## 6 Concluding Remarks  
This study aims to derive empirical formulations for predicting the maximum permanent local dent depth of both ring-stiffened cylinders and stringer-stiffened cylinders under dynamic mass impact. Based on the results of the present study, the following conclusions are drawn:  
* For the first time, the simple design equations to predict the maximum permanent local dent depth of a stiffened cylinder subjected to dynamic mass impact were successfully conducted in this study. In these equations, all effect parameters such as impact location factor, impact angle factor, and indenter shape factor were included. The proposed formulations were highly accurate and reliable according to the available test data and other existing formulations. Furthermore, they are convenient to use in the structure's strength and serviceability under risk conditions, during the initial design stage for safety concerns of marine stiffened cylinder structures. Figure 29: Comparison of predicted force-displacement relations using proposed formulations with other existing formulations for stringer-stiffener cylinders: (**a**) Model SS-C-1; (**b**) Model SS-C-2. * The numerical techniques developed in this paper have reasonable accuracy and reliability for predicting the extent of the local denting damage on stiffened cylinder structures under dynamic collisions. Therefore, it can be applied for further parametric investigations of any actual offshore stiffened cylinder structures for developing design guidelines and benchmarking studies on collision problems. * In case studies, the importance of the strain-rate hardening definition was investigated. The accuracy of numerical results was strongly dependent on the strain-rate hardening definition. Therefore, it is suggested that dynamic material properties should be applied to define plasticity at high strain rates. * The energy to be dissipated will result in larger deformations for larger impact velocities. When the impact velocities increase larger than 8 m/s, the increase in stiffness due to the strain rate effect is clear. When the impact velocity increases further, the resistance of the ring-stiffened cylinder against collision decreases due to the tripping of ring-stiffeners near the impact area. * The extent of local denting damage of the stiffened cylinder was strongly dependent on the impact locations. The permanent dent depth of the unstiffened cylinder approximately doubled in the ring-stiffened cylinder. It was also significantly reduced with each location in the longitudinal direction of the stiffened cylinder. The maximum permanent dent depth almost occurred at the mid-length of the cylinder, and it decreased gradually to the endplate at the boundary conditions because of the membrane stretching of the upper surface of the cylinder shell. * When considering the effect of the striker header shape, the most severe case is a hemispherical indenter, which resembles highly localized point loading. The resistance of the ring-stiffened cylinder against collision when the load is applied with a hemispherical indenter type was lower than that of the knife-edge and rectangular indenter types by 19% and 32%, respectively. For the stringer-stiffened cylinder, the resistance of cylinder when the load is applied through a hemispherical indenter is much lower than that of the knife-edge and rectangular indenter types by 26% and 37%, respectively. For future works, it is recommended that further studies appear to be necessary to develop the simple design equations to predict the residual strength of dented ring- or/and stringer-stiffened cylinders under hydrostatic pressure, axial compression, as well as longitudinal bending or combinations thereof. Moreover, when the permanent dent depth is known by using the proposed formulation in this study, the reduction factor is quickly predicted. Then, this factor can be multiplied with the ultimate strength of an intact cylinder to obtain the residual strength of the dented ring- or/and stringer-stiffened cylinders.