Hollow Spheres Subjected to Sustained and Variable Loads

Abstract

This paper discusses the elastic‐plastic response of thick‐walled hollow spheres subjected to internal and external pressures, and radial temperature gradient. The kinematic hardening rule is used in the analysis, and finite constitutive equations are developed for constant loading situations. In the case of variable loading, the yield condition for a material having residual stress and strain, and the incremental stress‐strain relationships are first derived. Then an incremental method is worked out so that the stresses and strains of the hollow sphere at any loading stage can be determined. By piecing several elastic and plastic solutions together, various hollow‐sphere problems can be solved in closed forms. Finally, to attack more complex problems, a general formulation is presented and on this basis a program is developed to determine the response of the hollow sphere for the next loading stage and the corresponding elastic‐plastic boundaries of the deformation. The stress‐strain state for any loading or unloading stage is still found from the analytical solutions. Consequently, the program can produce satisfactorily accurate results.