## 1 Introduction  
Significant research work has been presented in order to simulate the behavior of underwater vehicles under severe loading conditions. For instance, [PERSON] [1] illustrated the effect of shock pressure loading on a ring-stiffened submersible hull using finite element analysis. The failure analysis indicated that fibers failed in tension while matrix failed in shear when the explosion charge exceeded 25 kg TNT. Furthermore, [PERSON] [2] worked on minimizing the weight of pressure hull by enhancing the pressure hull strength taking into consideration both hydrostatical pressure and underwater explosion. Additionally, the results indicated that the dynamic motion of the pressure hull has an accordion mode, a whipping mode and a breathing mode. Also, [PERSON] et al. [3] derived an empirical formula for predicting the collapse strength of composite cylindrical structures under hydrostatic pressure as a function of important design parameters such as the geometric dimensions and the layered angle. In addition, [PERSON] et al. [4] experimentally investigated the dynamic performance of ship body coated by rubber. The results demonstrated that the coating was not effective at reducing the low-frequency whipping motion excited by the bubble pulse. However, it was able to moderate the high-frequency response excited by shock wave. Moreover, [PERSON] et al. [5] numerically and experimentally investigated the effect of underwater explosions (UNDEX) on rectangular plates. It was revealed that the underwater explosion failures can be predicted using the strain rate effects. Also, [PERSON] et al. [6] illustrated the global responses of ship subjected to UNDEX. The results demonstrated that the UNDEX waves changed the added masses on the ship and effectively affected the global responses of its body. On the other hand, [PERSON] et al. [7] examined the transient dynamic responses of submarine pressure hull exposed to hydrostatic pressure and shock loading. It was concluded that the collapse depth (maximum diving) of the submarine pressure hull was about 700 m. In addition, they observed that the loading condition depends not only on the hydrostatic pressure but also on the shock loading. Likewise, [PERSON] and [PERSON] [8] studied experimentally and numerically the dynamic response of a cylinder subjected to UNDEX. The results illustrated that the largest strains on a cylinder subjected to a far-field side-on UNDEX occurred near the two ends on the near side of the cylinder to a far field explosive charge. Additionally, the damage occurred at the center on the opposite side of the cylinder. Similarly, [PERSON] and [PERSON] [9] combined FSI code and finite element modeling techniques to investigate the dynamic response of a thick-section hollow composite cylinder. The results showed that the fluid-structure coupling has a significant effect on stress distributions within the structure. Furthermore, [PERSON] and [PERSON] [10] predicted numerically the damage response of submerged imperfect cylindrical structures exposed to UNDEX. Based on these results, the introduction of initial imperfections greatly affected the response of the cylinder when compared with the response of a perfect cylinder. On the other hand, [PERSON] and [PERSON] [11] demonstrated the shock response of a ship section to non-contact UNDEX using the finite element software package ABAQUS. It was revealed that the fluid thickness and size of fluid mesh effectively affects and improve the modeling accuracy. Additionally, [PERSON] and [PERSON] [12; 13] performed a numerical study to obtain the shock response of an underwater hybrid structure subjected to UNDEX. [PERSON] et al. [14] predicted the damage features of RC slabs subjected to air and UNDEX. The shock wave propagation and damage mechanisms from contact explosions in air and water were compared. The dynamic response of the RC slab is highly localized in the air contact explosion.