverhulme/Royal Academy of Engineering, The Parade, Cardiff CF24 3AA, Wales, United Kingdom]
	Augarde, C. E. [Civil Engineering, School of Engineering and Computing Sciences, Durham University, Durham, United Kingdom]
	Mahapatra, D. R. [Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India]
	Rabczuk, T. [Department of Civil Engineering, Institute for Structural Mechanics, Bauhaus-Universität, Weimar, Germany]
	Pont, S. D. [University Paris-Est, Laboratoire Central des Ponts et Chausses, BCC-LCPC, 58 bld Lefebvre, 75732 Paris, France]
Publication date :	2011
Journal title :	International Journal for Numerical Methods in Engineering
Volume :	86
Issue/season :	4-5
Pages :	637-666
Peer reviewed :	Yes (verified by ORBilu)
Audience :	International
ISSN :	00295981
Keywords :	[en] Boundary integration ; EXtended finite element method ; Linear elastic fracture mechanics ; Smoothed finite element method ; Strain smoothing ; Enriched finite elements ; Enrichment schemes ; Extended finite element method ; Higher order elements ; Mesh-less methods ; Numerical experiments ; Simple modifications ; Smoothing techniques ; Strong discontinuity ; Weak discontinuity ; Brittle fracture ; Fracture mechanics ; Polynomial approximation ; Finite element method
Abstract :	[en] 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). © 2011 John Wiley & Sons, Ltd.
Target :	Researchers ; Professionals ; Students ; General public
Permalink :	http://hdl.handle.net/10993/12113
DOI :	10.1002/nme.3156

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