Analysis of pillow effect for isosceles triangular membranes of mesh reflector antenna by the weak form quadrature element method

The pillow effect is a key weakening factor in the surface accuracy of mesh antennas. Previous studies, however, have significant limitations in such antennas because they have been largely based on specific assumptions, which have failed to investigate the effects of mesh membrane material characteristics on the pillow effect. Thus, in this study, static analysis of a triangular membrane was performed using the weak form quadrature element method to explore the effects of material parameters in various directions on the pillow effect in polar coordinates. Because of its lack of central symmetry, the strain–displacement relations from Föppl–von Kármán membrane theory in polar coordinates were improved for calculations in triangular membranes. In polar coordinates, the triangular membrane domain was mapped into one sector for the discretion of integrals using bilinear interpolation. The convergence of the method results was examined, and the accuracy was demonstrated by comparing the computed deflections to those from the finite element method. Based on the present method, the effects of material properties on the pillow effect in different sections of a triangular membrane were examined, as was the influence of the shape of an isosceles triangle.