Keywords: deployable structures, pantographs, scissor-like element, cable-stiffened.

Deployable structures or foldable structures are structures which are purposely designed with internal mechanisms so that they can be transformed from a compact geometry to an expansive one, fully (or largely) automatically without (or with little) manual intervention. While most structures are designed to be inherently stiff and stable at all times, deployable structures have to have at least one mechanism that is utilised for the deployment, which is then somehow suppressed once the structure reaches its designated fully deployed configuration. Analysis of deployable structures thus tends to reside on the edge of mainstream structural analyses. The focus of this chapter is towards pantographic structures, either mast or antennae structures from simple pantographs, or more free-flowing structures from modified/articulated scissor-like elements. The argument for cable-stiffened deployable structures is put forward as a good solution for large deployable backbones, particularly for the pantographic (scissor-like-element) variants. Such structures have both passive single-segment cable elements as well as active cables, which are multi-segmented cables with internal nodes running over pulleys. The active cable can then be used to activate the deployment of the deployable backbone, as well as being the means by which to pre-stress the fully deployed structure. The argument for analysis of such cable-stiffened deployable structures in the force method is put forward, and the matrix formulation for macro-elements is also expounded. The analysis shows matrix reduction in general cases where there are internal unloaded nodes in a structure, or structural components, but it is particularly useful for components of deployable structures which are made up of more fundamental structural elements and hence typically have internal unloaded nodes with unusual kinematic conditions to allow the deployment mechanism. The chapter shows how the technique is applied to both an active cable and a two-dimension pantograph element. Matrices for these two elements have been built up from fundamental bar and beam elements, assembled firstly as large matrices, before specific conditions at the internal nodes are applied and the matrices then reduced step by step. Results from the analysis are then contrasted with experimental results from a deployable pantographic antenna to gain insight into the validity of such an approach.

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