Introduction

In chapter 3 we studied the way in which stretching and bending effects combine to carry axially symmetric loads applied to a uniform elastic cylindrical shell. In chapter 4 we investigated the way in which applied loads of a more general kind are carried by in-plane stress resultants alone, according to the membrane hypothesis. It became clear when we examined the resulting deflections of the shells in chapter 7 that this hypothesis is untenable in certain circumstances, and that indeed, in such cases the bending effects, explicitly neglected in the membrane hypothesis, might well sustain a major portion of the applied loading.

We have reached the point, therefore, where we must consider the more general problem of a shell which is capable of carrying the loads applied to it by a combination of bending and stretching effects. This is our task in the present chapter.

An important idea which we shall develop is that it is advantageous to regard the shell as consisting of two distinct surfaces which are so arranged to sustain the ‘stretching’ and ‘bending’ stress resultants, respectively; and indeed, the chapter as a whole explores various consequences which flow directly and indirectly from this idea.

In section 8.2 we introduce the ‘two-surface’ idea to the equilibrium equations, and show that we may treat the two surfaces separately provided we introduce appropriate force-interactions between them. The ‘stretching surface’ is identical to a shell analysed according to the membrane hypothesis, and we may therefore use directly the work of chapters 4–7 for this part.