Calculation of the elastic deformations of the revolution membranes.

Several applications, both on the ground and in space, are envisaged for large, light parabolic reflectors which are compact when folded. In this paper the aim is to calculate by a differential method the deformed meridian line and the creased zone of an elastic inflatable revolution membrane. Conversely, one can calculate the original meridian line which, under a given pressure, transforms into a selected meridian line, in this case parabolic. The theory is confirmed by the deformation measurements of a cap in 36-microm thick polyester film cut out of a sphere 4 m in diameter.