Optimal dimensioning of inflatable antennas.
BOUZIDI, R.
Nantes University

The performances of the parabolic reflectors are directly related to the size and the shape quality of their reflective surface. The rigid large reflectors, used in the space applications, are penalized by their areal mass and space available in the launchers. The inflatable structures have a range of well-known advantages: lightness, reduced folded volume when launching, etc. The inflatable antennas are an emblematic application because of the sizes which they can reach. Nevertheless these structures have a disadvantage enough penalizing them: The evolution of the unloaded initial shape to the inflated one induces a significant change of their geometry. It becomes difficult to imagine, by solving the direct problem, an acceptable initial form. It is then advantageous to optimize the initial form so that once deployed, the structure approaches a parabolic profile as well as possible. The answer can be established by the formulation of the inverse problem: what it must-being the initial shape of the inflatable antenna so that it reaches a quasi-perfect parabolic surface after inflation?

This study describes the numerical tools used to solve the inverse problem. The studied structure is a lenticular inflatable antenna surrounded by an inflatable torus. Optimization is carried out at the same time on the geometrical, mechanical, and of loading parameters. The geometrical ones relate to the initial shape of the lens represented by a polynomial series, and the small radius of the surrounding torus. The mechanical parameters are the Young modulus, the Poisson's ratio and the thickness of the membrane. The loading parameters are the pressures in the lens and in the torus. The cost function to be minimized is the Root Square Mean Error (RSME) of the deployed surface compared with the perfect parabola. The results obtained prove that the tools thus developed are an interesting means and useful for the optimal dimensioning inflatable antennas.