Shakedown Analysis of Hollow Spheres

Abstract

This paper presents a detailed investigation of the shakedown behavior of thick‐walled hollow spheres subjected to cyclic temperature and sustained internal and external pressures. It is found that under sustained and cyclic loadings, the steady states can always be attained for kinematic hardening materials, and the shakedown mode is usually determined by the response during the first cycle. A program is thus developed to determine the mode of the response and the interaction diagram. Then, various steady‐state solutions can be derived following the elastic‐plastic deformation patterns using the general formulation and the incremental method developed in another paper published by Jiang in 1994. Based on a thorough study of the hollow‐sphere behavior, we find that nine different kinds of response are possible. The steady‐state solutions for all these cases are discussed and given in this paper.