Working Shape Optimization Design of Cable Net Active Reflector

The main research of this paper is to determine a working paraboloid that approximates an ideal paraboloid under the adjustment constraint of the reflecting panels of the cable net, in order to obtain the best reception effect of the celestial electromagnetic waves after being reflected by the reflection panels. This paper presents an algorithm for optimal design the shape of active reflector in working state. Firstly, the main cable nodes in the working lighting area are screened, and the rotation matrix equation is established to transform the coordinates of the main cable nodes in the lighting area. Then the first optimization is carried out to optimize the proximity between the ideal parabolic and the reference sphere, and the optimal parabolic surface equation under the ideal condition of the illumination region is constructed. Finally, the optimization objective is to minimize the square sum of error of the radial distance between the working parabolic nodes and the nodes on the corresponding ideal parabolic, so that the working parabolic is as close as possible to the ideal parabolic and meets the engineering design constraints, and the second nonlinear optimization with constraints is carried out. This method can obtain the optimal expansion configuration scheme of the actuators in the working lighting area. The numerical example shows that the optimization results meet the engineering design constraints in the elastic range and are convenient for engineering implementation.