Reliability-based topology optimization of uncertain building systems subject to stochastic excitation

Topology optimization has traditionally been developed in a deterministic setting, notwithstanding the considerable uncertainties that generally affect both the system as well as the excitation. Therefore, the development of methods that are capable of describing the performance of uncertain systems in a fully probabilistic setting would represent an important step forward. In particular, the ability to consider reliability constraints written in terms of first excursion probabilities posed on systems driven by general stochastic excitation would allow a wide variety of important design scenarios to be modeled. This paper is focused on proposing a simulation-centered reliability-based topology optimization framework to this end. In particular, an approach is developed based on defining, from the argumentation of the simulation process, an optimization sub-problem that not only approximately decouples the probabilistic analysis from the optimization loop, but takes a form that can be extremely efficiently solved. By solving a limited sequence of sub-problems, solutions are found that rigorously meet the first excursion constraints of the original problem. A series of case studies are presented illustrating the potential of the proposed framework.