MATRIX FORMULATION OF MACRO-ELEMENTS FOR DEPLOYABLE STRUCTURES

This paper deals with the computer analysis of a particular class of d eployable structures, which we have developed over recent years. These structures consist only of rods, hindged together to form a deployabl e backbone, of some passive cables, which are slack when the backbone is fully or partially folded but become taut when it is fully deployed , and one or more active cables, which activate deployment and set up suitable states of prestress, once the structure is in its fully deplo yed configuration. We discuss one aspect of the computer analysis of t hese structures, namely the task of setting up the equilibrium and fle xibility matrices required for the deployment, prestressing and struct ural response computations of three macro-elements: the active cable, i.e. a slender, constant-tension element consisting of two or more str aight segments; the pantograph unit, consisting of two coplanar, strai ght beams joined by a shear connector; and the backbone module for the octahedral mast, which consists of a flat, square cross of rods and a n additional rod going through a pivot-and-slider joint at the centre of the cross. Compact matrices for these elements are derived using a recently developed matrix reduction technique. Three applications of t hese macro-elements are given, illustrating their use in simple deploy able structures.