## 1 Introduction  
Underwater explosions are one of the main threats to warships in the ocean [1; 2; 3]. Unlike the air blast, the bubbles formed by the underwater explosion products may cause fatal damage to ships. Therefore, researchers have been continuously studying the explosion bubbles and the structural damage response. At first, most of these studies were focused on the far field. Widely used far-field bubble load models were given by [PERSON] [4], [PERSON] [5], and [PERSON] [6], respectively. However, with the progress of weapon technology, there are more and more scenes of ships being attacked by near-field underwater explosions. When the distance between the explosive and the structure becomes closer, the bubble shows some new complex phenomena in its evolution, and damage to the structure is more likely to occur, so research conclusions regarding the far field are difficult to fully apply. To further explore the near-field explosion bubbles and the damage rules caused by them, scholars have used experimental and simulation methods to carry out their studies in recent years. Some scholars have focused on the load law of explosive bubbles near boundaries. Through a recently developed computational framework that couples a finite volume compressible fluid dynamics solver with a finite element structural dynamics solver, [PERSON] et al. [7] found three different modes of bubble collapse. By using the CEL method to study the evolution process of an underwater explosion bubble under boundary conditions near the water surface, near a submerged cylinder and the rigid bottom, [PERSON] [8] evaluated the CEL method's ability to predict underwater explosion load near the interface. Similarly, [PERSON] et al. [9] also applied the CEL method to study the interaction between the explosive bubble and the rigid wall. It can be seen that the CEL method has considerable applicability in research on near-field underwater explosions. Some researchers focused on the structural responses in the near-field underwater explosion situation. In terms of local damage, [PERSON] [10], [PERSON] [11],and [PERSON] [12] conducted many close underwater explosion experiments on square plate structures. The research results provide a powerful criterion for predicting the local damage to ships. Considering the excellent energy absorption characteristics of sandwich structures, [PERSON] [13], [PERSON] [14], and [PERSON] [15] studied these anti-impact performances under an underwater explosion load, providing a basis for the effective protection of offshore structures. In addition, [PERSON] [16] and [PERSON] [17] studied the effect of the covering layer on the anti-impact performance of the steel plate structures, analyzed the optimal parameters of the covering layer, and provided a new idea to improve the vitality of the ship. To explore the overall damage rule of near-field underwater explosion bubbles to ships, the simplified hull girders (SHGs) with similar response characteristics to the real ship have become an important research object. In the paper by [PERSON] [18], the coupling effect of overall motion and local deformation on SHG was discussed through an experiment case. Likewise, [PERSON] et al. [19; 20] conducted experimental studies on the overall damage characteristics of the same SHG at various load conditions. The results show that there are two main kinds of damage phenomena: hogging damage related to shock wave and sagging damage caused by bubble pulsation. Moreover, [PERSON] et al. [21] used the three-dimensional boundary integral method to simulate the interaction between surface ships and near-field underwater explosion bubbles, finding that bubbles' negative pressure effect is an important reason for sagging damage. [PERSON] et al. [22; 23] twice analyzed the sagging damage mechanism of SHGs under various explosion cases, mainly using the CEL simulation method based on experimental verification.