Extension of the string-on-foundation method to study the shock wave response of an immersed cylinder

This paper presents a simplified method for assessing the damage of a non-stiffened immersed cylinder subjected to the primary shock wave produced by an underwater explosion. The interaction between water and cylinder is split into two different phases. In the first phase, the kinetic energy which is transmitted by the shock wave to the cylinder is derived from explosion parameters. In the second phase, the cylinder deforms and the additional pressure created by interaction between water and deforming shell is calculated. To simulate the response of a cylinder clamped at its extremities, an analytical method based on the so-called rigid-plastic string on rigid-plastic foundation model is proposed. Closed-form expression is derived for evaluating the final shell deflection and used to highlight the influence of water added mass on cylinder damage. The proposed method is then validated by comparing, for a given cylinder and different shock factors, the resulting damage with finite element results. It appears that for high shock factors (i.e. K ≥ 2), the method allows for a good estimation of the cylinder shell deflection. It however underestimates significantly the deformed area when the shock factor is around 1.5 or lower. Additional research work is on-going to take into account deep immersion effects as well as ring-stiffening of the cylindrical shell.