Topology and size optimization of viscous dampers with discrete design variables by outer approximation

We propose a novel seismic retrofitting approach for the topology and size optimization of fluid viscous dampers using discrete design variables. The design variables are the damping coefficients of the dampers, and they are chosen from catalogs, leading to practical optimal design solutions. The optimization problems considered are formulated as mixed 0–1 nonlinear programming problems. An algorithm based on outer approximation and that relies on first-order information is proposed to find optimized designs with modest computational resources and time. The effectiveness of the proposed approach is demonstrated through optimal seismic retrofitting of three-dimensional irregular frame structures. In the optimization problem formulation, the retrofitted structures are subjected to realistic seismic ground acceleration records with constraints on inter-story drifts and total story accelerations.