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).
| Original language | English |
|---|---|
| Pages (from-to) | 637-666 |
| Number of pages | 30 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 86 |
| Issue number | 4-5 |
| DOIs | |
| Publication status | Published - 2011 Apr 29 |
| Externally published | Yes |
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Keywords
- Boundary integration
- EXtended finite element method
- Linear elastic fracture mechanics
- Smoothed finite element method
- Strain smoothing
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
- Numerical Analysis
Cite this
On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). / Bordas, S. P A; Natarajan, Sundararajan; Kerfriden, Pierre; Augarde, Charles Edward; Mahapatra, D. Roy; Rabczuk, Timon; Pont, Stefano Dal.
In: International Journal for Numerical Methods in Engineering, Vol. 86, No. 4-5, 29.04.2011, p. 637-666.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)
AU - Bordas, S. P A
AU - Natarajan, Sundararajan
AU - Kerfriden, Pierre
AU - Augarde, Charles Edward
AU - Mahapatra, D. Roy
AU - Rabczuk, Timon
AU - Pont, Stefano Dal
PY - 2011/4/29
Y1 - 2011/4/29
N2 - 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).
AB - 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).
KW - Boundary integration
KW - EXtended finite element method
KW - Linear elastic fracture mechanics
KW - Smoothed finite element method
KW - Strain smoothing
UR - http://www.scopus.com/inward/record.url?scp=79953067834&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79953067834&partnerID=8YFLogxK
U2 - 10.1002/nme.3156
DO - 10.1002/nme.3156
M3 - Article
AN - SCOPUS:79953067834
VL - 86
SP - 637
EP - 666
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 4-5
ER -