Cylindrical shells under symmetric loading

Abstract

Introduction The subject of this chapter is the behaviour of thin elastic circular cylindrical shells when they are loaded by forces which are symmetrical about the axis of the cylinder. Cylindrical shells have structural applications in many fields of engineering, and the loading is often symmetrical, especially in pressure-vessel applications. Some of the results of this chapter will be directly useful and applicable in design. The behaviour of cylindrical shells when they are loaded by non-symmetric forces will be discussed later, particularly in chapters 8 and 9. The main reason for the inclusion of the present topic early in the book is that it is uniquely instructive . Although it is obviously a particularly simple problem on account of the symmetry, it does nevertheless illustrate well some basic features of the behaviour of shell structures which reappear repeatedly, as we shall see, in much more complicated problems later in the book. In particular we shall be able to see clearly how the shell mobilises both stretching and bending effects in order to carry the applied loading. The problem will also illustrate how the choice of suitable dimensionless groups enables us to present useful results in the most economical way. Lastly we note that the symmetrically-loaded cylindrical shell provides a good introduction to the behaviour of symmetrically-loaded general shells of revolution, which will be discussed in chapter 11. Our first problem (section 3.4) is the simplest of all: a semi-infinite shell which is loaded either by uniformly distributed radial shearing force or bending moment at its edge, as shown in fig. 3.1.