## 4 Verification
### Distorted Model I  
This section delves into the verification of the scaling law for distorted model I, where the sole distinction lies in the attached plate thickness compared to the reference model. To this end, a sequence of distorted models I were developed based on the reference model, as described in Section 4.1. These models encompass a range of arbitrarily selected plate thicknesses spanning from 1.0 mm to 1.8 mm, corresponding to plate thickness distortion factors (\(h_{pd1}/h_{pm}\)) that extend from 0.7692 to 1.3846. While maintaining the same plate length as that of the reference model, the impact block was designed to ensure congruence with its counterpart in the reference model in terms of dimensions. A comprehensive breakdown of the dimensions of the stiffened plate specimens and their corresponding impact blocks is presented in Table 7. Figure 14 provides an illustrative representation of distorted model I (model 2), including its associated impact block. Figure 13: Normalized comparison of sectional moment and force (reference model). (**a**) Sectional moment of S1; (**b**) sectional force of S1; (**c**) sectional moment of S2; (**d**) sectional force of S2. With the determined dimensions of the attached plates and stiffeners for each distorted model I, the structural mass can be calculated by substituting the geometric parameters from Table 7 into the equations. Subsequently, the structural mass factor is obtained using Equation (17), utilizing the structural mass of distorted model I and the reference model. This factor enables the corrected impact mass to be calculated using Equations (18) and (19). To ensure consistency, the numerical simulations were configured with identical boundary conditions and contact restrictions as those applied to the reference model, ensuring uniformity across all cases involving distorted specimens. Two groups of distorted model I were established for comparative analysis: one with uncorrected load cases and the other with corrected load cases. In the uncorrected group, the load cases consisted of an impact mass of 0.4 t and initial impact velocity of 3.0 m/s, aligned with those of the reference model. In contrast, the corrected group applied load cases in which the impact mass was adjusted according to the procedure outlined in Equation (19). A summary of the loading cases employed in the two simulation groups is presented in Table 8.  
Furthermore, Table 9 presents the resistance characteristics, including the plastic displacement and peak acceleration, for the reference model, uncorrected group, and corrected group. Figure 15 shows a visual comparison of these resistance behaviors. The results indicate that the correction procedure yields remarkably similar predictions for plastic displacement and peak acceleration, with absolute differences of less than 2.06%, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No.** & **Item** & **Unit** & **Model 1** & **Model 2** & **Model 3** & **Model 4** & **Model 5** \\ \hline Specimen & Attached plate thickness & mm & 640 \(\times\) 340 & 640 \(\times\) 340 & 640 \(\times\) 340 & 640 \(\times\) 340 & 640 \(\times\) 340 \\  & Attached plate thickness & mm & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 \\  & Stiffener & mm & \(\pm\frac{35.0\times 1.1}{12.5\times 1.5}\) & \(\pm\frac{35.0\times 1.1}{12.5\times 1.5}\) & \(\pm\frac{35.0\times 1.1}{12.5\times 1.5}\) & \(\pm\frac{35.0\times 1.1}{12.5\times 1.5}\) & \(\pm\frac{35.0\times 1.1}{12.5\times 1.5}\) \\  & \(M_{S}\) & t & 0.00278 & 0.00312 & 0.00346 & 0.00380 & 0.00414 \\  & \(\lambda_{M_{S}}\) & - & 0.8443 & 0.9481 & 1.0519 & 1.1557 & 1.2596 \\ \hline Impact block & \(R_{I}\) & mm & 80 & 80 & 80 & 80 & 80 \\  & \(v_{0}\) & m/s & 3.0 & 3.0 & 3.0 & 3.0 & 3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Relevant geometrical parameters of distorted model I.  
Figure 14: Schematic of model 2 system (unit: mm).