Computation of limit and shakedown loads using a node-based smoothed finite element method

H. Nguyen-Xuan, T. Rabczuk, T. Nguyen-Thoi, T. N. Tran, N. Nguyen-Thanh

Research output: Contribution to journalArticlepeer-review

82 Citations (Scopus)


This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal-dual algorithm. An associated primal-dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal-dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods.

Original languageEnglish
Pages (from-to)287-310
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Issue number3
Publication statusPublished - 2012 Apr 20


  • Finite element method
  • Limit analysis
  • Node-based smoothed finite element method (NS-FEM)
  • Primal-dual algorithm
  • Shakedown analysis
  • Strain smoothing

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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