This dissertation presents a computational framework for structural design applications based on 3D graphic statics using polyhedral force diagrams. At the core of this framework is the development of a generalised theoretical foundation for 3D graphic statics, underpinned by the formulation of three datastructures for addressing a wide range of equilibrium problems involving spatial systems of forces: a polyhedral cell, the multi-cell polyhedron, and generalised cell networks. The three datastructures along with the relevant operations and geometric algorithms are implemented in an open-source library with interactive user interfaces to common computational design environments targeting both architects and structural engineers. The framework is developed with the goal of maximising the inherent benefits of computational graphic statics, which diminish with increasing complexity of spatial structures: legible visualisation of force equilibrium, intuitive designer interactivity in real time, and provision of new structural design insights. In contrast to conventional numerical approaches to structural design that are dependent on predefined formsbefore any analysis can be executed, the presented framework enables new design methodologies that explore the geometry of forces as the catalyst for design, analysis, and optimisation of spatial structures. These new potentials are illustrated through numerous examples, showcasing how the framework could be used to address structural design problems in a variety of new ways that are simply not possible with existing, form-dependent tools. Beyond equilibrium design and analysis,the practical relevance of this research in architectural fabrication and construction is demonstrated through the MycoTree project, a 1-to-1 built prototype of a spatially branching structure made of load-bearing mycelium components.
Institute of Technology in Architecture
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