Initial shape optimization for ECDMA based on coupled structural-electrostatic theory

The electrostatically controlled deployable membrane antenna (ECDMA) is a promising structure with many outstanding advantages, such as low surface density, large aperture and high surface precision. However, it is a huge challenge to describe the coupled structural-electrostatic filed between the membrane and electrode accurately. This paper applied nonlinear finite element method and the virtual work principles to obtain the coupled structural-electrostatic field governing equilibrium equations. Then the coupled model, a 5m diameter, f/2, curved membrane antenna finite element model was built in which the electrostatic force changed when the membrane deflection occurred. We simulated with this model, compared to the previous model using the parallel capacitor relationship and got some interesting conclusions: 1) the parallel capacitor relationship is not applicable when the membrane deflection and the gap are in the same order of magnitude; 2) the coupled structural-electrostatic field governing equation can be a enjoyable replacement of the parallel capacitor equation. Finally, based on the coupled model, we optimized the initial shape of the membrane and acquired a high precision membrane surface.