A Generalized Analysis of Conically Bent Plates by Large-Deflection Theory

Abstract

This paper presents a general method of solution for the problem which concerns bending plates into cones. The plates considered are those whose thickness obeys the power-law. The large-deflection theory of von Kármán for plates is employed and the distortion of the cross-section of the bent plate is obtained in terms of generalized hypergeometric functions. Numerical examples are given and results are presented in graphic form. It is shown that by tapering the plate according to a negative power-law, the cross-sectional distortions can be reduced considerably. Also discussed is an analogy between the anticlastic deformation of a plate bent into a cone and the lateral deflection of a conical shell subjected to normal pressure.