Rigid-Plastic Deformation of a Ring-Stiffened Shell Under Blast Loading

Abstract

An approximate solution for the plastic deformation of a ring-stiffened cylindrical shell in response to a nonaxisymmetric, exponentially decaying pressure load, is presented. The analogy between the ring-stiffened cylindrical shell and a rigid-plastic string-on-foundation with discrete plastic resisting elements is used to find closed-form solutions for the transient and final deformations of the shell. Dynamic equilibrium of the central bay of the shell and the adjacent ring-stiffeners results in an inhomogeneous wave equation with inhomogeneous boundary conditions for the string. The initial-boundary value problem is solved by the method of eigenfunction expansion and a suitable orthogonality condition. The zeroth mode for the string describes rigid-body motion of the bay due to the remaining inertia of adjacent stiffeners. Permanent deformations are obtained using a plastic unloading criterion whereby the velocity and strain rate for each eigenmode vanish simultaneously. In the example problem, higher eigenmodes decay and vanish rapidly and final shell deformations are primarily governed by lower eigenmodes. The structural model gives qualitatively correct transient deflections and would be amenable to fine-tuning with numerical analysis and experimental evidence.