Shaping of rollable, singly curved, parabolic shell reflectors

A novel, rollable, singly curved, parabolic shell reflector and its nontrivial shaping method were developed. The rollable shell reflector was a monolithic thin rectangular plate with linearly varying thickness, and it was able to roll up elastically around a mandrel. A system of end moments and loads was used to shape the linearly thickness-tapered plate into a parabolic cylinder, and a mathematical model was deduced to predict the shape accuracy of the thin plate based on nonlinear beam theory. A certain parabolic cylinder reflector was analyzed by the proposed shaping method. The optimized shape accuracy agreed well with the simulation result, and it was able to meet the precision requirement. The proposed shaping method provided a promising technology for enabling a high-precision parabolic cylinder shell reflector with different apertures.