Geometrical modeling of a metallic mesh deformation of the parabolic reflector

Abstract

A geometrical model of the well-known “mattress” effect, which is similar to the one observed at the opening of an umbrella, is built. The main hypothesis is that the surface of metallic mesh of a parabolic reflector takes a form closed to the minimal surface in the isotropic case. The fact that, for the orthotropic metallic mesh, the sum of the principal curvatures is farther from zero than in the isotropic case is taken into account. The model’s reliability domain is thoroughly studied. The mathematical apparatus of the model is the classical differential geometry.