# Effect of Dynamic Loading Conditions on Maximizing Energy Dissipation of Metallic Dampers
## 5 Conclusions  
This study proposed a novel methodology to develop a metallic damper coupled between a bridge pier and the upper part of a bridge. This study focused on enhancing the energy dissipation capability of the metallic damper with respect to different target capacities. Simplified finite element modeling and an optimization method were proposed, using finite element analysis and the SQP algorithm. First, optimization was performed with FE static analysis by applying various static load conditions to determine the optimal shape. Due to the limitation of the static optimization, further study based on dynamic analysis was completed. It was confirmed that optimized shapes for different earthquakes could be derived through this dynamic optimization process. The main conclusions obtained in this study can be summarized as follows.  
* The optimized shape obtained through the static analysis showed an hourglass shape in which the width of both ends was increased, and the width of the center was reduced. This trend was similar to the results of previous studies. However, in the static analysis, it was difficult to determine the different optimal shapes for all stroke sizes, or to determine an appropriate virtual stroke for optimization.
* Through optimization with static analysis, the stiffness of the damper increased. Accordingly, the optimized shape dissipated a large amount of energy when the damper was deformed due to large earthquakes. In the case of small earthquakes, however, the optimized damper may undergo less deformation and dissipate only a small amount of energy. Identical results were obtained using the structural prototype bridge FE model.
* Thus, further optimization based on a dynamic analysis was carried out to determine the optimal shapes that dissipate the maximum amount of energy during relatively small earthquakes. To generalize the optimization method based on the dynamic analysis, an ideal analytical model was proposed with the spring set and concentrated mass.
* Through the proposed analytical model, an additional optimized shape for small earthquake accelerations was developed. The optimized shape at low acceleration and high frequency exhibited a slight reduction in width at both ends, unlike previous results. The new shape could lead to a greater amount of energy dissipation for small seismic loading.  
Based on these findings, further studies will be conducted regarding practical applications. The analysis process of this study during the dynamic optimization procedure had been fairly simplified. Therefore, in the future research, a study of how to select the most efficient object function under various earthquake excitations--including energy dissipation, effective stiffness, or structural displacement--will be conducted. More realistic target structures will be applied as the optimization conditions, including an analysis of resonance with respect to their natural frequencies and intrinsic damping. Furthermore, experimental research will be conducted, along with the realistic conditions for the validation of the optimization.  
**Author Contributions:** Conceptualization, J.W.P. and Y.M.L.; methodology, G.-H.Y. and J.-H.Y.; software, G.-H.Y.; validation, J.W.P. and Y.M.L.; formal analysis, J.W.P. and J.-H.Y.; investigation, J.W.P.; resources, J.-H.Y.; data curation, J.W.P.; writing--original draft, J.W.P.; writing--review and editing, G.-H.Y. and Y.M.L.; supervision, G.-H.Y. and Y.M.L.; project administration, Y.M.L.; funding acquisition, Y.M.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Research Foundation of Korea (NRF) grant number NRF-2019R1A2C1090426 and the APC was also funded by the NRF.  
This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2019R1A2C1090426).  
The authors declare no conflict of interest.