Design of geodesic cable net for space deployable mesh reflectors

The main purpose of this paper is to design the geodesic cable net for space deployable mesh reflectors by means of the geodesic differential equation, which is different from the traditional quasi-geodesic cable net. In order to generate the geodesic cable net, two main problems must be addressed. One is to generate the geodesics on the paraboloidal surface, and the other is to form the geodesic cable net according to the prescribed topology. Therefore, through the analysis of geodesic curvature, a general numerical method is presented to calculate the geodesics between arbitrary two points on the paraboloidal surface. Then according to the structural characteristics of mesh reflectors, a dynamic boundary adjustment method is proposed to address the second problem. The key of the method is an optimization model that adjusts the internal geodesics to form the triangular cable net by moving the end-points along the dynamic boundaries. Finally, the feasibility and effectiveness of the proposed design method of geodesic cable net are validated by three numerical examples.