Stress Analysis of a Circular Cylinder with a Spherical Inclusion under Tension

Abstract

This paper presents an analytical solution for an infinite circular cylinder having a spherical inclusion when the cylinder is subjected to tension at infinity. In this analysis, two types of inclusions, i.e., a perfectly bonded inclusion (displacements and tractions are continuous) and a slipping inclusion (tractions and normal displacements are continuous and shear traction vanishes) are discussed. The solution is based on the Dougall's displacement potentials approach and is deduced through making use of simple forms of spherical and cylindrical harmonics. The boundary conditions on the cylinder at infinity and around the inclusion are fully satisfied with the aid of the relationships between the spherical and cylindrical harmonics. The solution is represented in the form of graphs and the effects of the inclusions on the stress distribution are clarified. From the analyzed results, it is found that the stresses around the inclusion are considerably affected by the interface conditions.