Solutions for Some Problems of Elasticity Theory

Abstract

In this chapter we present solutions of a few concrete problems of the theory of elasticity using the semi-inverse method. All problems have practical application in engineering. We illustrate the type of problems that can be solved by the “classical” methods of the previous chapter. Also, we write some solutions in a form that allows comparison with the solutions obtained by elementary strength of materials and rod theories. Since in engineering applications the rod is, probably, one of the most often used elements, we treat, in detail, important problems of extension, torsion, and bending formulated for an elastic rod. These problems (determination of the stress strain and deformation state of a prismatic rod loaded by a system of forces and couples applied at the ends of the rod) are called the Saint-Venant problems.