Form-finding and shape adjustment of cable-membrane reflectors

Abstract

Cable-membrane reflector is a highly nonlinear flexible structure, which can represent a specific surface shape under the proper combination of cable tension and membrane stress. AstroMesh reflector is a representative of cable membrane reflector, which has advantages of large aperture, easy folding, and light weight, and is increasingly utilized in space antenna reflectors. In this paper, a finite element model of the cable-membrane structure is established together with the corresponding incremental equilibrium equation which provides the sensitivity of the nodal position with respect to the geometric parameter of the cables and triangular membranes. A form-finding strategy is detailed, which aims at a configuration with the reflector nodes locating on a specified paraboloid while all cables and membranes are tensioned uniformly as possible. In addition, the surface precision of the reflector is reduced due to the inevitable errors in the manufacturing process. Therefore, the tension ties in the cable network is designed to be adjustable to solve this problem. Carefully changing the length of these cables can increase the reflector surface precision, which is referred as shape adjustment. An adjustment strategy with model updating is proposed. The model updating using the measured positions of the reflector nodes can dramatically reduce the discrepancy of the finite element model with respect to the actual reflector, thus remarkably improving the efficiency of shape adjustment. Numerical example and physical experiment demonstrate the effectiveness of the proposed method.