A deformation theory without ad hoc assumption of an axisymmetric circular cylinder

Abstract

The refined theory and the decomposed theorem of plates are converted into the refined theory and decomposed theorem of the axisymmetric circular cylinder. The refined theory provides the solutions of the axisymmetric circular cylinder without ad hoc assumptions. Expressions are obtained for all the displacements and stress components in terms of the axis displacement, and its derivatives by using Bessel’s Function and axisymmetric general solutions. On the basis of the refined theory developed in the present paper, solutions are obtained for a circular cylinder with homogeneous and non-homogenous boundary conditions, respectively. For the circular cylinder with homogeneous boundary conditions, the refined theory provides exact solutions that satisfy all of the governing equations. The exact solutions can be decomposed into two parts: the 2-orders equation and the transcendental equation. In the case of non-homogenous boundary conditions, the approximate governing equations are accurate up to the 2-order terms with respect to the radius of the circular cylinder.