Minimum-cost optimization of nonlinear fluid viscous dampers and their supporting members for seismic retrofitting

This paper presents an effective approach for achieving minimum-cost designs for seismic retrofitting using nonlinear fluid viscous dampers. The damping coefficients of the dampers and the stiffness coefficients of the supporting braces are designed by an optimization algorithm. A realistic retrofitting cost function is minimized subject to constraints on inter-story drifts at the peripheries of frame structures. The cost function accounts for costs related to both the topology and the sizes of the dampers. The behavior of each damper-brace element is defined by the Maxwell model, where the force–velocity relation of the nonlinear dampers is formulated with a fractional power law. The optimization problem is first posed and solved as a mixed integer problem. For the reduction of the computational effort required in the optimization, the problem is then reformulated with continuous variables only and solved with a gradient-based algorithm. Material interpolation techniques, which have been successfully applied in topology optimization and in multi-material optimization, play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for 3-D irregular frames are presented and discussed.