Performance-based seismic retrofitting of frame structures using negative stiffness devices and fluid viscous dampers via optimization

In this paper, an optimization approach for the seismic retrofitting of inelastic moment resisting frames (MRFs) equipped with nonlinear fluid viscous dampers (FVDs) and negative stiffness devices (NSDs) is presented. The goal of the optimization is to minimize a cost-related objective function, which accounts for the cost of the supplemental FVDs and NSDs. The mechanical properties and the topological layout of both the FVDs and NSDs are considered as design variables and simultaneously optimized during the optimization process. A loss estimation analysis is utilized as a performance constraint, where the PEER framework is adopted. The structural response is evaluated using a nonlinear time history analysis (NTHA), which accounts for the nonlinear behavior of the MRF elements, FVDs, and NSDs. The optimization problem is formulated using differentiable functions only, making it suitable for an efficient gradient-based optimization solution scheme. The gradients are efficiently derived using the adjoint sensitivity analysis approach. Two numerical examples show the robustness and efficiency of the presented methodology, where the optimized design relies on NSDs and FVDs in both examples.