High surface accuracy and pretension design for mesh antennas based on dynamic relaxation method

Abstract Cable truss structures are widely used in large satellite antennas with ultrahigh electromagnetic performance. The electromagnetic performance is directly determined by the mesh reflector's surface accuracy, which triggers research on the pretension design. In this paper, a novel pretension design method for both high surface accuracy and uniform tension distribution is proposed based on the dynamic relaxation (DR) method. In this approach, members of the cable network are regarded as string elements with 3 degrees of freedom to resist the axial tensile force, and members of the supporting truss are regarded as Euler-Bernoulli beams with 6 degrees of freedom to resist the axial and transverse forces and the bending and torsion moments. The DR method is adopted to find the static equilibrium of the whole mesh antenna, including both the cable mesh and the supporting truss. Thus, the deformation of the cables and rods and their interactive effects are fully captured. Then, to find an expected high-precision mesh surface with a uniform tension distribution, the inverse iteration algorithm (IIA) is adopted to adjust the original cable lengths of the cable network in each DR calculation cycle until the convergence criterion is met. Finally, this approach is effectively applied to the pretension design of symmetric and asymmetric mesh antennas, and the results indicate that the method is effective in obtaining both high surface accuracy and uniform tension distribution with high computational efficiency.