## 3 Case Studies
### Effect of Striker Header Shapes  
In practice, ring or/and stringer-stiffened cylinder structures are prone to impact in many ways, such as a striking ship, which may collide with these structures by its bow, stern, or side. For example, the collision scenarios of ship and tension leg platforms are presented in Figure 11. In this study, three types of ship of 4000 tons' class with various bow shapes were applied. Three typical striker header shapes as hemisphere type, knife-edge type, and rectangular type have been investigated, as shown in Table 6. The striking ship was modelled as a rigid body. However, in the actual case, the striking ship may also deform due to collision forces.  
Figure 10: Effects of impact angle on the extent damage of the ring-stiffened cylinder.  
Figure 9: Effects of impact location on the extent damage of ring-stiffened cylinder.  
The collision simulations were conducted with different impact velocities for assessing the permanent extent damage. It is noted that the diameter and the width of indenting surfaces are the same as the mid-bay length of the struck ring-stiffener cylinder. The corners of the rectangular and knife-edge indenter were filleted. The first case resembles bulbous bow impact and the second case stern or side impact of a unity vessel and offshore accommodation barge vessel, respectively. For the same impact condition, the numerical results for each type of indenter shape are plotted in Figure 12. In this figure, the maximum permanent dent depth (\(d\)) was non-dimensional with a radius of cylinder (\(R\)), while energy ratio (\(\lambda_{E}\)) was the ratio the kinetic energy of striker (\(E_{k}\)) and energy absorption capacity of struck structure (\(E_{a}\)), as determined in next section. It is clear that the most serious case is a hemispherical indenter type which resembles highly localized loading. The resistance of the cylinder against collision when the load is applied with the hemispherical indenter type was lower than that of the knife-edge and rectangular indenter types by 19% and 32%, respectively. Furthermore, when the load is applied with a rectangular indenter, the resistance is much better than that of the hemispherical and knife-edge indenter cases. In this case, the load is applied in a very large contact area at the initiation of collision. For the knife-edge indenter, a critical point is the strain concentration at the contact points with the knife-edge ends and the cylinder, as displayed in Figure 13.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ship Model Used in Simulations** & & & & \\  & & & & Offshore accommodation \\  & Bulk Carrier ship & Utility vessel [36] & barge [36] \\ \hline Overall length (m) & 76.0 & 65.0 & 71.0 \\   Breadth (m) & 16.0 & 14.4 & 20.0 \\   Depth (m) & 5.5 & 6.0 & 6.0 \\   Draft (design) (m) & 4.2 & 4.0 & 3.5 \\   Deadweight (ton) & 4000 & 4000 & 4000 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Main properties of ship collision.  
Figure 11: Ship collision scenarios.  
Figure 12: Extent damage of ring-stiffened cylinder for various types of indenter shapes.  
Figure 13: Deformed shape with different indenter surfaces: (**a**) hemispherical indenter; (**b**) knife-edge indenter; and (**c**) rectangular indenter.  
The behavior of ring-stiffened cylinder structures under impact loadings with a hemispherical indenter was described in Figure 14. The displacement evolutions were divided into three stages: 1--elasto-plastic deformation, 2--elastic spring-back, and 3--elastic vibration (permanent set of damage). Furthermore, the patterns of deformation are shown in Figure 15. The magnitudes of dent depth were increased gradually from \(d=0\) mm (intact model) until maximum dent depth \(d=1336.4\) mm. Then, it was reduced to permanent dent depth with \(d=947.2\) mm after the spring-back occurred. It is noted that the typical deformation progresses from the first contact to final permanent deformation also followed the response of displacement-time relationship in Figure 14.