## 3 Simulation Model
### Validation of Simulation Model  
To investigate the validity of the calculation method and the established model, the SHG structure in [PERSON]'s experiment was calculated in this case [23]. The loading conditions were as follows: TNT mass was 0.01 kg, detonation distance from the explosive to SHG's bottom plate was 0.25 m (impact factor SF = 0.180). Figure 4 compares stress nephograms with experimental photos [23] at different times. In the legend, S. Mises means Mises stress, SNEG means the bottom surface of the shell element, and Avg: 75% is the software default nephogram average threshold. After the explosive was detonated, the free-floating SHG first produced the initial upward movement, with slight overall hogging deformation and stress concentration at the midship. Then, during the subsequent bubble evolution process, the upper part of the bubble gradually tended to be irregular due to the joint influence of the structure and the free liquid surface. At 20 ms, the bubble in the expansion stage continued to drive the SHG upward. However, mainly due to the inertial effect and material resilience, the structure recovered from the hogging bend to the horizontal state. Moreover, a W-shaped stress concentration appeared in the middle of the side plates, indicating a downward bend trend. Subsequently, under the action of the shrinkage bubble's low pressure, the structure moved downward. The middle part of the SHG bent down significantly, and the side plates appeared to be folded due to compression, causing overall sagging damage. At the later stage of shrinkage, the bubble broke into bubble swarms under the combined action of air, structure, and free liquid surface. At 55 ms, the SHG's sagging amplitude was restored to a certain extent because of the relief of the low-pressure bubble.  
Figure 3: Displacement results of middle section.  
Figure 2: Arrangements diagram of underwater explosion simulation.  
Figure 5 presents the fold shape of the side plates. The local buckling yield is also well reproduced in the calculation, and the fold direction and crease pattern are consistent with the experimental results.  
Figure 3 compares the calculated displacement of the SHG middle section with the experimental values. The maximum positive displacement in the experiment was 0.0379 m, and the calculated result was 0.0472 m, with an error of 24.54%. The maximum negative displacement in the experiment was \(-\)0.0772 m, and the calculated result was \(-\)0.0791 m, with an error of 2.46%. The bubble pulsation period in the experiment was 52.1 ms, and the calculated result was 53.5 ms, with an error of 2.69%. From Figure 3, it can be seen that the variation trend between the experimental results and the calculated results is similar, showing a good correlation. However, the calculated results are larger, which may be because: (1) In the experiment, there are flexible ropes at both ends of the SHG for auxiliary positioning. (2) The CEL method regards the wave velocity as a constant value of the sound speed in the water. However, the closer to the center of the explosive, the greater the impact wave velocity will be, even reaching up to twice the speed of sound in water, which will lead to slower attenuation of the shock wave and a larger overall impulse. (3) The idealization and simplification in the simulation ignore the possible influence of structure manufacturing. In general, the current error is acceptable for the complex and strongly nonlinear problem of near-field underwater explosion damage to ships.  
Figure 4: Comparison between experimental photos [23] and calculated cloud pictures: (**a**) 0 ms, (**b**) 5 ms, (**c**) 11 ms, (**d**) 20 ms, (**e**) 45 ms, (**f**) 55 ms.  
Figure 5: Fold shape of side plates: (**a**) experimental photo [23]; (**b**) calculated cloud picture.  
The above comparison shows that the simulation technology and finite element model used can reliably solve the overall and local responses of SHGs subjected to near-field underwater explosion bubbles, which can be used for further work.