## 3 Similarity Methodology  
### The Scaling Law for Perfect Similar Stiffened Plates (Reference Model)  
A prototype representing a stiffened plate extracted from an actual ship structure and subjected to a low-speed impact was considered. A perfectly similar scaled model made of the same material as the prototype was designed to exhibit geometric similarity with the prototype across all dimensions and is referred to as the reference model. [PERSON] [10] proposed a correction method for the impact velocity, considering dimensionless numbers associated with the impact velocity \(v_{0}\), dynamic flow stress \(\sigma_{d}\), and structure mass \(M_{S}\). Although this method demonstrated significant improvements, it primarily focused on geometric parameters such as the plate length L and the corresponding overall scaling factor, while neglecting other dimensions. Previous studies [6,22] have highlighted that the dynamic responses of stiffened plates involve a combination of bending and membrane behavior, which is extensively discussed in Section 2.3. In particular, the fully plastic bending moment, \(M_{0}\), and plastic normal force, \(N_{0}\), were identified as crucial factors in the energy-absorption mechanisms of these structures. The \(M_{0}\) and \(N_{0}\) for the stiffened plate can be computed using Equations (6) and (7). Hence, in situations where bending and membrane actions are the dominant behaviors, as governed by the sectional static moment \(S_{S}\) and sectional area \(A_{S}\), it is essential to ensure consistency between the sectional static moment \(S_{S}\) and sectional area \(A_{S}\) of the scaled model and the prototype stiffener configuration. Building on this foundation, the present method incorporates relevant quantities encompassing the geometric dimensions, including plate thickness and section attributes, represented by the sectional static moment (\(S_{S}\)) and area (\(A_{S}\)) of the integrated stiffener section. Because impact events affecting struck masses are localized concerns, it is reasonable to concentrate on the sectional geometric characteristics of a segment within a stiffened  
Figure 7: Normalized comparison of sectional moment and force (**a**) Sectional moment of S1; (**b**) sectional force of S1; (**c**) sectional moment of S2; (**d**) sectional force of S2. plate that includes both a stiffener and an attached plate delimited by two adjacent stiffeners, as shown in Figure 8a. Considering the deformation mode depicted in Figure 8b during impact, the axis used to compute the static moment \(\text{S}_{\text{S}}\) was defined as the plastic neutral axis, dividing the sectional area of the integrated stiffener section into two equal parts. The resistance responses of the structure are represented using a segment of the stiffened plate, which is referred to as an integrated stiffener. Additionally, the plastic deformation (\(\delta\)) of the stiffened plate is considered as a characteristic parameter for capturing the dynamic plastic behavior during the impact event. Consequently, the plastic deformation of a stiffened plate with \(N\) stiffeners is hypothesized to be influenced by the aforementioned relevant parameters and can be expressed as follows:  
\[\delta=f(L,h_{p},N,\rho,A,M_{0},\sigma,\sigma_{0},v_{0},M_{S},M_{I},A_{S},S_{S }), \tag{8}\]  
By the observation of the low-velocity impact event in Section 2.3, the stress \(\sigma_{0}\) is introduced as an estimate of stress during impact, with the assumption of neglecting the strain rate effect.