Simultaneous analysis and design optimization for seismic retrofitting of hysteretic structures with fluid viscous dampers

Fluid viscous dampers, if properly sized and placed, can significantly improve the performance and safety of existing structures during an earthquake. This has motivated the development of several approaches to optimize the design of fluid viscous dampers. The optimization approaches available typically have an iterative nature, and in every iteration, expensive time-history analyses are performed. This paper presents a novel optimization-based approach for retrofitting hysteretic structures with fluid viscous dampers that does not require the computation of time-history analyses. The sizing and placement of the dampers are defined using a simultaneous analysis and design optimization approach based on nonlinear programming. In this approach, the equations of motion are treated as equality constraints of the optimization problem. As a consequence, design sensitivity analysis methods are not needed to calculate the gradients of the objective and constraint functions. Two design scenarios are considered: structures with hysteretic behavior retrofitted with linear or nonlinear fluid viscous dampers. The optimization variables include the damping coefficients of the dampers and the structural response over time. The manufacturing cost of the dampers is minimized, with constraints on the inter-story drifts. A continuation scheme on the design-driving inter-story drift constraints is proposed to effectively solve the class of problems considered. The numerical results demonstrate that the proposed approach can solve complex design optimization problems using reasonable computational resources and time. It is also shown that, thanks to the proposed approach, additional constraints can be incorporated in the problem formulation with minimal modeling effort, and without the need to develop additional sensitivity analyses for computing the gradients of the added constraints. The Julia codes used in this study are freely available on GitHub: https://github.com/pollinico/SAND_opt_nonlinFVDs.