An XFEM based kinematic limit analysis formulation for plane strain cracked structures using SOCP

Authors

  • Tran Trung Dung
    Faculty of Construction & Electricity, HCMC Open University, Viet Nam
  • Le Van Canh
    Department of Civil Engineering, International University, Viet Nam
  • Lam Phat Thuan
    Faculty of Civil Engineering and Applied Mechanics, University of Technical Education, Viet Nam

Keywords:

Limit analysis (LA); Extend finite element method (XFEM); Second-order cone programming (SOCP).

Abstract

This paper extends a numerical procedure for limit analysis based on extended finite element method (XFEM) and second-order cone programming (SOCP) to plane strain cracked structures. The cracked structures are easily modelled and simulated using XFEM because it allows discontinuities across elements, and these discontinuities are recognized by means of level set method. The resulting discretization formulation is then cast in a form which involves second-order cone constraints, ensuring that the underlying optimization problem can be solved by highly efficient primal-dual interior point algorithm. The efficiency of the present approach is illustrated by examing several numerical examples.

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References

Hill R. (1952). On discontinuous plastic states, with special reference to localized necking in thin sheets. Journal of the Mechanics and Physics of Solids, Vol. 1, pp. 19-30.

Ewing D. J. F. (1967). A series-method for constructing plastic slip-line fields. Journal of the Mechanics and Physics of Solids, Vol. 15, pp. 105-114.

Ewing D. J. F., Richards C. E. (1974). The yield-point loading of singly-notched pin loaded tensile strips. Journal of the Mechanics and Physics of Solids, Vol 22, pp. 27-36.

Yan A. M. (1997). Limit analysis of cracked structures by mathematical programming and finite element technique. Computational Mechanics 24 (1999), 319-333.

Vu Duc Khoi (2001). Dual limit and shakedown analysis of structures. Doctoral thesis, University of Liege.

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Received: 04-06-2020
Accepted: 04-06-2020
Published: 31-08-2013

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How to Cite

Dung, T. T., Canh, L. V., & Thuan, L. P. (2013). An XFEM based kinematic limit analysis formulation for plane strain cracked structures using SOCP. HO CHI MINH CITY OPEN UNIVERSITY JOURNAL OF SCIENCE - ENGINEERING AND TECHNOLOGY, 3(1), 50–58. Retrieved from https://journalofscience.ou.edu.vn/index.php/tech-en/article/view/402

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Copyright (c) 2013 Tran Trung Dung; Le Van Canh; Lam Phat Thuan

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.