Optimization-based minimum-cost seismic retrofitting of hysteretic frames with nonlinear fluid viscous dampers

In this paper, we discuss an optimization-based approach for minimum-cost seismic retrofitting of hysteretic frames with nonlinear fluid viscous dampers. The proposed approach accounts also for moment-axial interaction in the structural elements, to consider a more realistic coupling between added dampers and retrofitted structure. The design variables of the problem are the damping coefficients of the dampers. Indirectly, the design involves also the stiffness coefficients of the supporting braces. In the optimization analysis, we minimize a realistic retrofitting cost function with constraints on inter-story drifts under a suite of ground motion records. The cost function includes costs related to the topological and mechanical properties of the dampers' designs. The structure is modeled with a mixed finite element approach, where the hysteretic behavior is defined at the beams' and columns' cross sections level. We consider damper-brace elements with a visco-elastic behavior characterized by the Maxwell model. The dampers' viscous behavior is defined by a fractional power law. Promising results obtained for a two-story, a nine-story, and a 20-story 2-D frames are presented and discussed.