Fracture of a thin-walled spherical vessel affected by internal pressure

Abstract

A problem on the fracture of a thin-walled spherical vessel affected by increasing internal pressure is formulated. The material properties both in the stage of hardening and in the stage of softening (prefracture) are described. The mathematics of the catastrophe theory is used to write down the equilibrium equations and to find the critical value of pressure, at which the vessel fails.