The Analysis of Stress and Deformation

This book was prepared for a course in the mechanics of deformable bodies at the authors' institution, and is at a level suitable for advanced undergraduate or first-year graduate students. It differs from the traditional treatment by going more deeply into the fundamentals and giving less emphasis to the design aspects of the subject. In the first two chapters the principles of stress and strain are presented and a sufficient introduction is given to the theory of elasticity so that the student can see how exact solutions of problems can be derived, and can appreciate the nature of the approximations embodied in some commonly used simplified solutions. The third chapter is devoted to the bending of beams, and the fourth chapter treats the instability of elastic systems. Applications to axially symmetric problems, curved beams, and stress concentrations are discussed in Chapter 5; applications to torsion problems are discussed in Chapter 6; applications to problems of plates and shells are discussed in Chapter 7. Applications to problems involving viscous and plastic behavior are treated in Chapter 8, and problems of wave propagation are treated in Chapter 9. An introduction to numerical methods of solving problems is given in Chapter 10. An introduction to tensor notation by means of the equations of elasticity is given in Appendix I. Experimental methods of determining stresses by means of strain gages, brittle coatings, and photoelasticity are described in Appendices II and III. A brief introduction to variational methods is presented in Appendix IV. The material in the book is laid out so that a short course can be based on Chapters 1, 2, 3, 4, and 8 and Appendices II and III. Some of the special aspects of the subject and some of the details of the derivations are left to the problems; the assignment of homework should be made with this in mind. To indicate to the student the nature of the more advanced parts of the subject, some topics are included that would not necessarily be covered in the formal course work. The book is aimed primarily at those students who will pursue graduate work, and it is intended to give a good preparation for advanced studies in the field. It should also give a good foundation to students primarily interested in design who would cover the more applied aspects of the subject in courses on design. The authors wish to express their appreciation to those members of the California lnstitute of Technology community whose suggestions and efforts have helped to bring our lecture notes into book form