A Numerical Method Considering the Bauschinger Effect for Large Deflection Analysis of Elastic-Plastic Circular Plates

Abstract

In numerical analysis of elastic-plastic problems of various structures, the Prandtl-Reuss equation, which are expressed by the stress-strain matrix [D^p] introduced by P. V. Marcal and Y. Yamada, have been used very often with the finite element method or the finite difference method. In these equations, however, the Bauschinger effect is not considered. In order to investigate the elastic-plastic behavior of any structure subjected to cyclic loading, the Bauschinger effect should be taken into account. In this paper, the Bauschinger effect is considered with the use of Ziegler's modification of Prager's kinematic hardening rule, and the stress-strain relations are expressed using the matrix [D^p]. Application is made with the finite difference method to the large deflection analysis of elastic-plastic circular plates subjected to a cyclically varying uniform pressure. The results obtained are compared with those using the Prandtl-Reuss equations for a few cycles of reversed loading.