A Cauchy system in the linear theory of thin shells of revolution

Abstract

The differential equations of the linear theory of thin shells of revolution as derived by A. Kalnins in terms of eight fundamental state variables from the Reissner-Meissner equations, and subject to appropriate boundary conditions, are reduced to a system of integro-differential equations of the Riccati type subject to initial conditions. The reduction is meaningful on theoretical grounds since it offers an alternative description of a boundary value problem in terms of a Cauchy system, and valuable from a numerical point of view. on account of the inherent stability of the resulting sequential algorithms. A discussion on rigorous and computational aspects closes the presentation.