Professor and Senior Research Fellow.
On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)
Article first published online: 1 MAR 2011
Copyright © 2011 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Special Issue: Extended Finite Element Method
Volume 86, Issue 4-5, pages 637–666, 29 April - 6 May 2011
How to Cite
Bordas, S. P. A., Natarajan, S., Kerfriden, P., Augarde, C. E., Mahapatra, D. R., Rabczuk, T. and Pont, S. D. (2011), On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). Int. J. Numer. Meth. Engng., 86: 637–666. doi: 10.1002/nme.3156
- Issue published online: 28 MAR 2011
- Article first published online: 1 MAR 2011
- Manuscript Accepted: 4 JAN 2011
- Manuscript Revised: 26 NOV 2010
- Manuscript Received: 1 JUL 2010
- smoothed finite element method;
- boundary integration;
- eXtended finite element method;
- strain smoothing;
- linear elastic fracture mechanics
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.