Strain smoothing in FEM and XFEM

Stéphane P A Bordas, Timon Rabczuk, Nguyen Xuan Hung, Vinh Phu Nguyen, Sundararajan Natarajan, Tino Bog, Do Minh Quan, Nguyen Vinh Hiep

Research output: Contribution to journalArticle

210 Citations (Scopus)

Abstract

We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The numerical results indicate that for 2D and 3D continuum, locking can be avoided. New plate and shell formulations that avoid both shear and membrane locking are also briefly reviewed. The principle is then extended to partition of unity enrichment to simplify numerical integration of discontinuous approximations in the extended finite element method. Examples are presented to test the new elements for problems involving cracks in linear elastic continua and cracked plates. In the latter case, the proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. Two important features of the set of elements presented are their insensitivity to mesh distortion and a lower computational cost than standard finite elements for the same accuracy. These elements are easily implemented in existing codes since they only require the modification of the discretized gradient operator, B.

Original languageEnglish
Pages (from-to)1419-1443
Number of pages25
JournalComputers and Structures
Volume88
Issue number23-24
DOIs
Publication statusPublished - 2010 Dec 1
Externally publishedYes

Fingerprint

Locking
Smoothing
Cracks
Membranes
Finite element method
Continuum
Finite Element
Costs
Extended Finite Element Method
Partition of Unity
Insensitivity
Formulation
Thin Plate
Numerical integration
Computational Cost
Discontinuity
Shell
Simplify
Crack
Membrane

Keywords

  • Accuracy
  • Convergence
  • Extended finite element method
  • SFEM
  • Smoothed finite element
  • XFEM

ASJC Scopus subject areas

  • Computer Science Applications
  • Civil and Structural Engineering
  • Mechanical Engineering
  • Modelling and Simulation
  • Materials Science(all)

Cite this

Bordas, S. P. A., Rabczuk, T., Hung, N. X., Nguyen, V. P., Natarajan, S., Bog, T., ... Hiep, N. V. (2010). Strain smoothing in FEM and XFEM. Computers and Structures, 88(23-24), 1419-1443. https://doi.org/10.1016/j.compstruc.2008.07.006

Strain smoothing in FEM and XFEM. / Bordas, Stéphane P A; Rabczuk, Timon; Hung, Nguyen Xuan; Nguyen, Vinh Phu; Natarajan, Sundararajan; Bog, Tino; Quan, Do Minh; Hiep, Nguyen Vinh.

In: Computers and Structures, Vol. 88, No. 23-24, 01.12.2010, p. 1419-1443.

Research output: Contribution to journalArticle

Bordas, SPA, Rabczuk, T, Hung, NX, Nguyen, VP, Natarajan, S, Bog, T, Quan, DM & Hiep, NV 2010, 'Strain smoothing in FEM and XFEM', Computers and Structures, vol. 88, no. 23-24, pp. 1419-1443. https://doi.org/10.1016/j.compstruc.2008.07.006
Bordas SPA, Rabczuk T, Hung NX, Nguyen VP, Natarajan S, Bog T et al. Strain smoothing in FEM and XFEM. Computers and Structures. 2010 Dec 1;88(23-24):1419-1443. https://doi.org/10.1016/j.compstruc.2008.07.006
Bordas, Stéphane P A ; Rabczuk, Timon ; Hung, Nguyen Xuan ; Nguyen, Vinh Phu ; Natarajan, Sundararajan ; Bog, Tino ; Quan, Do Minh ; Hiep, Nguyen Vinh. / Strain smoothing in FEM and XFEM. In: Computers and Structures. 2010 ; Vol. 88, No. 23-24. pp. 1419-1443.
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