Analysis of surface error for orthotropic rectangular membranes in mesh reflector

Abstract The pillow effect is a common surface error in mesh antennas, resulting in a reduction of surface accuracy. Previous studies, however, have significant limitations in investigating the effect of mesh membrane materials on the pillow effect due to specific assumptions. Given this, in this paper, a clamped membrane subjected to point load is modeled firstly to obtain the deflection for the calculation of surface error, in which the weak form quadrature element method (QEM) is used to solve the model and the Foppl-von Karman membrane theory is employed to formulate the quadrature element analysis. The convergence of the method is examined, and the accuracy is demonstrated by comparing the computed deflections to ones from FEM. A weighted angle is proposed to illustrate the angle between the material directions and the principal directions of the deformed surface. By adjusting the weighted angle and material properties, the employment of orthotropic materials can significantly decrease the surface error. For example, the surface error can drop by 22.16% in rectangular membranes, and a 16.00% reduction can be achieved in triangular membranes.