Inverse problem for shape control of flexible space reflectors using distributed solar pressure

This paper investigates controlled elastic deflection of thin circular space reflectors using an inverse problem approach to non-linear thin membrane theory. When changing the surface reflectivity across the membrane, the distributed loads due to ambient solar radiation pressure can be manipulated optically, thus controlling the surface shape without using mechanical or piezo-electric systems. The surface reflectivity can in principle be modulated using uniformly distributed thin-film electro-chromic coatings. We present an analytic solution to the inverse problem of finding the necessary reflectivity distribution that creates a specific membrane deflection, for example that of a parabolic reflector. Importantly, the reflectivity distribution across the surface is found to be independent of membrane size, thickness and solar distance, enabling engineering of the reflectivity distribution directly during the manufacture of the membrane.