Applications of a "Virtual" Force Density Method

Abstract

The Force density Method [FDM], since Linkwitz and Schek¿s first development [8] in 1970¿s, has been well known as a powerful tool for analytical form-finding and static analysis of self-stressed structures like tensile membranes and cable networks [12]. Actually force density is always associated to a real stress state of the structure under a field of applied forces that, combined with other boundary conditions (constraints, etc.), allows the shape to evolve and improve). The approach proposed in this paper enables the technique to become more versatile so that it is possible to extend its application to different kinds of problems. In particular, changing the connection matrix and introducing virtual forces, morphogenesis can be related to general spatial frame structures looking at geometrical requirements as form and function irrespective of the applied stress field. As a demonstration of the capabilities of this tool, three different applications on current issues in free-form architecture are tested by means of a commercial NURBS based software and a VB based algorithm. One of these applications concerns the preliminary design of the roof structure of Ponte Parodi project, by UNStudio Amsterdam, a multifunctional building to be located on the waterfront of Genoa, Italy.