Optimal Design of Initial Surface Profile of Deployable Mesh Reflectors Via Static Modeling and Quadratic Programming

Large deployable high-frequency RF mesh reflectors are being envisioned for future space missions. This paper presents an initial study on surface shaping of such a mesh reflector. The deployable mesh reflector in consideration is modeled as a three-dimensional truss and a mathematical model considering static equilibrium of member tensions and external mounting forces is derived. Two optimization methods then are proposed to systematically determine an initial profile of the reflector. The initial profile so determined warrants that the deformed reflector surface matches the one by design and that the member tension forces fall in a specified range. The proposed mounting strategy is demonstrated on an 835-node mesh reflector.