Computational Mechanics

, Volume 63, Issue 1, pp 1–22 | Cite as

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

  • Heng Peng
  • Yinghua LiuEmail author
  • Haofeng Chen
Original Paper


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.


Direct method Shakedown analysis Stress compensation method Large-scale Elastoplastic structures 



The authors would like to thank the support of the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 11325211), the National Natural Science Foundation of China (Grant No. 11672147) and the Project of International Cooperation and Exchange NSFC (Grant No. 11511130057) during the course of this work.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Engineering Mechanics, AMLTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of StrathclydeGlasgowUK

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