Estimation of the response of a deeply immersed cylinder to the shock wave generated by an underwater explosion

The work presented in this paper is focused on the development of a simplified method to study the structural response of a deeply immersed cylinder subjected to the primary shock wave generated by an underwater explosion. The proposed analytical model is based on the string-on-foundation method initially developed by Hoo Fatt and Wierzbicki, who converted the two dimensional boundary value problem of a cylindrical shell to an equivalent one-dimensional problem of a plastic string on a plastic foundation. This method has already been extended by the authors to study the shock wave response of an unstiffened cylinder immersed in shallow water. The present work focuses on deep-immersed cylinders subjected to both high hydrostatic pressure and explosion shock wave. The elastic deformation energy of the cylinder under hydrostatic pressure is first calculated and used to determine the initial conditions of the dynamic problem. Cylinder deflection and plastic deformation energy are then calculated for various immersion depths. When confronted to numerical results, the proposed model appears to underestimate the increase of deflection and absorbed energy with the immersion depth. A thorough analysis of the results post-processed from Ls-Dyna/USA finite element simulations highlights a new mechanism which is due to the action of hydrostatic pressure that continues to push inward the immersed cylinder. In order to improve the analytical model, a correction factor on the hydrostatic pressure is introduced but it is finally concluded that a new mechanism dedicated to the late action of the hydrostatic pressure still needs to be developed.