Abstract
This paper develops a new finite element method (FEM)-based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. The hardening model is a simple two-surface model of plasticity with a fixed bounding surface. The initial yield surface can translate inside the bounding surface, and it is bounded by one of the two equivalent conditions: (1) it always stays inside the bounding surface or (2) its centre cannot move outside the back-stress surface. The algorithm gives an effective tool to analyze the problems with a very high number of degree of freedom. Our numerical results are very close to the analytical solutions and numerical solutions in literature.
Highlights
Shakedown analysis for hardening structures has been investigated by many researchers
The isotropic hardening law is generally not reasonable in situations where structures are subjected to cyclic loading because it does not account for the Bauschinger effect and rejects the possibility of incremental plasticity
We have presented a finite element method (FEM)-based upper bound algorithm for shakedown analysis of bounded kinematic hardening structures with von Mises yield criterion
Summary
Shakedown analysis for hardening structures has been investigated by many researchers. The isotropic hardening law is generally not reasonable in situations where structures are subjected to cyclic loading because it does not account for the Bauschinger effect and rejects the possibility of incremental plasticity. The unbounded kinematic hardening model has already been introduced theoretically by Melan [1] and later by Prager [2]. Applications of this model have been investigated by Maier [3] and Ponter [4]. The unbounded kinematic hardening model cannot estimate the plastic collapse and incremental plasticity but only low-cycle fatigue, while low-cycle fatigue limit with the kinematical hardening model seems not to be essentially different from the perfectly plastic model, cf. Gokhfeld and Cherniavsky [5] and Stein and Huang [6]
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