SHOCK-WAVE DAMAGE OF RING-STIFFENED CYLINDRICAL-SHELLS

A solution methodology for the nonlinear plastic response of the centr al bay of a ring-stiffened cylindrical shell subject to shock-wave loa ding is presented. The solution is based on a simple structural model that uses an analogy between a cylindrical shell and a string-on found ation in which ring stiffeners are modeled as lumped masses and spring s. By requiring dynamic equilibrium within the central bay of the shel l, one may reduce the problem to solving an inhomogeneous wave equatio n for which the motion of the ring stiffener is introduced into one of the boundary conditions of the string. The initial-boundary-value pro blem is solved by using a modified Galerkin approximation. The mode sh ape used to describe the local or bay deformation in the Galerkin appr oximation is determined from the experimental profile of an actual dam aged shell. A Galerkin approximation not only yields a simple solution for the transient deformations of the shell, but it also has an advan tage over an exact solution in that it can be easily extended to shell s subject to asymmetric pressure loading with arbitrary time variation . The Galerkin solution is shown to approach two extreme cases of dyna mic loading for the exponentially decaying pressure load: impulsive lo ading and static loading. A final deformed profile of the shell is obt ained by using the concept of plastic unloading waves. The solution fo r the transient deflection is a stepping stone to the evaluation of st rains and is therefore important in establishing a failure criterion f or the shell. The analytical results presented herein may therefore be instrumental in establishing design criteria for prevention of failur e of the ring-stiffened shell.