Toni Kotnik

Interactive particle swarm optimization for the architectural design of truss structures

This paper presents an interactive framework for the design of truss structures with aesthetic criteria. The truss chords are described using NURBS, a tool widely used in computer aided design (CAD) programs to describe free-form geometry. This allows for a convenient interface between the optimization scheme, a particle swarm optimizer, and the user. Driven from the fact that aesthetic design goals are not easily quantifiable, key elements are introduced and implemented herein towards an interactive framework for algorithmic design of truss structures. Within this framework, the user can visually assess interesting solutions, save them for later assessment, actively drive the optimization towards individual aims, re-initialize the optimization with a set of available solutions, or restart the design process. A criterion is introduced as a means of quantifying subjective goals, expressing the similarity of the shape of candidate solutions with respect to reference designs. The framework is tested on a benchmark case and then applied to the design of a truss tower. The effectiveness of the similarity criteria, as well as the ability of the user to drive the process towards specific design goals is demonstrated.

Geometry of Structural Form

This paper describes a precise geometric method for the inscription of structural constraints into architectural form. Based on techniques from graphic statics, the force distribution in building structures is visualized using geometric diagrams. This diagrammatic representation allows a formal description that shows the relationship between the force flow and the structural form. The formal character of this description enables the direct implementation of a parametric truss geometry that maintains major structural behavioral characteristics under deformation. An interactive model of a structural freeform roof is developed through this link between a parametric truss definition and a design-driving NURBS surface. This allows for an intuitive exploration of the constrained design space in real time. Formal explorations and the comparison with built examples demonstrate the effectiveness of this approach.

Curved Bridge Design

This paper presents a novel approach for the interactive design of linear structures in space. A method is introduced, that provides a maximum of formal freedom in the design of funicular, hence efficient, structures. For a given deck geometry, defined by a design driving NURBS curve via parametric modeling techniques, a tailored relaxation routine allows for controlled, real-time form-finding of the spatial funicular. Subsequently, the equilibrium of the deck is constructed using techniques from graphic statics, combined with a least-square optimization technique. Finally, the method is applied to a design example.