Thermal Load Effects on Precision Membranes

The potential for placing large, ultralightweight precision re ectors in space is currently being investigated throughuseofmembranestructures. Their capacityfor reducing launchmassand stowedvolumeis being exploited. However, on-orbit performance will require an understanding of the effects of thermal loads on re ector surface precision. Thermal load effects cut both ways, and selective heating of the re ector may someday be used to effect desirable changes in the surface proŽ le. Both theoretical and experimental analyses are provided of an in atedmembrane re ector with a thermal load acting on its surface. A goalwas to compare temperature-induced changes in shape with the results obtained for enforced boundary displacements along the entire rim, which has previously been shown to be an effective control strategy. The Hencky/Campbell problem is solved numerically (Hencky, H., “Uber den Spannungszustand in Kreisrunde Platten,” Z. Mathematics and Physics, Vol. 63, 1915, pp. 311–317; Campbell, J. D., “On the Theory of Initially Tensioned Circular Membranes Subjected to Uniform Pressure,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 9, 1956, pp. 84–93), but with a thermal strain imposed.Thenonlinear Ž nite element codeABAQUS is then used for comparison.Themodel was studied for different temperature proŽ les, varying both in temperature magnitude and spatial extent. Finally, a preliminary experiment is performed, using infrared thermography to measure the membrane surface temperature, and these results are compared to the theoretical models.