## 3 Similarity Methodology
### Criteria for Distorted Stiffener Configuration (Distorted Model II)  
Rolled and built-up T-type stiffeners are commonly used in the practical engineering of large-scale hull structures, as illustrated in Figure 2. However, replicating these T-type stiffeners in small-scale models is challenging, because of the significant welding deformations caused by the reduced stiffener thickness. To mitigate manufacturing complications, substituting T-type stiffeners with flat bars has become a prevalent practice in small-scale model testing. Nonetheless, such substitutions introduce discrepancies between the prototype and replicated stiffened plates. Consequently, the establishment of criteria that ensure that distorted stiffened plates with flat bars demonstrate a dynamic performance similar to that of their T-type counterparts is crucial. To further explore and enhance the applicability of distorted similarity, this section introduces the concept of distorted model II, based on the foundation laid by distorted model I in Section 3.2. This new concept focuses on distorted stiffener configurations, as depicted in Figure 11. Distorted model II maintains consistent geometric dimensions with distorted model I, encompassing the attached plate length, thickness, and stiffener numbers and spacing, while deviating only in the stiffener configuration (using flat bars). The replacement of a T-type stiffener with a flat bar stiffener results in distinct sectional geometric characteristic deviations and significantly affects the integrated stiffener behaviors. Consequently, it becomes imperative to establish a criterion ensuring that the dynamic responses in distorted model II closely resemble those of distorted model I, based on the sectional geometric attributes. Building on the framework of distorted similarity delineated in Section 3.2, a corrective criterion is established using the dimensionless numbers outlined in Equation (9). These dimensionless numbers are applied to both distorted model II and distorted model I, with the subscript d2 denoting the former. Meanwhile, the scaling factor for the distortion of any variable \(X\) between distorted model II and distorted model I is defined as follows:  
\[\eta_{X}=X_{d2}/X_{d1}, \tag{20}\]  
Therefore, distorted model II holds an overall scaling factor relationship, as in \(\eta_{L}=\eta=1\). Given identical overall dimensions (attached plate length) and convergent strain rates, an intrinsic consistency was confirmed for the initial velocity, as illustrated in Table 4.  
Achieving perfect similarity by matching all dimensions with their counterparts in distorted model I appears unattainable for distorted model II, which is equipped with a flat-bar configuration. Here, it is possible to adjust the geometric parameters of the flat bar, thus accommodating the fulfillment of the pivotal governing parameters and attaining partial consistency. In light of the prominent influence of bending and membrane action, the correction approach focuses on preserving the dimensionless numbers \(\Pi_{6}\) and \(\Pi_{7}\), which characterize the dynamic behaviors consistent with those of the distorted model I.  
Figure 11: Schematics of distorted model I and distorted model II. Therefore, the dimensionless numbers \(\Pi_{6}\) and \(\Pi_{7}\) related to the sectional static moment \(S_{S}\) and sectional area \(A_{S}\), respectively, are considered as follows:  
\[\underbrace{\left[\frac{A_{Sd2}}{L_{d2}^{2}}\right]}_{(\Pi_{6})_{d2}}=\underbrace {\left[\frac{A_{Sd1}}{L_{d1}^{2}}\right]}_{(\Pi_{6})_{d1}}\rightarrow\eta_{A_{ S}}=1, \tag{21}\]  
\[\underbrace{\left[\frac{S_{Sd2}}{L_{d3}^{3}}\right]}_{(\Pi_{7})_{d2}}= \underbrace{\left[\frac{S_{Sd1}}{L_{d1}^{3}}\right]}_{(\Pi_{7})_{d1}}\rightarrow \eta_{S_{S}}=1, \tag{22}\]  
It is evident that Equations (21) and (22) ensure the consistency of the other dimensionless numbers, including \(\Pi_{5}\), which is related to the impact mass.