## 6 Result of Case Studies
### Model 3--LNG Cargo Containment Boxes with Hull Structure  
The size of an NO96 cargo containment flat box is approximately 1.2 \(\times\) 1.0 m\({}^{2}\), and the flat boxes are evenly erected longitudinally and transversely in the LNG cargo tank. Therefore, the supporting conditions for each flat box should depend on the LNG cargo tank configuration, such as the type/scantling of longitudinal stiffeners, longitudinal spacing, web spacing, transverse frame, and longitudinal girder. In this study, one set of the flat boxes located at the longitudinal stiffener position with the dimensions of the LNG carrier hull structure, as shown in Table 8, was considered for Model 3. The boundary condition for Model 3 is similar to the condition of an actual onboard LNG cargo tank. An additional stress concentration using hull deflection against the sloshing impact pressure was implemented through a longitudinal stiffener, as shown in Figure 17. Therefore, Model 3 is expected to have higher difference values of shear and bending stresses calculated using the TIRF and DIR than those of Model 2, owing to this additional nonlinear boundary condition, i.e., the hull structure and bottom of the LNG cargo containment boxes. Figures 18-20 are the representative time series of the shear and bending stresses of 5.0 ms of rise time of the external impact pressure for Load X (3 \(\times\) 3), Load J (3 \(\times\) 1), and Load A (1 \(\times\) 1) (Figure 5), respectively. The stress response time series using the TIRF (solid line) were triangle-shaped; however, the stress response time series using the DIR (dot line) were a concave, up-and-down shape, which means that the integrated areas calculated using the impact time for both the TIRF and DIR were not considerably different from each other. Figure 16: Box and whisker plots for the difference in the peak bending stresses and impulse values using TIRF and DIR. \begin{table}
\begin{tabular}{c c c c} \hline
**Hull Plate Thickness [mm]** & **Longitudinal Spacing [mm]** & **Frame Spacing [mm]** & **Longitudinal Stiffener—Angle Type [mm]** \\ \hline
14 & 810 & 2800 & \(200\times 90\times 9/14\) \\ \hline \end{tabular}
\end{table} 
Table 8: Dimension of the LNG carrier hull structure for Model 3. The peak stress and impulse values of the shear stress and bending stress responses for all the series analyses regarding the 12 load areas (Figure 5) of Model 3 are summarized in Tables 9 and 10, respectively. Figure 17: Stress concentration through hull deflection in Model 3. Figure 18: Reference shear and bending responses for Load X (uniform pressure \(3\times 3\) load case) using TIRF and DIR for impact pressure of 5.0 ms of rise time: (**a**) Reference shear responses with linear boundary conditions, (**b**) Reference bending responses with linear boundary conditions, (**c**) Reference shear responses with nonlinear boundary conditions, and (**d**) Reference bending responses with nonlinear boundary conditions. Figure 19: Reference shear and bending responses for Load J (3 \(\times\) 1 load case) using TIRF and DIR for impact pressure of 5.0 ms of rise time: (**a**) Reference shear responses with linear boundary conditions, (**b**) Reference bending responses with linear boundary conditions, (**c**) Reference shear responses with nonlinear boundary conditions, and (**d**) Reference bending responses with nonlinear boundary conditions. Figure 20: Reference shear and bending responses for Load A (1 \(\times\) 1 load case) using TIRF and DIR for impact pressure of 5.0 ms of rise time: (**a**) Reference shear responses with linear boundary conditions, (**b**) Reference bending responses with linear boundary conditions, and (**d**) Reference bending responses with nonlinear boundary conditions. The maximum difference in the peak shear stress and impulse with the linear condition using the TIRF and DIR for all the loaded cases were found to be 8.4% and 7.8%, respectively as shown in Figure 21. The error percentage was higher than the shear stress difference in Model 2.