Topology optimization of structures subjected to nonstationary stochastic dynamic excitation

The most critical loads that civil structures must withstand are often stochastic, dynamic and frequently nonstationary in nature; however, this class of loading has received relatively little attention in topology optimization of structures. Existing methods that attempt to incorporate nonstationary effects are limited in scope or rely on approximations that restrict their applicability. This paper introduces a general and computationally efficient framework for topology optimization under nonstationary stochastic excitation by modeling the load as an amplitude-modulated filtered white noise. An augmented system is then obtained by combining the structural and excitation models, which allows for the calculation of the structure response covariances by solving a first-order ordinary matrix differential equation. A key contribution of this work is the derivation of closed-form sensitivities for a broad class of time-dependent objective functions, obtained through an exact adjoint formulation that avoids the approximations used in prior studies and enables large-scale topology optimization. The approach is illustrated for two benchmark buildings subjected to nonstationary ground motions, demonstrating the efficacy of the method to obtain optimized structures subjected to nonstationary stochastic excitation. Additionally, a comparison of the optimized designs for both stationary and nonstationary excitations is presented. This comparison indicates that, for typical seismic excitations, a design obtained assuming a stationary excitation is nearly identical to those obtained considering the nonstationary load.