Inextensional Packaging of Thin Shell Slit Reflectors

Carbon-fibre-reinforced-plastic reflector antennas based on a thin shell that is folded elastically have been recently developed; this paper presents a new concept for packaging reflectors of this type. The idea is to cut the surface into 6-8 petals along curved lines, whose shape is such that in the packaged configuration the petals wrap around a central part. During deployment, they open out and unwrap, driven by the energy stored during folding. Analytical expressions are derived for the stresses induced by inextensional elastic folding of a doubly-curved shell. A simple, approximate method for analysing the packaging scheme is introduced, and its predictions are used to set up an optimization scheme that determines the cutting pattern required to achieve optimal packaging of the reflector, for a given yield stress and elastic modulus of the material. For a dish with diameter of 0.9 m an optimised cutting pattern is determined, and then a detailed finite-element analysis and an experimental verification of the curvatures induced by packaging are carried out. These results confirm that these predictions from the approximate analysis are accurate and conservative. A reduction in diameter of 3 is achieved for this particular dish.