Axisymmetric solution of the end-problem for a semi-infinite elastic circular cylinder and its application to joined dissimilar cylinders under uniform tension

Using transform methods, axisymmetric end-problem for a semi-infinite elastic circular cylinder is reduced to a system of singular integral equations. The kernels of the integral equations are found to contain Cauchy as well as generalized Cauchy-type singularities. The dominant part of the equations is separated and analyzed to determine the index of the singularity for differing boundary conditions at the end. An approximate method is used to obtain a system of simultaneous algebraic equations from the system of singular integral equations. As an application, axisymmetric solution for joined dissimilar elastic semi-infinite cylinders under uniform tension is solved and various physical quantities of interest, such as normal and shear stresses at the interface, are obtained.