## 6 Results and Analysis  
### Propagation of Shock Wave  
In this study, the MICEPH is subjected to shock wave and bubble pulse owing to UNDEX. Its performance depends mainly on the strength of the waves and the resilience of its structure. The stand-off point at node (\(A\)) was first struck by the shock wave. The charge is located at different stand-off distances--5.5 m, 15.5 m and 20.5 m--measured from the stand-off point. In the modelling procedures, two output variables were provided for the acoustic pressure: (i) the acoustic pressure (POR), which represents the total dynamic pressure in the wave formulation analysis including additional pressure induced by the incident and scattered waves; and (ii) the absolute acoustic pressure (PABS), which is the sum of the acoustic pressure and hydrostatic pressure. The acoustic pressure magnitudes are in Pascal [56]. Figure 7 demonstrates the POR at which the total dynamic pressure  
Figure 5: Finite element modeling of: (a) cross-elliptical submersible pressure hulls, and (b) fluid domain. Figure 6: The location of charge (source point (RP\({}_{2}\))) and stand-off point (RP\({}_{1}\)). instantaneously occurs at the time of explosion (zero time instant) due to total wave formulation. Also, the figure shows the spherical shape of the shock wave and the initial instantaneous shock wave propagation at the time of the explosion due to different explosive weights and stand-off distances. It can be observed that the maximum shock wave pressure determined was \(3.471\times 10^{7}\) Pa due to 30 kg TNT at offset distance of 5.5 m. Figure 7b-d illustrates the computed POR field distribution due to 20 kg TNT at offset distances of 5.5 m, 15.5 m and 20.5 m. The maximum shock wave pressure measured was \(2.373\times 10^{7}\) Pa, \(6.777\times 10^{6}\) Pa and \(4.853\times 10^{6}\) Pa at explosive offset distance 5.5 m, 15.5 m and 20.5 m, respectively. The location of the source and standoff point greatly affect the computed POR field distribution, propagation and its magnitude. Figures 8 and 9 present the computed POR field distribution at several time instants at the front and back sides of fluid domain. The propagation of the shockwave and the dynamic pressure in the surrounding water were clearly presented in these figures. The figures demonstrated that there are some radial POR waves that hits the structure and consequently leads to some deformations. Furthermore, it was observed that the dynamic pressure is affected by the reflections and the emissions from the pressure hull in addition to the incident field from the source point. When the shock wave hits the cross-pressure hull, it is reflected and generates negative pressure. Also, it is interaction with the incident wave decreases the dynamic pressure in the surrounding fluid. This is attributed to the fact that the water cannot withstand tension. That is why the total dynamic pressure acquired negative values as illustrated in the figures. Furthermore, cavitation occurs immediately after the incident shock wave hits the MICEPH. Additionally, local cavitation around the MICEPH was observed once the acoustic pressure declines to the steam pressure of the fluid. Subsequently, when the local cavitation disappears, the load of the fluid on the pressure hull generates vibrations. Additionally, Figure 9 illustrates that the shock wave propagates symmetrically from the stand-off point to the aft and fore,  
Figure 7: Computed POR field at the zero time instant due to total wave formulation. while it expands in the perpendicular direction. The aforementioned results are in accordance with the results reported in [2; 43; 59]. Also, Figure 9 presents the volume changes in gas bubbles. If the oscillating gas bubble is close enough to the pressure hull, the differential pressure will be created.