A basis reduction method using proper orthogonal decomposition for shakedown analysis of kinematic hardening material

摘要

In this paper, the authors firstly propose a new basis reduction method of lower bound shakedown analysis for the perfectly-plastic material, based on the proper orthogonal decomposition. The proposed method contains the plastic incremental analysis with some pre-chosen monotonic increasing loadings, the proper orthogonal decomposition and the elastic analysis with the initial strain. The basis reduction method presented can be implemented, independently of the optimization solution process of lower bound shakedown problem. Once the bases would be evaluated for given independent loadings, it could be used for the shakedown analysis with different load angles and the number of reduced bases does not depend on the number of integration points used for the finite element discretization. Secondly, expressing the back stress of lower bound shakedown problem for the kinematic hardening material by the linear combination of fictitious elastic stress fields, the number of design variables related to the back stress is reduced to the number of load vertices and the computational scale of shakedown analysis of kinematic hardening material would be decreased significantly by the combination of the basis reduction method of self-equilibrated stress field proposed in this paper. Numerical examples show that the proposed method is effective and precise computationally.