The stiffness of tensegrity structures

Abstract

The stiffness of tensegrity structures comes from two sources: the change of force carried by members as their length is changed, and the reorientation of forces as already stressed members are rotated. For any particular tensegrity, both sources of stiffness may have a critical role to play. This paper explores how the stiffness of two example tensegrity structures changes as the level of prestress in a member varies. It is shown that, for high levels of prestress, an originally stable tensegrity can be made to have zero stiffness, or indeed be made unstable.

A zero-stiffness elastic shell structure

“…A classical example of this behaviour is provided by tensegrity structures [Calladine 1978;Guest 2011], which typically rely on prestress in order to be able to act as structures at all. However, even for tensegrities with rigid compression members, increasing the relative level of prestress can reduce the stiffness Figure 1.…”

Geometry: The leading parameter for the Poisson’s ratio of bending-dominated cellular solids

“…The beam model corresponding to a stiff framework can still deform by stretching (length extension) of the beams; this is called the stretching-dominated deformation -of great importance for structural engineering, e.g. utilised in trusses (Dewdney, 1991;Lewandoski, 2004;Rinke and Kotnik, 2010), tensile-only structures (Berger, 2005), tensegrities (Connelly and Back, 1998;Guest, 2011) and as well in micro-structured material designs (Cheung and Gershenfeld, 2013;Hutchinson and Fleck, 2006). The beam model corresponding to a flexible bar-and-joint framework may be rigid due to enforced constant angles at the vertices; however, by beam bending (Fig.…”

Prismatic tensegrity structures with additional cables: Integral symmetric states of self-stress and cable-controlled reconfiguration procedure

“…In this section, the tangent stiffness matrix K will be derived for two purposes: 1. establish the relationship between nodal displacements (to first order) and driving force caused by imposed adjustments of member lengths so that provide a means for predicting the structural response during the process of reconfiguration; 2. the smallest eigenvalue of K is used subsequently to evaluate the rigidity of the structures since it is associated with the most flexible mode of displacements (Guest, 2011). Before that, the fundamental assumptions are first stated as follows:…”