Simultaneous optimization of topology and supplemental damping distribution for buildings subjected to stochastic excitation

Abstract

Supplemental damping devices present an attractive means to improve the structural system. Typically, dampers are designed after the structural system is selected, and they are added to increase structural damping and effectively reduce the dynamic response. On the other hand, topology optimization offers a possibility to obtain an efficient structural system but not the damper placement. Therefore, this study proposes a framework to obtain simultaneously optimal topology as well as the size and spatial distribution of discrete supplemental viscous damping devices for stochastically-excited buildings. The excitation is modeled as a stationary zero-mean filtered white noise, the excitation model is combined with the structural model to form an augmented representation, and the stationary covariances of the structural responses of interest are obtained by solving a Lyapunov equation. The objective function is defined in terms of the stationary covariance. A gradient-based method is used to update the design variables, and the sensitivities are computed using an adjoint method requiring the solution of an additional Lyapunov equation. The proposed topology optimization scheme is illustrated to obtain the optimal lateral resisting system together with the discrete dampers distribution for buildings subjected to stochastic ground motion. The results presented herein demonstrate the efficiency of the proposed approach to perform simultaneous optimization of topology and damper distribution of stochastically excited structures.

Human-Induced Vibration Serviceability: From Dynamic Load Measurement towards the Performance-Based Structural Design

“…For reliability-based control strategies, the randomness of the system, including the eternal load and structure, is considered, and the purpose is to maximize the dynamic reliability or minimize the financial cost while keeping the reliability larger than a threshold value. This trend has been affecting the research field of vibration control under seismic excitation [112,113] and wind excitation [114,115], where the modern techniques represented by topology optimization have been utilized.…”

Inverse optimal damper placement via shear model for elastic–plastic moment-resisting frames under large-amplitude ground motions

“…Idels and Lavan [37] tackled a realistic simultaneous optimization problem of discrete member sections of a structural frame and nonlinear viscous dampers. Gomez et al [38] simultaneously treated the topology optimization of main frames and the damper optimization in building structures. Saitua et al [39] incorporated the procedure of strengthening of structural members into the damper design to cope with the increase of the member stress by adding the dampers.…”

Topology optimization of multi-story buildings under fully non-stationary stochastic seismic ground motion

“…Gomez and Spencer (2019) addressed the topology optimization of structural systems under stationary stochastic excitation via random vibration theory. They developed an exact, yet very efficient, approach based on the adjoint method to facilitate the gradient-based numerical solution of the corresponding optimization problem, see also (Gomez et al 2020(Gomez et al , 2021). An energy-based design criterion has been considered by Angelucci et al (2021a) for the topology optimization of linear elastic multi-story buildings subjected to earthquake, under the simplifying assumption of stationary stochastic seismic ground motion.…”