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

Bordas, S.P.A.; Natarajan, S.; Kerfriden, P.; Augarde, C.E.; Mahapatra, D.R.; Rabczuk, T.; Dal Pont, S.

Abstract

By using the strain smoothing technique proposed by Chen et al. [1] for meshless methods in the context of the finite element method (FEM), Liu et al. [2] 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: (1) relative insensitivity to mesh distortion; (2) lack of isoparametric mapping; (3) avoidance of volumetric and shear locking; (4) suppression of the need to compute the derivatives of the shape functions; (5) possible super- convergence in the energy norm. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically the convergence properties in which conditions 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 standard enriched FEM (e.g. XFEM).

Citation

enriched finite element approximations (XFEM/GFEM/PUFEM). International Journal for Numerical Methods in Engineering, 86(4-5), 637-666. https://doi.org/10.1002/nme.3156

• Journal Article Type: Article
• Publication Date: 2011-04
• Deposit Date: Jan 24, 2011
• Journal: International Journal for Numerical Methods in Engineering
• Print ISSN: 0029-5981
• Electronic ISSN: 1097-0207
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 86
• Issue: 4-5
• Pages: 637-666
• DOI: https://doi.org/10.1002/nme.3156