Abstract
A numerical method is proposed to optimize the design of a space inflatable membrane reflector. The initial geometry is expressed by polynomial series weighted by a set of shape parameters. The problem is formulated as a minimization of a cost function representing the difference between the effective shape of the reflector and a perfect parabolic surface. The minimization is performed using the Nelder–Mead method or downhill simplex method. The cost function is computed at each vertex of a simplex defined in the space of optimization parameters by solving direct problem thanks to a finite element method. The finite element model handles geometrical non-linearities and takes into account phenomena like membrane wrinkling and torus buckling which may affect the reflector shape when inflated.
Highlights
The interest of using large spacecraft structures involving thin film surface has been identified since the 1950s
This study presents a design tool of a parabolic reflector made of inflatable lens supported by torus
The direct problem is solved by a non linear finite element analysis to compute the deformed shape of the structure
Summary
The interest of using large spacecraft structures (expandable or inflatable) involving thin film surface has been identified since the 1950s. The first inflatable space structures were the communication balloons of the Echo series. The larger one was a 30 m diameter balloon deployed using inflation gas. Technology developments have been made to demonstrate the potential of space inflatable structures [1,2]. In 1996 the Jet Propulsion Laboratory (JPL) performed the first experiment of deploying in space an inflatable lenticular antenna [3,4]. The structure is a 14 m parabolic reflector supported around its perimeter by an inflatable torus. The whole framework was attached to a Spartan satellite by the means of three 28 m inflatable struts (see Fig. 1). In this paper we propose a method to design optimally this kind of reflector that could be used as solar concentrator or radiometer system
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