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

Heng Peng, Yinghua Liu, Haofeng Chen

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.
Language English 1-22 22 Computational Mechanics 63 1 15 May 2018 10.1007/s00466-018-1581-x Published - 31 Jan 2019

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Elasto-plastic
Multiplier
Formulation
Mathematical programming
Stiffness matrix
Robust control
Residual stresses
Finite Element Solution
Residual Stress
Iterative Procedure
Stiffness Matrix
Stress Field
Direct Method
Mathematical Programming
Finite Element
Iteration
Numerical Examples
Three-dimensional
Series
Vertex of a graph

Keywords

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

Cite this

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abstract = "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.",
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In: Computational Mechanics , Vol. 63, No. 1, 31.01.2019, p. 1-22.

Research output: Contribution to journalArticle

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