Topology and sizing optimization of nonlinear viscous dampers for the minimum-cost seismic retrofitting of 3-D frame structures

In this paper, we present a new methodology for achieving minimum-cost retrofitting design solutions. Nonlinear fluid viscous dampers and their supporting braces are optimally distributed in irregular 3-D frames and optimally sized. For generating optimal design solutions useful for practitioners, a realistic cost formulation is chosen as the objective function to be minimized. Constraints are imposed on inter-story drifts at the peripheries. These are evaluated with nonlinear time-history analyses considering realistic ground acceleration records. The behavior of each damper-brace system is defined based on the Maxwell's model for viscoelasticity. A fractional power-law is used to describe the nonlinear force-velocity relation of each damper. The stiffening contribution of the supporting brace and of the damper is represented by linear springs. The damper-brace elements are divided into size-groups, that is, elements with the same mechanical properties. The properties of each size-group of dampers (damping coefficient and supporting brace stiffness), and the dampers' distribution in the structure are optimally defined. The optimization problem is first posed and solved as a mixed-integer problem. To reduce the computational effort required in the optimization, the problem is then re-formulated with continuous variables only and solved with a gradient-based algorithm. Material interpolation techniques play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for a 3-D irregular frame are presented and discussed.