Shock-Wave Damage of Ring-Stiffened Cylindrical Shells

Abstract

A solution methodology for the nonlinear plastic response of the central bay of a ring-stiffened cylindrical shell subject to shock-wave loading is presented. The solution is based on a simple structural model that uses an analogy between a cylindrical shell and a string-on foundation in which ring stiffeners are modeled as lumped masses and springs. By requiring dynamic equilibrium within the central bay of the shell, one may reduce the problem to solving an inhomogeneous wave equation for which the motion of the ring stiffener is introduced into one of the boundary conditions of the string. The initial-boundary-value problem is solved by using a modified Galerkin approximation. The mode shape used to describe the local or bay deformation in the Galerkin approximation is determined from the experimental profile of an actual damaged shell. A Galerkin approximation not only yields a simple solution for the transient deformations of the shell, but it also has an advantage over an exact solution in that it can be easily extended to shells subject to asymmetric pressure loading with arbitrary time variation. The Galerkin solution is shown to approach two extreme cases of dynamic loading for the exponentially decaying pressure load: impulsive loading and static loading. A final deformed profile of the shell is obtained by using the concept of plastic unloading waves. The solution for the transient deflection is a stepping stone to the evaluation of strains and is therefore important in establishing a failure criterion for the shell. The analytical results presented herein may therefore be instrumental in establishing design criteria for prevention of failure of the ring-stiffened shell.