# Effect of Dynamic Loading Conditions on Maximizing Energy Dissipation of Metallic Dampers
## 2 Design Concept and Optimization Approaches
### Design Concept of a Prismatic Metallic Damper  
As noted, an ideal damper should be reliable in performance, dissipate sufficient energy, and exhibit stable hysteretic behavior against the seismic load. The minimum qualification of reliability can be guaranteed with respect to metallic dampers, since they dissipate seismic energy through plastic deformation after yielding [16]. However, increasing the energy dissipation capacity and the stability is necessary for developing an effective metallic damper [15]. In terms of capacity and stability, the two key points can be summarized as follows. First, the energy dissipation should be maximized [17]. This maximization can be expressed as the increase in the area of the hysteresis loop of the metallic damper under cyclic loading. To achieve the efficiency, a total volume of the material usage should be constrained in the maximization process. Second, the shape or material components of the damper should not cause a stress concentration or excessive plastic strain at a particular point in the member [18]. Through these objectives, a better-performing metallic damper can be obtained. To achieve the goals presented above, researchers can either improve existing shapes of metallic dampers, or find new optimal shapes, via one of two methods: (1) an experimental evaluation based on a geometry derivation through mechanical calculation, or (2) an optimization process using iterative computing. In the former case, the performance is evaluated via several experiments based on a few different shapes--usually 5-10 shapes [1, 8, 10, 17, 19, 20, 21]. On the other hand, the latter process combines numerical analysis with a computational optimization scheme to find the optimal shape from repetitive computation. For such an optimization, various techniques, such as Tabu search [22], the simulated annealing algorithm [13; 23], the response surface methodology [14], evolutionary optimization [24; 25; 26], and topology optimization [27; 28; 29], can be applied. All of these related studies are based on FE analysis; it has been proven that the analysis results of FE modeling (FEM) are very similar to the experimental results [1; 8; 10; 13; 14; 22]. In general, computational optimization based on FEM is applied for upgrading metallic dampers already in use. In contrast, trial-and-error methods based on experimental development have been commonly utilized to develop new types of metallic dampers. However, in this paper, computational optimization was not exploited to improve an existing form, but to find a new and optimal metallic damper geometry. The design concept of this study directly focuses on investigating optimum shape derivations for metallic dampers with respect to different static or dynamic loading conditions. In this study, a simple concept of a metallic damper is proposed--one that is designed to be additionally installed between the superstructure and the lower column of the bridge. The conceptual installation conditions are illustrated in Figure 1. The basic size and shape of the damper is presented in the form of a rectangular parallelepiped with a total length of 1200 mm, a width of 800 mm, and a thickness of 40 mm (Figure 2). Only one end of the damper is allowed to move in one lateral direction; the other perpendicular movements or moments are fixed. It was assumed that no initial vertical force was applied to the damper. Only the reaction forces of the damper in the vertical direction could occur by boundary conditions, due to the lateral loading. These dampers are structurally simple, easy to design, and capable of dissipating all the seismic energy in multi-axis directions. However, the analytical models of this dampers were allowed to deflect only in 2-dimensional directions in this study. Thus, the out-of-plane deformations and buckling of the metallic damper were not considered. This limitation simplified the optimization process as much as possible, considering the complexity in the dynamic responses of the damper.