This dissertation is concerned with thin-walled reflector structures that
can be folded elastically. The Spring-Back Reflector which was recently
invented by Hughes Space Corporation, is a state-of-the-art flexible paraboloidal
deployable reflector based on this approach. A key feature of this deployable
structure is its simplicity; it is simply folded elastically into half,
like a 'taco' shell and stored above the spacecraft, in the normally unused
space in the top of the rocket fairing. To deploy it, the restraining
cords are released and the reflector deploys by releasing its stored strain
energy, hence it 'springs back' into shape. This passive deployment
sequence means that there are no motors, controls or hinges that could malfunction
Due to its inherent flexibility, the Spring-Back Reflector suffers from
distortions which result from the residual strains of the manufacturing process.
This is potentially a severe limitation on the applicability of this
reflector. The current remedy is to mechanically adjust the surface
in orbit, however, this is neither ideal nor in keeping with the simplicity
of the original concept.
The purpose of this research is to develop stiffening methods for this
reflector in order to reduce these distortions. Working within the constraint
of a passively deployed system, these methods are required to stiffen the
reflector in its deployed configuration, and yet still allow it to be flexible
enough to be folded elastically.
An innovative stiffening system is proposed. This consists of a circular
skirt connected to the rim of the original reflector, in effect preventing
the original shell from deforming in its lowest stiffness eigenmode. A
key feature of the stiffening systemis a series of cuts and slits in the
skirt, which allow it to buckle when the reflector is being packaged, thus
reducing the stiffness and hence, enabling the reflector to be folded elastically.
A preliminary study of the effectiveness and viability of this stiffening
system, which uses extensive geometrically non-linear finite element simulations,
on a simplified 1/10th scale model is presented. These results are validated
with a series of experiments. The configurations with the greatest
potential were optimised, to minimise the packaging strains while maximising
the stiffness of the reflector. This involved hundres of variations
of the stiffening system, a procedure to automatically remesh the finite
element models was also devised. Optimized models were found to be
many times stiffer than the original structure and to have acceptable peak
packaging strains. It was also demonstrated that configurations with
circumferential slits are more effective than those with radial cuts, as
the slits are able to reduce the peak strains while the continuous skirt provides
higher deployed stiffnesses.
Once a thorough understanding of the behaviour of these small-scale models had been obtained, the effects of stiffening a 4.6 m diameter full-scale Spring-Back Reflector were investigated. Mathematical expressions for the geometry were derived to describe the complex reflector. Small-scale optimization results were used as a framework for the optimization of the full-scale reflectors, limiting the search space and also allowing for 'informed guess' starting points. The resulting optimals exceeded the expected targets and it is now feasible to design reflectors which are nearly 7 times stiffer, with peak stresses half that of the breaking strength of the material.
The ability of the stiffened Spring-Back Reflector to withstand the distortions
resulting from the maufacturing process, was examined. Firstly, a method
of replicating the residual stresses and corresponding distortions was devised
on the assumption that both stiffened and unstiffened reflectors experience
similar residual strains during the manufacturing process. It was then
demonstrated that the stiffening system reduces these distortions by approximately
one hundred times. This results in extremely good shape accuracy and
hence, the operating frequency range of the Spring-Back Reflector can potentially
be more than doubled.
In conclusion, the new stiffening system has been shown to significantly
reduce the distortions caused by the manufacturing process, thus increasing
the surface accuracy. The deployed stiffness has been increased by more
than six fold. This was accomplished by stiffening the reflector in
its deployed configuration yet with the help of slits, still allowing it
to be folded elastically, i.e. without compromising the simplicity of the
[Cambridge University | CUED | Structures Group | Geotechnical Group]