For liquid crystal elastomers in the thin film limit, an interplay of material and structural non-linearities is observed. These membranes can display fine-scale features both due to wrinkling that one expects in thin elastic membranes and oscillations of the local optical axis that one expects in elastic liquid crystals. In this talk we present an energy-minimization approach based on relaxation and Gamma-convergence to describe the effective energy density of thin membranes of liquid crystal elastomers by providing a detailed characterization of the fine-scale features. Importantly, we show existence of a regime where one has shear strain but no shear stress and all the fine-scale features are in-plane with no wrinkling. This may act as a mechanism preventing formation of wrinkles in membranes under complex boundary conditions. Based on this feature, current work is being carried on on the design of wrinkle-free inflatable reflectors and mirrors with potential applications in satellites and space probes.