Constructing Highly Accurate Inflatable Parabolic Dish Reflector Antennas and Solar Concentrators

A finite element code was written to calculate the pressure-deflected shape of a membrane surface of revolution. It was used to assess the shape quality of inflated parabolic, spherical, and ellipsoidal lenticular geometries. The code is called FAIM – finite element analyzer for Inflatable Membranes. It is a geometric nonlinear finite element code written specifically to calculate the deflection and stresses of a structurally loaded membrane. FAIM has been validated against exact analytical solutions for both small and extremely large deformations that are up to eight orders of magnitude larger compared with the starting undeflected shape. Simulations reveal that to fabricate a very accurate and precise inflated membrane mirror relative to the design parameters, one must not only accurately measure and input the moduli in both meridional and hoop directions but an accurately measured Poisson's ratio as well. For very small aperture diameters, the initial uninflated shape may be fabricated by thermo-forming the membrane. However, for aperture diameters exceeding one meter, the membrane mirror is built with discrete gores that are joined together with tapes at the seams. This provided the impetus to write a companion computer code FLATE, to calculate the gore shape using a slight modification of the solution to the inverse transformation equation to account for the presence of the seam tapes. After the gore shape is determined, the resulting final inflated shape is calculated and verified using FAIM. Sensitivity analyses can now be carried out to determine the resulting surface shape as a function of the different sources of error: gore width, gore length, perimeter attachment uncertainties, thermal effects, variation of material properties over the membrane continuum and inflation pressure changes. Of particular interest is the use of the code to guide the preliminary design of a membrane optic for the proposed SALTUS project: Single Aperture Large Telescope for Universe Studies. The SALTUS is a 14-meter class space observatory operating in the mid to far-infrared. Over its nominal 5-year mission it will fully characterize interstellar cloud chemistry as well as the formation and evolution of planetary systems like our own. The code has been shown to be more robust than equivalent commercial analytical packages in so far as membrane and cable element combinations are concerned.