Optimal topological design of structures subjected to non-stationary stochastic excitations

Topology optimization procedures are emerging as powerful tools for guiding the identification of enhanced structural systems that can meet the minimum weight and cost requirements while ensuring superior structural performances. Within this framework, it is too evident that the elaboration of efficient design solutions requires an accurate prediction of the structural response induced by natural or man-made hazards. In case of structural systems located within earthquake-prone areas, for instance, disregarding the aleatory uncertainty of the seismic excitation would lead to sub-optimal and poorly performing systems, or even to design solutions that do not comply with safety requirements. Unfortunately, handling with uncertainties into topology optimization problems is really challenging because the satisfactory description of the design domain requires a very large design vector. Hence, this work illustrates a novel approach for the optimal design of lateral resisting systems in multi-story buildings subjected to seismic ground motions. Herein, the base excitation is simulated as fully non-stationary stochastic process and the topology optimization problem is formulated in such a way to minimize the dynamic compliance of linear elastic multi-story buildings via the Solid Isotropic Material with Penalization approach. In order to accommodate the use of efficient gradient-based optimization algorithms, the sensitivity of the dynamic responses is performed analytically by means of an approximated procedure that involves sub-assemblies of the whole design domain. Stability and effectiveness of the proposed optimum design procedure are demonstrated via numerical examples where the non-stationary properties of the stochastic excitations are tuned to mimic different soil conditions.