Static Axisymmetric End Problems in Semi-infinite and Finite Solid Cylinders

Abstract

Our earlier technique for a semi-infinite strip (Kim and Steele, 1990) is extended to study general end problems and corner singularities for semi-infinite and finite solid cylinders with free walls. For handling general end conditions, we expand the displacement and stress in term of the Dini series which are the solutions of the cylinders with mixed wall conditions. The relation between the harmonic coefficients of the end displacement and stress is then formed, which we call the end stiffness matrix. One advantage of the end stiffness matrix approach is that the procedure for finite cylinders can be easily built up from that of semi-infinite cylinders. For some end conditions which may yield singular stresses, the nature of the singularity is investigated by the asymptotic analysis of the Dini series coefficients of the stresses. The problems studied by Benthem and Minderhoud (1972) and Robert and Keer (1987) are solved with the present approach.