Digital shaping: Meshless computational methods for form generation in architectural design

Doctoral thesis, 2022

This thesis explores methods for integration of structural analysis into a digital design, specifically by introducing the family of meshless methods—usually found in physics and mechanical engineering—into the context of a design process and the materials typically used for structures in the built environment. The thesis takes the design process for the Mexico City Airport project as a point of departure. The project is presented as an example of digital shaping and motivates the research to focus on structural nodal connection. Three historical case studies where nodal connections are used in different ways are introduced and followed by the formulation of four research questions. These questions motivate the contextualisation, which is divided into four parts; the use of form representation in digital design, design conditions from materials and production, computational methods for shape finding and numerical methods for structural analysis. A particular focus in the thesis is dedicated to the development of a meshless method
called Force flux peridynamics (FFPD). This method is hypothesised to be suitable in digital design partly because the point cloud discretisation is relatively easy to automate and partly because of the ability to simulate complex phenomena such as brittle fracture. Such capabilities could be especially helpful in supporting the design of lightweight components. The five papers that are included in the thesis follow a trajectory from large to
small. The first paper describes the computational design work with the roof of the new international airport for Mexico City. The second paper addresses one of the challenges faced in that project with material inefficiency for nodal connections. The third paper explores a generative approach for creating lightweight porous structural components inspired by bone growth. The fourth paper presents Force Flux Peridynamics, an extension/modification of the peridynamics theory that allows for variable particle sizes and an irregular particle distribution through the introduction of the force flux density concept. The development is motivated by the limitations of the current theory from a design process point of view. The new formulation enables the simulation of phenomena such as yielding and brittle fracture and is shown to correlate with Griffith’s theory of fracture. The final paper then applies FFPD to the simulation of concrete, where fracture plays an essential role in mechanical characteristics.