Form-finding design of cable-mesh reflector antennas with minimal length configuration

Deployable cable-mesh reflector antenna is one popular kind of satellite antennas for space applications. The form-finding design of cable-mesh antennas, which aims to determine the pre-tensioned equilibrium state with a satisfactory reflector surface shape, is vital and indispensable. The tension uniformity of the cables plays an important role in maintaining the stability of the surface shape of on-orbit cable-mesh antennas. A new iterative form-finding technique based on force density method is presented to implement the uniform-tension design of cable-mesh antennas. First, equilibrium equations of the front, the rear and the whole cable nets are derived based on force density method. Then, based on the equilibrium equations, an iterative form-finding strategy is proposed. In the design process, force densities of all the cables are updated simultaneously to achieve the uniform tension of the front and rear nets, and node positions of the front net are iteratively modified to ensure that they are exactly located on the paraboloid. Finally, three typical cable-mesh antennas are employed to illustrate the feasibility and effectiveness of the method. Simulation results show that the front and rear cable nets of the obtained cable-mesh antennas are both minimal length configurations with the tension ties being inclined appropriately.