Book contents
- Frontmatter
- Contents
- Preface
- List of symbols
- 1 Introduction
- 2 Generalised Hooke's law for an element of a shell
- 3 Cylindrical shells under symmetric loading
- 4 Purely ‘equilibrium’ solutions for shells: the membrane hypothesis
- 5 The geometry of curved surfaces
- 6 Geometry of distortion of curved surfaces
- 7 Displacements of elastic shells stressed according to the membrane hypothesis
- 8 Stretching and bending in cylindrical and nearly-cylindrical shells
- 9 Problems in the behaviour of cylindrical and nearly-cylindrical shells subjected to non-symmetric loading
- 10 Cylindrical shell roofs
- 11 Bending stresses in symmetrically-loaded shells of revolution
- 12 Flexibility of axisymmetric bellows under axial loading
- 13 Curved tubes and pipe-bends
- 14 Buckling of shells: classical analysis
- 15 Buckling of shells: non-classical analysis
- 16 The Brazier effect in the buckling of bent tubes
- 17 Vibration of cylindrical shells
- 18 Shell structures and the theory of plasticity
- Appendices
- Answers to selected problems
- References
- Index
8 - Stretching and bending in cylindrical and nearly-cylindrical shells
Published online by Cambridge University Press: 02 February 2010
- Frontmatter
- Contents
- Preface
- List of symbols
- 1 Introduction
- 2 Generalised Hooke's law for an element of a shell
- 3 Cylindrical shells under symmetric loading
- 4 Purely ‘equilibrium’ solutions for shells: the membrane hypothesis
- 5 The geometry of curved surfaces
- 6 Geometry of distortion of curved surfaces
- 7 Displacements of elastic shells stressed according to the membrane hypothesis
- 8 Stretching and bending in cylindrical and nearly-cylindrical shells
- 9 Problems in the behaviour of cylindrical and nearly-cylindrical shells subjected to non-symmetric loading
- 10 Cylindrical shell roofs
- 11 Bending stresses in symmetrically-loaded shells of revolution
- 12 Flexibility of axisymmetric bellows under axial loading
- 13 Curved tubes and pipe-bends
- 14 Buckling of shells: classical analysis
- 15 Buckling of shells: non-classical analysis
- 16 The Brazier effect in the buckling of bent tubes
- 17 Vibration of cylindrical shells
- 18 Shell structures and the theory of plasticity
- Appendices
- Answers to selected problems
- References
- Index
Summary
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.
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- Information
- Theory of Shell Structures , pp. 217 - 268Publisher: Cambridge University PressPrint publication year: 1983