Spherical elastic–plastic structures under internal explosion: Approximate analytical solutions and applications

This paper is devoted to the research of closed-form solutions for the failure prediction of a hollow elastic–plastic sphere undergoing an internal explosion. The problem is dealt with using a time scale corresponding to a time scale for vibration mechanics. A simplified solution, which involves relatively thin spheres, is presented. This method enables us to reduce the partial derivative equation system representing the problem to a simple differential equation. For perfectly plastic behaviour or linear work-hardening, a closed-form solution is obtained if there is no plastic unloading. The simplified method is then applied to a simplified technological problem which consists of anticipating the behaviour of the spherical bottom of a PWR 900 nuclear reactor submitted to a steam explosion. Comparisons between solutions generated from finite element calculations and solutions generated from the simplified method are carried out and show a good agreement, thereby validating the simplified method.