Introduction

The ideas and equations which we have developed in chapter 8 provide tools for the solution of a wide range of practical problems. The aim of the present chapter is to give examples of some of these applications. The order follows roughly that of chapter 8.

The first example is concerned with a cylindrical tube which is partly full of a heavy fluid and acts as a beam between supports at its ends. We shall be able to make direct use of results from chapter 8 in determining the stresses and displacements in the shell, and we shall find that the pattern of behaviour depends strongly on the value of a certain dimensionless group Ω (to be defined in (9.9)) which involves the length, radius and thickness of the shell.

The next group of examples involves the response of a cylindrical shell to forces applied at one end while the other end is supported in various different ways which are met in engineering applications. The applied forces all vary periodically in the circumferential direction. The solutions will involve mainly the ‘long-wave’ behaviour of the shell, and it is advantageous to begin by setting out some standard ‘beam-on-elastic-foundation’ results which will be useful in the subsequent work. The last example in this group concerns the response of a cylindrical shell to a radial point load.

The final problem to be considered in this chapter is the response of a spherical shell to a radial point load: this may be discussed in terms of a ‘nearly-cylindrical’ shell.