Principal stress line computation for discrete topology design

Abstract

Principal stress-lines are pairs of orthogonal curves that indicate trajectories of internal forces. Subsequently, these curves idealize paths of material continuity, and naturally encode the optimal topology for any structure for a given set of boundary conditions. Stress-line analysis has the potential to offer a direct and geometrically-provocative approach to optimization that can synthesize both design and structural objectives. However, its application in design has generally been limited due to a lack of standardization and parameterization of the process for generating and interpreting stress lines. Addressing these barriers, this thesis proposes a new implementation framework that enables designers to take advantage of stress-line analysis to inform conceptual structural design. Central to the premise of this research is a new conception of structurally-inspired design exploration that does not impose a singular solution, but instead allows for the exploration of a diverse high-performance design space in order to balance the combination of structural and architectural design objectives. Specifically, the thesis has immediate application for the topological design of both regular and irregular thin shell structures predominately subjected to in-plane and compressive structural actions.