Probabilistic Performance-Based Topology Optimization of Structural Systems

Recently societal needs have led to a growing number of tall buildings worldwide. This has led to a concerted effort to develop more sustainable structures, one aspect of which involves saving resources through the development of novel, efficient load-resisting systems. Accordingly, topology, or layout, optimization techniques offer a means of achieving this goal. The use of deterministic topology optimization methods for structural design leads to structures with reduced redundancy when inefficient material is removed since the structures are essentially pushed to their limiting capacities. This has significant implications for building design as structures are subject to a number of uncertainties that must be considered during the design process to ensure satisfactory performance. It is particularly important to account for the stochastic loading conditions and resulting structural responses using first excursion probabilities for compatibility with current design methodologies. The possibility of performing topology optimization within this setting has not yet been investigated.

To address this need, this thesis presents a series of methods that are a first effort towards the development of a topology optimization framework for structural design that rigorously includes the effect of the uncertain and stochastic nature of the structural design problem using first excursion probabilities. In particular, these methods efficiently consider the design of structures under stationary and non-stationary loading processes, and consider serviceability and habitability constraints written in terms of displacement- and acceleration-based response quantities, respectively. The techniques presented in this thesis are categorized as decoupling methods and develop a series of localized approximations of the original optimization problem, each of which is defined through a single reliability analysis while taking on a traditional deterministic form. Therefore, the optimization problem may be efficiently solved using established gradient-based algorithms. The probabilistic analysis is evaluated using simulation-based techniques in order to consider the large-scale nature of the reliability problem. A number of examples are provided throughout this thesis in order to illustrate the applicability and efficiency of the approach. This research significantly contributes to the field of reliability-based topology optimization while enhancing the usefulness of topology optimization methods for the preliminary design of buildings.