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

S. P A Bordas, Sundararajan Natarajan, Pierre Kerfriden, Charles Edward Augarde, D. Roy Mahapatra, Timon Rabczuk, Stefano Dal Pont

Research output: Contribution to journalArticle

123 Citations (Scopus)

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 languageEnglish
Pages (from-to)637-666
Number of pages30
JournalInternational Journal for Numerical Methods in Engineering
Volume86
Issue number4-5
DOIs
Publication statusPublished - 2011 Apr 29
Externally publishedYes

Fingerprint

Finite Element Approximation
Smoothing
Finite Element Method
Finite element method
Higher-order Elements
Strong Discontinuity
Smoothing Techniques
Meshless Method
Fracture Mechanics
Approximation
Discontinuity
Numerical Experiment
Fracture mechanics
Polynomial
Polynomials
Experiments

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

Bordas, S. P. A., Natarajan, S., Kerfriden, P., Augarde, C. E., Mahapatra, D. R., Rabczuk, T., & Pont, S. D. (2011). On the performance of strain smoothing for quadratic and 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

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 journalArticle

Bordas, S. P A ; Natarajan, Sundararajan ; Kerfriden, Pierre ; Augarde, Charles Edward ; Mahapatra, D. Roy ; Rabczuk, Timon ; Pont, Stefano Dal. / On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). In: International Journal for Numerical Methods in Engineering. 2011 ; Vol. 86, No. 4-5. pp. 637-666.
@article{cbc54f92edcb47c2977034af4b7b3d69,
title = "On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)",
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).",
keywords = "Boundary integration, EXtended finite element method, Linear elastic fracture mechanics, Smoothed finite element method, Strain smoothing",
author = "Bordas, {S. P A} and Sundararajan Natarajan and Pierre Kerfriden and Augarde, {Charles Edward} and Mahapatra, {D. Roy} and Timon Rabczuk and Pont, {Stefano Dal}",
year = "2011",
month = "4",
day = "29",
doi = "10.1002/nme.3156",
language = "English",
volume = "86",
pages = "637--666",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "4-5",

}

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 -