Introduction and Mathematical Preliminaries

The theory of elasticity comprises a consistent set of equations which uniquely describe the state of stress, strain and displacement at each point within an elastic deformable body. Solutions of these equations fall into the realm of applied mathematics, while applications of such solutions are of engineering interest. When elasticity is selected as the basis for an engineering solution, a rigor is accepted that distinguishes this approach from the alternatives, which are mainly based on the strength of materials with its various specialized derivatives such as the theories of rods, beams, plates and shells. The distinguishing feature between the various alternative approaches and the theory of elasticity is the pointwise description embodied in elasticity, without resort to expedients such as Navier’s hypothesis of plane sections remaining plane.