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

Topology optimization has been mainly addressed for structures under static loads using a deterministic setting. Nonetheless, many structural systems are subjected to uncertain dynamic loads, and thus efficient approaches are required to evaluate the optimal topology in such kind of applications. Within this framework, the present paper deals with the topology optimization of multi-story buildings subjected to seismic ground motion. Because of the inherent randomness of the earthquakes, the uncertain system response is determined through a random vibration-based approach in which the seismic ground motion is described as filtered white Gaussian noise with time-varying amplitude and frequency content (i.e., fully non-stationary seismic ground motion). The paper is especially concerned with the assessment of the dynamic response sensitivity for the gradient-based numerical solution of the optimization problem. To this end, an approximated construction of the gradient is proposed in which explicit, exact derivatives with respect to the design variables are computed analytically through direct differentiation for a sub-assembly of elements (up to a single element) resulting from the discretization of the optimizable domain. The proposed strategy is first validated for the simpler case of stationary base excitation by comparing the results with those obtained using an exact approach based on the adjoint method, and its correctness is ultimately verified for the more general case of non-stationary seismic ground motion. Overall, this validation demonstrates that the proposed approach leads to accurate results at low computational effort. Further numerical investigations are finally presented to highlight to what extent the features of the non-stationary seismic ground motion influence the optimal topology.