Optimal self-stress determination for high-accuracy mesh reflectors design considering the pillow distortion

Abstract

The pillow distortion is a significant barrier to the high-accuracy design of mesh reflector antennas, which is caused by the compatible deformation between the flexible cable network and the metallic mesh, manifested as the pillow-like distortion of the mesh reflecting surface. The pillow effect deviates the mesh surface from the desired paraboloidal shape leading to the surface error. Unfortunately, current researches usually neglect this effect in the mesh reflector design due to its complicated formulation. Focusing on this phenomenon, this paper proposed an optimal self-stress determination method for high-accuracy mesh reflector design. Firstly, a mechanism model of pillow distortion is proposed based on the cable-membrane constitutive models and coupling relations. The integrated equilibrium equation of the mesh reflector is established and solved by the dynamic relaxation (DR) method, which effectively analyses the influence of the pillow distortion on the mesh reflector. Then, considering the pillow distortion, a high-accuracy design method for the mesh reflector is proposed by optimising the geometrical sizes of the cable network and the metallic mesh combining the DR method with optimisation algorithm. Finally, the proposed method is effectively applied to the design of an eighteen-unit mesh reflector antenna, and the feasibility and effectiveness of the proposed method are demonstrated.