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On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

Authors

  • Stéphane P. A. Bordas,

    Corresponding author
    1. Cardiff School of Engineering Theoretical, Applied and Computational Mechanics, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, U.K.
    2. Theoretical Applied and Computational Mechanics, Leverhulme/Royal Academy of Engineering, The Parade, Cardiff CF24 3AA, Wales, U.K.
    • School of Engineering, Theoretical, Applied and Computational Mechanics, Queen's Building, Room S1.03, Cardiff University, CF24 3AA, Wales, U.K.
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  • Sundararajan Natarajan,

    1. Cardiff School of Engineering Theoretical, Applied and Computational Mechanics, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, U.K.
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    • Professor and Senior Research Fellow.

  • Pierre Kerfriden,

    1. Cardiff School of Engineering Theoretical, Applied and Computational Mechanics, Cardiff University, Queen's Buildings, The Parade, Cardiff CF24 3AA, Wales, U.K.
    2. Theoretical Applied and Computational Mechanics, Leverhulme/Royal Academy of Engineering, The Parade, Cardiff CF24 3AA, Wales, U.K.
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    • Lecturer.

  • Charles Edward Augarde,

    1. Civil Engineering, School of Engineering and Computing Sciences, Durham University, Durham, U.K.
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    • Senior Lecturer.

  • D. Roy Mahapatra,

    1. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India
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    • Assistant Professor.

  • Timon Rabczuk,

    1. Department of Civil Engineering, Institute for Structural Mechanics, Bauhaus-Universität, Weimar, Germany
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    • Professor.

  • Stefano Dal Pont

    1. University Paris-Est, Laboratoire Central des Ponts et Chausses, BCC-LCPC, 58 bld Lefebvre, 75732 Paris, France
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    • Researcher.


Abstract

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 © 2011 John Wiley & Sons, Ltd.

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