| Polyimide membrane reflector is a kind of new developing antenna technique. It is coated by a layer of metallic reflective media on thin film to implement reflection of electromagnetic waves. As the applications of membrane reflector can resolve the contradiction between the load-carrying capacity of launching system and the demand of reflector antennas with large aperture, the study on forming method and shape control has become present research focus. Firstly, electrostatically figured method is introduced in this paper, and then form-finding analysis and active shape control technology of electrostatically figured membrane reflector deployable antenna are investigated. The main work can be described in details as follows:1. The mathematical model of electrostatically figured membrane reflector is found, and the mechanical model is built as well. Then the electrostatically figured theory is verified by simulation analysis.2. As the structural feature of the electrostatically figured membrane reflector deployable antenna, a form-finding method based on non-linear element method is proposed and the analysis process is illustrated in detail in this paper. The results of the numerical example give the initial shape-state of the antenna and prove the effectiveness of this form-finding method.3. The on-orbit temperature field and thermal distortion are calculated. An optimization model of active shape control is built, and an optimal method based on advance-and-retreat method and non-linear element method is proposed to solve this problem. The results of the numerical show that the optimal method proposed in this paper is effective and the electrostatically figured membrane reflector deployable antenna can correct the on-orbit shape errors using active shape control.
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