Finite solid circular cylinders subjected to arbitrary surface load. Part I - Analytic solution

This paper presents a general framework for obtaining analytic solutions for finite elastic isotropic solid cylinders subjected to arbitrary surface load. The method of solution uses the displacement function approach to uncouple the equations of equilibrium. The most general solution forms for the two displacement functions for solid cylinders are proposed in terms of infinite series, with z- and θ-dependencies in terms of trigonometric and hyperbolic functions, and with r-dependency in terms of Bessel and modified Bessel functions of the first kind of fractional order. All possible combinations of odd and even dependencies of θ and z are included; and the curved boundary loads are expanded into double Fourier Series expansion, while the end boundary loads are expanded into Fourier-Bessel expansion. It is showed analytically that only one set of the end boundary conditions needs to be satisfied. A system of simultaneous equations for the unknown constants is given independent of the type of the boundary loads. This new approach provides the most general theory for the stress analysis of elastic isotropic solid circular cylinders of finite length. Application of the present solution to the stress analysis for the double-punch test is presented in Part II of this study.