A cell-based smoothed finite element method for kinematic limit analysis

Canh V. Le, H. Nguyen-Xuan, H. Askes, Stéphane P A Bordas, Timon Rabczuk, H. Nguyen-Vinh

Research output: Contribution to journalArticle

70 Citations (Scopus)

Abstract

This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second-order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged.

Original languageEnglish
Pages (from-to)1651-1674
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Volume83
Issue number12
DOIs
Publication statusPublished - 2010 Sep 17
Externally publishedYes

Fingerprint

Limit Analysis
Kinematic Analysis
Cones
Kinematics
Finite Element Method
Finite element method
Cell
Second-order Cone Programming
Computer programming
Volumetric Locking
Optimization Problem
Euclidean norm
Nonsmooth Optimization
Smoothing Techniques
Plane Stress
Plane Strain
Numerical Procedure
Quadratic form
Finite Element

Keywords

  • A sum of norms
  • CS-FEM
  • Limit analysis
  • Second-order cone programming
  • Strain smoothing

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

Cite this

Le, C. V., Nguyen-Xuan, H., Askes, H., Bordas, S. P. A., Rabczuk, T., & Nguyen-Vinh, H. (2010). A cell-based smoothed finite element method for kinematic limit analysis. International Journal for Numerical Methods in Engineering, 83(12), 1651-1674. https://doi.org/10.1002/nme.2897

A cell-based smoothed finite element method for kinematic limit analysis. / Le, Canh V.; Nguyen-Xuan, H.; Askes, H.; Bordas, Stéphane P A; Rabczuk, Timon; Nguyen-Vinh, H.

In: International Journal for Numerical Methods in Engineering, Vol. 83, No. 12, 17.09.2010, p. 1651-1674.

Research output: Contribution to journalArticle

Le, CV, Nguyen-Xuan, H, Askes, H, Bordas, SPA, Rabczuk, T & Nguyen-Vinh, H 2010, 'A cell-based smoothed finite element method for kinematic limit analysis', International Journal for Numerical Methods in Engineering, vol. 83, no. 12, pp. 1651-1674. https://doi.org/10.1002/nme.2897
Le, Canh V. ; Nguyen-Xuan, H. ; Askes, H. ; Bordas, Stéphane P A ; Rabczuk, Timon ; Nguyen-Vinh, H. / A cell-based smoothed finite element method for kinematic limit analysis. In: International Journal for Numerical Methods in Engineering. 2010 ; Vol. 83, No. 12. pp. 1651-1674.
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