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

Abstract

Summary 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. Copyright © 2017 John Wiley & Sons, Ltd.

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

“…This ratio can affect how the damper element will behave and the ease with which its first order differential equation can be approximated numerically. For the tuning procedure of the parameter ρ , we relied on the procedure discussed in Pollini et al During the nonlinear time‐history structural analysis, the response of each damper in each time‐step is approximated with a fourth‐order Runge‐Kutta method as suggested by Kasai and Oohara . A similar approach has been used in Akcelyan et al and by the authors in Reference Pollini et al…”

“…The approach presented and discussed in this paper constitutes an additional contribution to the retrofitting problem of nonlinear structures with nonlinear fluid viscous dampers, through a practical and computationally efficient optimization‐based approach. The proposed approach originates from previous work of the authors, where the minimum‐cost seismic retrofitting of linear structures with linear and nonlinear fluid viscous dampers was considered. However, in the eventuality of more severe seismic excitations, a nonlinear structural response should be considered.…”

Energy-Based Design Criterion of Dissipative Bracing Systems for the Seismic Retrofit of Frame Structures

“…Alternative approaches refer to the energy balance computed from time-history analyses [43,44], or optimization procedures [45]. Among the energy-based design methods, a criterion determining the minimum damping coefficients of the devices required to assign them the capability of dissipating a prefixed fraction β of the seismic input energy E I computed on each story [31,32] or the entire structure [12] was proposed by the author and co-authors.…”

Effectiveness evaluation and optimal design of nonlinear viscous dampers for inelastic structures under pulse‐type ground motions

“…To wit, using nonlinear viscous dampers with a low velocity exponent results in lower peak damping forces with the same energy dissipation amount, which leads to limited base shears and floor accelerations . General nonlinear fluid dampers have been evaluated in analysis and design of building structures recently . In these studies, the assessment of nonlinear fluid dampers is moving away from traditional deterministic techniques to probabilistic performance‐based methodologies …”

“…The response‐dependent feature of the linearized effective damping ratio substantially impedes the analysis and design of inelastic structures equipped with nonlinear viscous dampers, mainly because: (1) nonlinear time history analysis has to be conducted to accurately capture the structural responses; (2) it remains a highly iterative process to design and optimize nonlinear dampers for inelastic structures. In addition, the design and optimization of nonlinear dampers have been addressed in recent studies by directly linking the cost functions to the design variables of nonlinear viscous dampers . Gidaris and Taflanidis used a stochastic search approach to identify the fluid viscous dampers that minimize the life‐cycle cost of the buildings.…”