Rotating Shallow Elastic Shells of Revolution

Introduction. I n what follows, we wish to show that the problem of the rotating thin elastic shell of revolution is intriguing in the following sense. It is possible to obtain a solution by means of a linear theory which looks so reasonable that one expects the nonlinear effects to be of secondary nature. However, when one considers the problem on the basis of a nonlinear theory, one finds that nonlinear effects are not at all of a secondary nature. Moreover, while a straightforward elementary analysis of the principal aspects of the nonlinear problem is possible, a consideration of the finer structure of the problem leads to an interior-layer problem in which not only the nature but also the location of the layer has to be determined in the course of the analysis. For the sake of simplicity, our analysis is limited to the class of shells which are generally designated as shallow shells. Stresses and deformations in such shallow shells are governed by differential equations which are similar to the differential equations for finite deflections of flat plates as first obtained by von Kármán.