Shape adjustment of cable mesh antennas using sequential quadratic programming

Cable mesh structure is an important way to construct large space deployable antennas. Due to inevitable manufacturing and assembly errors and external environment disturbance, the reflector surface of cable mesh antennas has to be carefully adjusted to achieve required accuracy. This is achieved by altering the length of some cables capable of adjustment. In this paper a shape adjustment procedure based on optimization is presented. A rigorous cable element is first derived, which can treat the cable length variation and the geometric nonlinearity of cable mesh structures. Then the incremental expressions of the reflector surface displacement and the tension exerted on the rim truss are developed, and the surface error is explicitly related to the cable length variation. Finally the shape adjustment procedure is converted into a sequential quadratic programming problem which can effectively reduce the surface error and can be easily solved. A numerical example is presented to demonstrate the feasibility of the method.