Optimization design combined with coupled structural–electrostatic analysis for the electrostatically controlled deployable membrane reflector

• The coupled structural–electrostatic analysis procedure is introduced.
• An integrated optimization method of membrane shape accuracy and stress uniformity is proposed.
• The optimal controlling voltages are solved by a sensitivity analysis.
• The prestress is initially completely uniform and then modified by the reposition balance method.
• The coupled structural–electrostatic analysis procedure is necessary and the optimization method is efficient.

The electrostatically controlled deployable membrane reflector (ECDMR) is a promising scheme to construct large size and high precision space deployable reflector antennas. This paper presents a novel design method for the large size and small F/D ECDMR considering the coupled structure-electrostatic problem. First, the fully coupled structural–electrostatic system is described by a three field formulation, in which the structure and passive electrical field is modeled by finite element method, and the deformation of the electrostatic domain is predicted by a finite element formulation of a fictitious elastic structure. A residual formulation of the structural–electrostatic field finite element model is established and solved by Newton–Raphson method. The coupled structural–electrostatic analysis procedure is summarized. Then, with the aid of this coupled analysis procedure, an integrated optimization method of membrane shape accuracy and stress uniformity is proposed, which is divided into inner and outer iterative loops. The initial state of relatively high shape accuracy and uniform stress distribution is achieved by applying the uniform prestress on the membrane design shape and optimizing the voltages, in which the optimal voltage is computed by a sensitivity analysis. The shape accuracy is further improved by the iterative prestress modification using the reposition balance method. Finally, the results of the uncoupled and coupled methods are compared and the proposed optimization method is applied to design an ECDMR. The results validate the effectiveness of this proposed methods.