## 4 Results and Analysis  
### Bending Mode  
As can be seen from the pictures in the validation, when the SHG suffers from sagging damage subjected to the near-field explosion bubble, the two ends move like rigid bodies within a small elastic-plastic limit, and the overall bend is mainly composed of large plastic deformation near the midship, as shown in Figure 6. Moreover, the crease pattern at the bend position has certain regularity. In the process of sagging damage of the SHG, the upper part of the side plates becomes unstable under compression and gradually expands to form several plastic hinge lines. The deformation range of the lower part of the side plates is generally narrower than that of the upper part, specifically shown as W-shaped creases. The deformation of the bottom plate is relatively simple. The plastic hinge lines extend transverse and straight through the whole width. These plastic hinge lines form the overall bend in the SHG. After the plastic hinge lines are formed, the rotation around the yield area becomes easier, and the overall sagging amplitude is often further increased when subjected to bubble collapse force. For the W-shaped creases' local deformation mode on the side plates in this paper, an SHG sagging bend was composed of ten plastic hinge lines, eight on the side plates and two on the bottom plate, as shown in Figure 7.  
As the core deformation damage zone, it is important to predict the length of the potential bend zone when facing a near-field underwater explosion load. Therefore, the length of the bend zone, which is not affected by the transverse bulkhead, is analyzed below. Each part of the hull plate rotates around the plastic hinge lines during the bending process. That is, the bending moment plays a major role. In contrast, the energy dissipated by the expansion and contraction of the hull plates is small; therefore, it is ignored. \(L_{W}\) is used to indicate the length of the bend zone on the undeformed SHG, as shown in Figure 7. \(M_{m}\) represents the average bend moment of the SHG during the bending process. The angle that, at one end, rotates around the middle cross-section is recorded as \(\alpha\). It is assumed that the length of each plastic hinge line on the side plates \(l\) has a function related to the length of bend zone \(L_{W}\) and the height of the side plate \(H\); then, the length of different plastic hinge lines can be denoted as \(l_{i}(L_{W},H)\). The rotation angle of both sides of each plastic  
Figure 6: Deformation of sagging damage. Figure 7: Plastic hinge lines mechanism of W-shaped creases. hinge line is positively related to \(\alpha\), assumed to be \(\lambda_{i}\alpha\). The length of the plastic hinge lines on the bottom plate is the same as the ship width \(W\), and the rotation angle equals \(\alpha\). As the work of external bend moment equals the sum of dissipated energy of the side and bottom plates' plastic hinge lines, we have:  
\[2M_{m}\alpha=2M_{0}W\alpha+M_{0}\alpha\sum_{i}\lambda_{1}l_{i}(L_{W},H), \tag{6}\]  
where \(M_{0}\) is the ultimate bend moment per unit length. According to the principle that the \(L_{W}\) value should make the value of \(M_{m}\) the minimum, let \(\partial M_{m}/\partial L_{W}=0\); therefore, we have:  
\[\frac{\partial\sum_{i}l_{i}(L_{W},H)\lambda_{i}}{\partial L_{W}}=0. \tag{7}\]  
According to the geometric relations, \(\lambda_{i}\) is a constant for the determined plastic hinge lines mode. Therefore, \(L_{W}\) has a function that only depends on \(H\). To find the relation between \(L_{W}\) and \(H\), keeping the width of SHG unchanged, the sagging damage responses with height-width ratios of 0.4, 0.5, 0.6 and 0.7, under the same load conditions as Section 3.2, are calculated. The creases are all in a similar W-shaped pattern. The lengths of the bend zones are listed in Table 3 and fitted in Figure 8. The three functions in Figure 8 can fit the relationship between the bend zone's length and the side plates' height.