Integrated topology and nonlinear energy dissipation devices optimization of multi-story buildings under stochastic seismic excitation

This paper proposes a novel method to simultaneously optimize the topology and size and location of nonlinear energy dissipation devices under stochastic seismic excitation. The input excitation is modeled as a stationary filtered white noise. The energy dissipation devices are modeled as discrete nonlinear components in the structural system, while the remainder of the structure is assumed to be elastic, and represented with a finite element model that is optimized using a density-based approach. The equations of motion for the structure and the excitation are expressed in state space form and combined into an augmented system. Then, equivalent linearization, coupled with the Lyapunov equation, is employed to determine the structural response covariances that are used to define the objective function. The sensitivities with respect to the design variables are determined using the adjoint method and verified with a finite difference approximation, enabling the application of this formulation in topology optimization. A benchmark nine-story building equipped with metallic yielding devices under stochastic seismic excitation is used to demonstrate the efficacy of the proposed approach. The approach is validated by matching the responses computed from the Lyapunov equation to those of the Monte Carlo simulations. For the numerical example, the optimized design demonstrates that Triangular plate Added Damping and Stiffness (TADAS) devices dissipate nearly 70% of the input seismic energy, leading to a 47% reduction in inter-story displacement compared to a structure without supplemental damping. This novel approach offers a computationally efficient and robust tool for designing efficient buildings equipped with nonlinear energy dissipation devices to effectively mitigate responses under uncertain dynamic environments.