Thin-walled elastic shells analysed by a Rayleigh method

Abstract

Rayleigh successfully analysed inextensional deformation of thin elastic shells by using a simple energy method. Subsequent workers seem to have been put off from using similar methods for shells which suffer extensional as well as bending deformations by the fact that the calculations get messy. In this paper we develop the kinematic relation between surface strains and changes in Gaussian curvature, and show that this is a very convenient tool for use in energy calculations. We give two examples of energy calculations for shells loaded by point forces. We find that once the energy expressions have been set up, certain analogies with simpler and already-solved problems become obvious. This leads to simple solutions. A feature of the method is that physically important quantities are not obscured, and distinct regimes of structural action are clearly delineated.