ANALYSIS ON SHAPE ACCURACY ADJUSTMENT OF AN ACTIVE CABLE-MESH REFLECTOR

The linear incremental relationship between the end force and the end displacement of a cable is deduced based on the analytical catenary in order to construct a rigorous mechanical model for cable-mesh structures. The error distribution vector is introduced to represent the distribution of the shape error with respect to the design paraboloid, thus the direction and magnitude of the divergence of each node on the surface from its ideal position can be reflected. A shape adjustment algorithm is presented in which the position of the vertex of the design paraboloid and the displacement of the nodes out of the illuminated area are optimized. The optimization algorithm guarantees both the shape accuracy within the illuminated area and the minimal work during the adjustment. The numerical example shows that the method proposed achieves a good convergence.