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

By Stéphane P.A. Bordas, Sundararajan Natarajan, Pierre Kerfriden, Charles E. Augarde, D. Roy Mahapatra, Timon Rabczuk, S. Pont. 2011

182 citations recorded by the source corpus.

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.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/00cb82650d8f55ed3e7ac5b37e5b897388782503

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In Mechanics of Materials

Citations in the corpus

Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods (2015, methodology): “However, certain difficulties still exist as discussed in [10].”
Computation of limit and shakedown loads using a node‐based smoothed finite element method (2012, methodology): “The CS-FEM has been studied theoretically in [3–5], and further extended to the general n-sided polygonal elements (nSFEM or nCS-FEM) [6], dynamic analyses [7], incompressible materials using selective integration [8, 9], plate and shell analyses [10–12], fracture mechanics problems [13, 14], and li”