Authors
M. Konstantatou, M. Akbarzadeh, A. McRobie
Abstract
Graphic statics, a 19th century methodology for the design and analysis of trusses in static equilibrium, has re-emerged recently as a comprehensive framework for designing and analyzing materially efficient structures. Specifically, computational frameworks have been introduced for the structural morphogenesis of compression-only 3D polyhedral trusses by Akbarzadeh et al. (2015). Moreover, the fundamental relation between tension-and-compression 3D trusses in static equilibrium and 4D stress functions has been showed in McRobie (2016). Furthermore, a direct mathematical construction for generating pairs of reciprocal 4D stress functions, and by projection pairs of reciprocal 3D form and force diagrams, has been discussed in Konstantatou et al. (2018). The central role of stress functions in structural morphogenesis was already known by Maxwell (1864a) who used projections of polyhedral (Airy) stress functions to derive 2D trusses in static equilibrium while obtaining design and analysis freedoms. In this paper we apply these constructions to their higher-dimensional equivalents and show how structural morphogenesis of 3D polyhedral, trusses can also have as a starting point 4D stress functions of the form space. The presented direct method has a generative aspect where an underlying grammar can produce a wide range of typologies and can be applied to compression-and-tension cases.
