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

• Published in: Computational mechanics Vol. 63; no. 1; pp. 1 - 22
• Main Authors: Peng, Heng, Liu, Yinghua, Chen, Haofeng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2019; Springer; Springer Nature B.V
• Subjects: Algorithms; Classical and Continuum Physics; Computational Science and Engineering; Elastoplasticity; Engineering; Finite element method; Iterative methods; Mathematical programming; Matrix methods; Original Paper; Residual stress; Robust control; Robustness (mathematics); Shakedown analysis; Stiffness matrix; Stress distribution; Theoretical and Applied Mechanics; Direct method; Elastoplastic structures; Large-scale; Stress compensation method; Shakedown analysis
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-018-1581-x

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.