If a solar sail is to be of any use, it needs to be a rigid structure and maintain its ideal curvature and orientation, otherwise it would eventually fold-up over its center of mass like an umbrella does in a strong wind due to torque increasing radially with distance to its geometric center. Furthermore, for a solar sail to effectively translate weak momentum force of radiation pressure onto its rigid structure, it needs to be absolutely enormous, further increasing its radius, and ideally, the center of its mass would be along the axis of movement at its geometric center on a 2-dimensional plane perpendicular to the radiation source, otherwise its total torque translates into a spin.
So, this means that even though we're talking of relatively small force applied per its square area, the larger it is (to increase net force on it), the larger its radial distance towards its central axis, and the torque differential with it. So the larger it gets, the stronger its frame holding it together would have to be, which, with large area useful for any missions of reasonable length of time means, we're fast approaching limits of maximum stress loads on any materials known to man. Either that, or we're increasing its ability to cope with structural loads by adding more mass to it (reinforcing the structure), negating the point in having enormous solar sail in the first place. Thus my question.
How does one maintain flatness of a large solar sail, so it doesn't bend into a less-than-ideal concave / convex dish or fold onto itself? What kind of support structures are proposed to maintain this flatness, what are the limitations (maximum size) of such materials proposed, and could these limits be somewhat stretched by use of, say, Electroactive Polymers (EAP), e.g. Carbon Nanotubes can be used for ionic EAP that are also some of the strongest materials known to science, to maintain its flatness / ideal curvature by applying voltage to the frame?