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Applied Optics

Applied Optics


  • Vol. 20, Iss. 11 — Jun. 1, 1981
  • pp: 1983–1989

Calculation of the elastic deformations of the revolution membranes

P. Casal, C. Fayard, and B. Authier  »View Author Affiliations

Applied Optics, Vol. 20, Issue 11, pp. 1983-1989 (1981)

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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-μm thick polyester film cut out of a sphere 4 m in diameter.

© 1981 Optical Society of America

Original Manuscript: January 12, 1981
Published: June 1, 1981

P. Casal, C. Fayard, and B. Authier, "Calculation of the elastic deformations of the revolution membranes," Appl. Opt. 20, 1983-1989 (1981)

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  1. B. Authier, L. Hill, C. Fayard, “Optical Feasibility of Thin Film Spherical Solar Collectors of Material Science Experiments in Space,” (79-202), 30th International Astronautical Congress (IAF), Munich (1979).
  2. S. Timoshenko, Résistance des matériaux (Librairie Polytechnique, Paris, 1954).
  3. J. Courbon, Résistance des matériaux, tome 1 2 ìeme id. (Dunod, Paris1964), Chap. “Des voiles minces sans flexion.”
  4. B. Carnakan, H. A. Luther, J. O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969).
  5. C. Fayard, “Etude de membranes réfléchissantes gonflables,” these de Docteur-ingénieur, Université de droit, d'économie et des sciences d'Aix-Marseille, Faculté des sciences et techniques de Saint Jérôme, Marseille (Nov.1980).

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