## 2 Numerical Simulations Method and Response of Structure
### Dominant Behavior in Impact Event  
In this section, the dominant behaviors during the impact of the prototype stiffened plate are investigated. Numerical simulations obeying the settings in Section 2.2 were conducted on the prototype stiffened plate to obtain the sectional force and moment at significant sections. The prototype stiffened plates were subjected to impact from a hemispherical indenter with a mass of 400 t and an initial velocity of 3.0 m/s, as listed in Table 1. The resistance behaviors characterized by a final plastic displacement in the z-direction of 398.1 mm and a peak acceleration applied in the indenter of 20,184 mm/s\({}^{2}\) are plotted in Figure 5. The impact event focuses on the large deformation stage before failure. Additionally, it is illustrated that the acceleration and deformation initially increased and reached their peak, then gradually decreased until the impact indenter and structure separated. Regarding impact as a typical local problem, the integrated stiffener unit under the impact indenter represents a significant resistance characteristic of the entire stiffened plate, which should be investigated. Furthermore, the center section and extreme end of the integrated stiffener are significant sections, because they are essential sections where the  
Figure 5: Displacement and acceleration applied in prototype stiffened plate. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Symbol** & **Units** & **Value** \\ \hline Mass density & \(\rho\) & t/mm\({}^{3}\) & \(7.85\times 10^{-9}\) \\ Young’s modulus & \(E\) & GPa & 206 \\ Poisson’s ratio & \(\
u\) & - & 0.3 \\ Yield stress & \(\sigma\
u\) & MPa & 310 \\ Strength coefficient & \(K\) & MPa & 730 \\ Strain-hardening index & \(n\) & - & 0.23 \\ Necking strain & \(\epsilon_{n}\) & - & 0.23 \\ Fracture strain & \(\epsilon_{f}\) & - & 0.35 \\ Cowper–Symonds constant & \(D\) & s\({}^{-1}\) & 40.4 \\ Cowper–Symonds constant & \(q\) & - & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mechanical properties and material parameters. bending moment is maximum when subjected to an impact load at its midspan. The center section is denoted as S1, and the end section is denoted as S2, as shown in Figure 6.  
In addition, the comparative results were normalized using the fully plastic bending moment M\({}_{0}\) and fully plastic axial force N\({}_{0}\). The plastic bending moment and fully plastic axial force of the integrated stiffener section can be obtained using the following formulas [6]:  
\[M_{0}=\sigma_{0}S_{S}, \tag{6}\]  
\[N_{0}=\sigma_{0}A_{S}, \tag{7}\]  
where \(S_{S}\) is the static moment to the plastic neutral axis which divides the sectional area into two parts equally; \(A_{S}\) is the sectional area; and the flow stress \(\sigma_{0}\) is taken as the average value of the yield stress \(\sigma_{Y}\) and ultimate stress \(\sigma_{u}\), calculated as 441.5 MPa. With respect to the case of the prototype stiffened plate, the sectional area (\(A_{S}\)) is measured as 16,125 mm\({}^{2}\), while the static moment (\(S_{S}\)) amounts to 1,404,833 mm\({}^{3}\). Consequently, the plastic limit bending moment and the fully plastic axial force of the integrated stiffener section in the prototype are determined to be 620,233,600 N\(\cdot\)mm and 7,119,188 N, respectively. Figure 7 illustrates the normalized sectional moment and force obtained from the numerical simulations at S1 and S2 of the prototype specimen. With respect to the definition, M1, M2, and M3 are the bending moments around x-, y-, and z-axes, respectively, while M is the resultant (combined) moment. Similarly, F1, F2, and F3 are the sectional forces in the x-, y-, and z-directions, respectively, and F is the resultant force. Owing to the axis direction in the FE models shown in Figure 6, the negative axial force refers to the tensile force of the section. The analysis revealed that the maximum components of the resultant moment and forces corresponded to the bending moment (M1) and axial force (F2) of the section.