Analysis of the effect of bending rigidity on Gaussian Curvature for clamped and simply supported thin circular plates

Abstract

Abstract Negative Gaussian curvature in deformed surface subjected to concentrated loads is a key weakening factor on the surface accuracy of umbrella antennas. The negative impacts can be mitigated by increasing the bending rigidity of the reflector surface. Thus, firstly, this paper is concerned with the effect of bending rigidity on Gaussian curvature based on the analysis of bending circular thin plate with large deflection. Exact expressions of Gaussian curvature for deformed circular thin plates are derived using the analytical solution of the von-Karman plate equation and the properties of positive and negative for Gaussian curvature is investigated. After solving the zeroes of Gaussian curvature using the Newton iteration method, Gaussian curvature distribution of the deformed surface is obtained.