Elastic-Plastic Finite Element New Method for Lower Bound Shakedown Analysis

Abstract

Shakedown analysis methods have been well developed to determine the shakedown limit load of structures under various repeated loading situations. However, to take the limited kinematic hardening, geometric effect, and deformation into account, further research is required. A new numerical method is proposed for the lower bound shakedown analysis that applies the extended static shakedown theorem for limited kinematic hardening. The new method determines the shakedown limit load with two kinds of elastic-plastic finite element (FE) analyses: (1) the elastic-plastic loading and unloading analysis is carried out using the hardening model with the actual material parameters and (2) the elastic-perfectly plastic model with ultimate stress as the yield stress is used for the limit analysis. An incremental FE technique for finite strain plasticity is utilized to take the geometric effect into account. Furthermore, the deformation of the structure is monitored by checking the calculated deformation parameters. The method is applied to a square plate with a small central hole subjected to cyclic tensile load. The corresponding physical shakedown experiment of the above square plate was conducted for verification. The numerical result shows a good agreement with the experimental result. The new method provides a valid method for the structural lower bound shakedown analysis taking into account limited kinematic hardening, geometric effect, and deformation.