On the axially-symmetric deformations of a solid circular cylinder of finite length

Abstract

In this paper we solve the fundamental mixed problem and the second fundamental problem of the theory of elasticity for the axially symmetric deformations of a circular cylinder of finite length. Two variations of the mixed problem are solved: 1) arbitrary stresses are prescribed on the ends of the cylinder and displacements are prescribed on the lateral surface and 2) arbitrary displacements are given on the ends of the cylinder and arbitrary stresses are prescribed on the lateral surface. A particular case of the first problem is the bending of a thick circular plate whose lateral surface is rigidly clamped and which is acted upon by a laod applied over one of the end surfaces. The mixed problem for the cylinder was examined by Filon [1]; however, the boundary conditions pertaining to the tangenitial displacements on the ends of the cylinder were not satisfied. This problem was solved by an approximate method in [2].Other mixed problems concerning the elastic deformations of a finite length have been investigated in a number of papers [3, 14].