Extension of a Piecewise Uniform Composite Rod

Abstract

An exact analytical solution is obtained for the extension problem in the case of an infinitely long continuous round cylinder attached to an external hollow round cylinder. This mechanical system is considered as a composite rod whose components are made of elastic materials with different mechanical characteristics. The method of solving this problem is based on the approach proposed by the author of this paper to solve the plane stress state problem in a spatial formulation, which allows one to integrate the equilibrium equations in finite form. The distribution of displacements and stresses in the rod is discussed.