Improved theory of the elastic-plastic response of spherical containment vessels subjected to internal blast loading and its application

Abstract

Baker built the displacement equations of motion for a thin spherical shell to spherically symmetric internal blast loading, and further provided the analytical solution of the elastic-plastic response under a triangular decaying pressure, neglecting shell thinning and radius variation [1], which was widely used in the fields of analysis and design of explosion containment vessels. However, it appears that some improvements and corrections are needed when we revisit this classic problem. In this paper, the elastic-plastic response of thin spherical shells is investigated mathematically. The complete equations of motion for three models are developed. Then the main ideas of the analytical and numerical methods are presented, as well as some important procedures and results by using Laplace transform techniques, which are convenient to use and generalize. Three typical examples are solved to exhibit differences between our improved theory and Baker’s [1]. Furthermore, our models are employed to gain some insights into response regularities, including the effect of various degrees of strain-hardening on maximum displacements under impulsive loading, and the effect of loading duration on the shell displacement for a perfectly plastic material.