3-D form and Force Language: Proposal for a Structural Basis

Abstract

The usually declared archetype for structural behaviour is the lattice (bar-and-node) structure. It is true that structural manifestations in general - with great clarity - may be reduced to the two interconnected structural nuclei, the pin-jointed bar and the hinged node. The relation to the geometrical archetypes, the five regular Platonic polyhedra, is obviously unsatisfactory, as only the three triangulated polyhedra have particular structural qualities in being kinematically stable. The two remaining, the cube and the dodecahedron, are unclear and usually considered as structurally inferior or incomplete. This “Fullerian cosmology” - as it may be called - has dominated basic structural understanding for many years. The structural dual to the lattice type, the plate structure, which fits perfectly with the geometrical plane-to-point duality, not only at the level of topology and kinematic stability, but also at the level of metric geometry, magnitude of forces and elastic properties, is rarely taken into consideration. This structural duality, which was discovered around 20 years ago, has mostly been used to describe the particular qualities of the plate structure and not for its unifying qualities with the lattice structure, creating an entirety at the archetypical level of 3-D structures. This quality forms the basis for some simple unique correlations betwen geometry and structural mechanics, but it also implies that the usual basic hierarchy of 3-D geometry has to be altered accordingly. The paper will discuss some of the possibilities of creating a Form-and-Force Language on this basis.