• CN: 11-2187/TH
  • ISSN: 0577-6686

Journal of Mechanical Engineering ›› 2023, Vol. 59 ›› Issue (18): 154-164.doi: 10.3901/JME.2023.18.154

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An Efficient Numerical Algorithm for Shakedown Analysis Combined with Basis Reduction

WANG Yu, CHENG Gengdong, LI Kai   

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024
  • Received:2022-10-20 Revised:2023-06-02 Online:2023-09-20 Published:2023-12-07

Abstract: Shakedown analysis is an important issue in structural design and integrity assessment. Primal-dual eigenstress-driven method (PEM) for shakedown analysis of structures is an efficient two-level nested algorithm which can be integrated with commercial finite element software for practical engineering problems, but the computational efficiency still needs to be further improved. An efficient numerical algorithm for shakedown analysis is proposed by combining basis reduction and the PEM method. The residual stress field generated by each iteration of the PEM method is used as the basis vector, and superimposed with the elastic stress field of corresponding load vertex, the shakedown analysis problem is simplified to a one-dimensional optimization problem in which the number of optimization variables is reduced. An accurate estimation of the shakedown multiplier is obtained by using the one-dimensional search 0.618 algorithm and the PEM method. This algorithm avoids the tedious incremental plastic analysis and only performs finite times iteration of elastic analysis and efficient one-dimensional search, which can significantly improve the computational efficiency of the algorithm and obtain accurate residual stress field. Combined with the commercial finite element software ANSYS APDL, the effectiveness of the algorithm is further verified by three examples of circular square plate, Bree plate and three-dimensional frame.

Key words: shakedown analysis, basis reduction, primal-dual eigenstress-driven method (PEM), elastoplastic, one-dimensional search 0.618 algorithm

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