TABLE OF CONTENTS We shall consider, in this chapter, the basic ideas and relationships of the theory of elasticity. The treatment is divided into three broad sections: stress, strain and stress-strain relationships. The third section is deferred until the end of the chapter to emphasize the fact that the analysis of stress and strain, for example the equations of equilibrium and compatibility, does not assume a particular stress-strain law. In other words, the relationships derived in Sections 1.1 1.14 inclusive are applicable to non-linear as well as linearly elastic bodies.
Consider the arbitrarily shaped, three-dimensional body shown in Fig. 1.1. The body is in equilibrium under the action of externally applied forces P 1, P 2, and is assumed to comprise a continuous and deformable material so that the forces are transmitted throughout its volume. It follows that at any internal point O there is a resultant force ?P. The particle of material at O subjected to the force ?P is in equilibrium so that there must be an equal but opposite force ?P (shown dotted in Fig. 1.1) acting on the particle at the same time. If we now divide the body by any plane nn containing O then these two forces ?P may be considered as being uniformly distributed over a small area ?A of each face...
