Abstract

Part 1:R. Pandia Raj

Tensegrity structures can be considered as structures consisting of a continuous network of cables, together with discontinuous struts, that rely on prestress to be stiff and stable – they can be made rigid in a particular configuration by a state of self-stress. Tensegrity towers are a form of tensegrity structure which are compact in two dimensions, but extend in a third direction. The first tensegrity tower was built by Kenneth Snelson in 1948, and he was also responsible for the famous 1969 Needle Tower in Washington. The self equilibrated configurations of these structures were not found by formal analysis, but rather were based on the insight and experience of the designer. However, it is interesting that many of the found forms are highly symmetric, consisting of a repeat of a module that itself has high symmetry. We will show that incorporating this symmetry into a structural analysis of the tower gives great insight to find the equilibrium configurations of these structures. Further, the form-finding process for tensegrity structures with higher symmetry will also be discussed in the talk.

Part 2:Mark Schenk (CUED)

This talk describes a special class of ‘tensegrity structures’ that straddle the border between mechanisms and structures: Zero Stiffness Tensegrity Structures. Zero stiffness describes the ability of a structure to change its shape without requiring any external force. In other words, the structure will have a constant potential energy througout is working range and is therefore neutrally stable. We have introduced this concept to tensegrity structures by using special tension members with an apparent zero rest length. These can for instance be manufactured by coiling prestressed springs.

The zero-stiffness modes introduced to tensegrities in this way are not internal mechanisms, as they involve first-order changes in the special member lengths. Rather, these modes correspond to an infinitesimal affine transformation of the structure that preserves the length of conventional members. Furthermore, the modes are preserved over finite displacements. The zero-stiffness modes are present if and only if the directional vectors of those members lie on a projective conic: this geometric interpretation provides several interesting observations regarding zero stiffness tensegrity structures.