Theory of Shell Structures

Shell structures form key components in a very wide range of engineering enterprise. The theory of shell structures is an old and large subject, with a huge literature. However, this book is not a compilation of results from the past. Instead, it is an attempt to bring the essence of the subject within the grasp of engineers. It tackles the fundamental question of how bending and stretching effects combine and interact in shell structures from a physical point of view; and it shows that this approach leads to an understanding of the structural mechanics of shells in general, and to useful results in particular problems. The first half of the book is concerned mainly with the basic ideas and equations of equilibrium, geometry and elasticity, and their combination in various useful ways. In particular, it includes a simple treatment of the geometry of general curved surfaces. The second half of the book first investigates the behaviour of various practical shell structures under static loading. Then there are chapters on the buckling of shells, on vibration, and on the application of plastic theory to analysis and design.

This book attempts to bring the essence of shell structures within the grasp of engineers.

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.