A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

Heng Peng, Yinghua Liu, Haofeng Chen

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13 Citations (Scopus)
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In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalComputational Mechanics
Issue number1
Early online date15 May 2018
Publication statusPublished - 31 Jan 2019


  • direct method
  • shakedown analysis
  • stress compensation method
  • large-scale
  • elastoplastic structures

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