Analytical Solution to Transversely Isotropic Hollow Cylinder under Axisymmetric Surface Loading Using Variational Principle

Abstract

The behavior of axisymmetric cylinders under various surface loading has remained the topic of research for many years. Most of the solutions presented in the literature are load-specific. Therefore a general solution is sought to satisfy any boundary conditions prescribed on any surface. This paper presents a general solution to satisfy a wide combination of boundary conditions prescribed on the curved as well as on the flat ends of a cylinder. A hollow cylinder was considered, composed of transversely isotropic material. The formulation is based on the variational principle, resulting in a set of coupled governing equations and associated boundary conditions. The solutions to the coupled governing partial differential equations are obtained by systematically decoupling them, followed by the method of separation of variables and the Frobenius method. All the boundary conditions are satisfied by making use of either the Fourier or the Fourier–Bessel transformation. The solutions for various test cases were validated by comparing them against three-dimensional solutions obtained using finite-element analysis. The solution for the solid cylinder was obtained by considering the limiting case of the internal radius approaching Zero.