Introduction

In most of the chapters of this book we have assumed that the material from which a shell is constructed behaves under stress in a linear-elastic manner. The materials which are used in structural engineering generally have a linear-elastic range, but behave inelastically when a certain level of stress is exceeded. Moreover at sufficiently high temperatures irreversible creep may be the most significant phenomenon.

It is obvious that there are some circumstances in which it is necessary for the designer to understand the behaviour of shells in the inelastic range. This subject is a large one, and in this chapter we shall give an introduction to part of it.

The aim of the present chapter is to give a glimpse, mainly through a few specific examples, of the ways in which the structural analyst may tackle problems connected with inelastic behaviour of shells. In general our plan will be to set up the simplest problems which illustrate various important points. But first it is necessary to discuss some general questions in connection with the scope of plastic theory, and the circumstances in which it is valid.

Plastic theory of structures

Engineering problems involving shell structures in which plasticity of the material plays an important part may be divided roughly into three categories, as follows.

1. (i) In many shell-manufacturing processes large-scale plastic deformation over the surface enables flat plates to be deformed into panels of spherical shells, complete torispherical pressure-vessel heads, or highly convoluted expansion bellows. In all of these and similar cases the material undergoes strains well into the plastic range, and there are also large overall changes in geometry during the process of deformation.

2. […]