### Surface adjustment method of deployable cable antenna based on steepest descent algorithm

LIU Xiao1, WU Minger1,* , ZHANG Huazhen2

1. 1. Department of Structural Engineering, Tongji University, Shanghai 200092, China
2. Shanghai YS Information Technology Co.,Ltd., Shanghai 200240, China
• Received:2017-10-10 Revised:2018-02-09 Accepted:2018-03-06 Online:2018-06-25 Published:2018-03-06

Abstract:

Considering the geometric nonlinearity of cable structures and the high-degree coupling of nodal displacements, a reasonable optimization method is essential in order to improve the surface adjustment efficiency of cable antenna. The equilibrium matrix and flexibility matrix of double-layer cable-net structures were partitioned based on the topology. The gradient formula of surface error to the tensile forces of tension ties was derived in derivative form. The infinite norm of surface error gradient was used to determine the element of tension ties which has the most significant effect on the surface error. Based on the steepest descent algorithm, the negative gradient direction of surface error was chosen as the optimizing path. The surface error due to the length tolerances of cable elements is decreased by adjusting the tensile forces of tension ties. The double-layer cable-net model of AstroMesh antenna was established and some numerical surface adjustment experiments were carried out. Results indicate that the surface error after adjusting approaches zero.