## 6 Results and Analysis
### Responses of Submarine Pressure Hull to Uindex
#### 6.2.1 The Acceleration Response at Different Locations  
First, the response of the MICEPH in the axial direction is illustrated in Figure 11. The figure presents the time history response of \(Z\)-axial acceleration (\(A_{3}\)). UNDEX of 20 kg TNT at different offset distances of 5.5 m, 15.5 m and 20.5 m were discussed. At points E and F, located at the center of each end of the MICEPH, it was observed that the acceleration responses (\(A_{3}\)) were in the opposite directions and occurs at the same instance. The peak value of the acceleration is \(26\times 10^{3}\) m/s\({}^{2}\) at an offset distance of 5.5 m, and occurs at 4 m/s. This measurement then oscillates and decays after 4 m/s. In addition, while the offset distance increases, the acceleration decreases and acquires \(8.3\times 10^{3}\) m/s\({}^{2}\) and \(6.65\times 10^{3}\) m/s\({}^{2}\) at offset distances of 15.5 m and 20.5 m, respectively. This is attributed to increasing the standoff distance of the explosive charge. Also, the figure demonstrates that the bubble pulses show a minor impact on nodes \(E\) and \(F\). Similarly, Figure 12 plots the time history curves of \(Z\)-axial acceleration (\(A_{3}\)) for nodes \(C\) and \(D\). The curves illustrate that while the pressure hull stroked by the shock wave, node \(C\) moves to the left and node \(D\) moves to the right at the same time instance which causes the accordion motion. This is attributed to the propagated compressive pressure and its subsequent release on the MICEPH in the axial direction. The peak value at node \(D\) of the measured acceleration is \(27.4\times 10^{3}\) m/s\({}^{2}\) in the negative \(Z\)-direction, owing to a 20 kg TNT charge and an offset distance of 5.5 m. Likewise, at node \(C\), the peak value of acceleration is \(23.9\times 10^{3}\) m/s\({}^{2}\), which occurs at 2 m/s. Also, as the offset distance increases at node \(C\), the acceleration decreases and achieves \(4.6\times 10^{3}\) m/s\({}^{2}\) and \(2.8\times 10^{3}\) m/s\({}^{2}\) at offset distances of 15.5 m and 20.5 m, respectively. Similarly, the maximum acceleration at node \(D\) are \(5.1\times 10^{3}\) m/s\({}^{2}\) and \(3.2\times 10^{3}\) m/s\({}^{2}\) at offset distances of 15.5 m and 20.5 m, respectively. The aforementioned results demonstrate that the peak acceleration at nodes \(C\) and \(D\) were achieved before nodes \(E\) and \(F\). Figure 10: Finite element model of Multiple. Intersecting Cross Elliptical Pressure Hull (MICEPH) and the locations of different test points. Figure 11: The acceleration-time history (\(A_{3}\)) at nodes \(E\) and \(F\) due to 20 kg TNT on the pressure hull. Figure 12: The acceleration-time history (\(A_{3}\)) at nodes \(C\) and \(D\) due to 20 kg TNT on the pressure hull. On the other hand, Figure 13 illustrates the acceleration response (\(A_{2}\)) of the MICEPH in the vertical direction of nodes \(E\) and \(F\) under UNDEX of 20 kg TNT at offset distances of 5.5 m, 15.5 m and 20.5 m. It is observed that node E moves opposite to node \(F\) throughout the transient response of the MICEPH. Also, the figure illustrates the breathing motion caused by the expansion and subsequent contraction of the MICEPH. For instance, at node \(E\) and an offset distance of 5.5 m, the peak acceleration (\(A_{2}\)) is \(9.45\times 10^{3}\) m/s\({}^{2}\) in the \(Y\)-direction, while at node \(F\), the peak acceleration is \(8.96\times 10^{3}\) m/s\({}^{2}\) in the negative \(Y\)-direction and occurs at a time instance of 8 m/s. Furthermore, at higher offset distances of 15.5 m and 20.5 m, the peak measured accelerations are \(7.16\times 10^{3}\) m/s\({}^{2}\) and \(5.26\times 10^{3}\) m/s\({}^{2}\) in negative \(Y\)-direction at node \(E\). While at node \(F\), the peak accelerations are \(6.43\times 10^{3}\) m/s\({}^{2}\) and \(5.15\times 10^{3}\) m/s\({}^{2}\) in the \(Y\)-direction and occur at a time instance of 2 m/s.