The smoothed extended finite element method

S. Natarajan, S. Bordas, Q. D. Minh, H. X. Nguyen, Timon Rabczuk, L. Cahill, C. McCarthy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM), which shares properties both with the SFEM and the XFEM. The proposed method suppresses the need to compute and integrate the derivatives of shape functions (which are singular at the tip in linear elastic fracture mechanics). Additionally, integration is performed along the boundary of the finite elements or smoothing cells and no isoparametric mapping is required, which allows elements of arbitrary shape. We present numerical results for cracks in linear elastic fracture mechanics problems. The method is verified on several examples and comparisons are made to the conventional XFEM.

Original languageEnglish
Title of host publicationProceedings of the 6th International Conference on Engineering Computational Technology
Publication statusPublished - 2008 Dec 1
Externally publishedYes
Event6th International Conference on Engineering Computational Technology, ECT 2008 - Athens, Greece
Duration: 2008 Sep 22008 Sep 5

Other

Other6th International Conference on Engineering Computational Technology, ECT 2008
CountryGreece
CityAthens
Period08/9/208/9/5

Fingerprint

Finite element method
Fracture mechanics
Derivatives
Cracks

Keywords

  • Cracks without remeshing
  • Extended finite element method
  • Fracture mechanics
  • Partition of unity methods
  • Smoothed finite element method
  • Strain smoothing

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Natarajan, S., Bordas, S., Minh, Q. D., Nguyen, H. X., Rabczuk, T., Cahill, L., & McCarthy, C. (2008). The smoothed extended finite element method. In Proceedings of the 6th International Conference on Engineering Computational Technology

The smoothed extended finite element method. / Natarajan, S.; Bordas, S.; Minh, Q. D.; Nguyen, H. X.; Rabczuk, Timon; Cahill, L.; McCarthy, C.

Proceedings of the 6th International Conference on Engineering Computational Technology. 2008.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Natarajan, S, Bordas, S, Minh, QD, Nguyen, HX, Rabczuk, T, Cahill, L & McCarthy, C 2008, The smoothed extended finite element method. in Proceedings of the 6th International Conference on Engineering Computational Technology. 6th International Conference on Engineering Computational Technology, ECT 2008, Athens, Greece, 08/9/2.
Natarajan S, Bordas S, Minh QD, Nguyen HX, Rabczuk T, Cahill L et al. The smoothed extended finite element method. In Proceedings of the 6th International Conference on Engineering Computational Technology. 2008
Natarajan, S. ; Bordas, S. ; Minh, Q. D. ; Nguyen, H. X. ; Rabczuk, Timon ; Cahill, L. ; McCarthy, C. / The smoothed extended finite element method. Proceedings of the 6th International Conference on Engineering Computational Technology. 2008.
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