Interactive conceptual design of structural equilibrium based on sparse ground structures and ADMM

Conventional approaches to designing sound structural forms typically involve either adapting well-known or catalogued types or seeking optimal solutions to well-defined problems. Limited methods are available for generating and exploring structural forms outside of these established practices. This paper presents a computational design framework aimed at generating diverse yet efficient discrete structural forms in static equilibrium, while simultaneously defining their own problem boundaries, which is typical of early design stages. The method builds on two inner steps. In the first step, layout optimization based on sparse ground structures is employed to explore structural concepts beyond well-established types. In the second step, geometry optimization, the structural forms obtained from the layout step are refined to meet other user-defined design goals and constraints. This is accomplished by minimizing a proximity function following the concept of constraint projections, a method derived from the Alternating Direction Method of Multipliers (ADMM). This paper presents a new formulation for ensuring static equilibrium through the constraint projection method. Hence, the framework offers advantages in computation speed and flexibility of constraints. With no need for a predefined structure or topology, the framework enables an unbiased exploration of structural forms within changing boundary conditions following their subjective assessment by the user. This results in an interactive, flexible, and fast exploration of structural options, some of which would have been hard to predict, yet meet all expectations. The framework is implemented into a digital tool for the Rhino/Grasshopper environment, called Dragonfly3D. A series of application studies demonstrates its usability for conceptual structural design.