Geometrical modeling of parabolic reflector's metallic mesh deformation

This article shows construction of a geometrical model of a well-known 'mattress effect', it is similar to that observed while opening an umbrella. The main hypothesis is: the surface of metallic mesh of parabolic reflector — in an isotropic case — takes a shape close to a minimal surface. We have taken into account the fact that for the orthotropic metalic mesh the sum of principal curvatures is farther from zero than in the isotropic case. The area of model's reliability has been studied in detail. Mathematical apparatus of the model is the classical differential geometry.