Creating diverse and competitive designs in topology optimisation

In recent years, computational design methods have attracted much attention due to their capability and convenience in rapidly generating potential solutions to a design problem. Among various computational design techniques, topology optimisation, a performance-based design tool, has become increasingly popular, as it enables designers to create efficient and innovative structural forms. However, in the field of structural optimisation, a premium has often been placed on achieving the global optimal solution, and the obtained optimal structural layout may not satisfy all design requirements (e.g., aesthetic and functional considerations). Moreover, conventional optimisation methods usually operate like a "black box", in which designers are not allowed to exert their personal preferences on the evolving design. In practice, it is highly desirable to obtain diverse design solutions that possess high structural performance. This research aims to develop a systematic methodology under the computational framework of the bi-directional evolutionary structural optimisation (BESO) method to create diverse and competitive structural designs. This thesis provides three interrelated research studies focused on the development of different approaches to generating alternative design options. The developed approach from each study is readily applicable to different design stages. The first study proposes three stochastic approaches to generating diverse and competitive designs. The approaches include (1) penalising elemental sensitivities, (2) changing initial designs, and (3) integrating the genetic algorithm into the BESO method. Each approach can randomly change the search path of the standard BESO algorithm, thereby influencing the design outcome in a stochastic way. By using any of these approaches, the designer can obtain a new structural shape when the optimisation process is restarted every time. The numerical results from several 3D optimisation problems demonstrate that the proposed approaches are capable of producing a variety of efficient structural designs with distinctly different structural forms. The second study proposes a thinning algorithm based approach to controlling the structural complexity (i.e., the number of cavities and tunnels) for both 2D and 3D optimisation problems. This approach is developed by integrating the topology-preserving feature of the simple points into the BESO method. In this work, the structural complexity can be directly controlled by preserving the topological properties of the prescribed initial design. Designers can alter the topology of the initial design to achieve multiple design solutions with different topologies. The developed methodology has been successfully applied in the computational morphogenesis of various structures. The results demonstrate that the control of design diversity and structural performance can be well balanced. In the third study, a hole-filling method is integrated into the BESO method to control the number and size of existing cavities and tunnels during the form-finding process. The hole-filling method is implemented to fill in extra cavities with solid material and cover extra tunnels by building sheet-like patches. Compared with the second study, the structural complexity control can start from an initial full design. Thus, it requires less human intervention to impose the topological constraints. Moreover, the numerical results demonstrated that the generation of sheet-like components could considerably increase the stiffness of the optimised structure. Thus, the developed approach has great potential to help engineers and architects search for efficient structural designs with controllable topologies. The novel approaches proposed in this PhD project can be applied in all stages of a design process. The stochastic approaches are capable of generating a large number of unexpected designs with high performance. Thus, the obtained solutions can be a rich source of inspiration for the early-stage exploration of a design process. In the detailed design stage, the structural complexity control approaches allow designers to directly control the topology of the evolving designs. In this respect, the designers can integrate aesthetic preferences and other requirements into the optimisation process. The research outcome holds great potential for practical applications in architecture and engineering, where diverse and competitive solutions are in high demand.