Axisymmetric Problem for an Elastic Cylinder of Finite Length with Fixed Lateral Surface with Regard for its Weight

Abstract

We consider an elastic cylinder with regard for its weight. The conditions of sliding fixing are imposed on the lower base of the cylinder, its upper base is subjected to the action of an axisymmetric normal load, and the lateral surface is fixed. The Hankel integral transform is used to reduce the problem to an integral equation of the first kind for normal stresses acting on the fixed cylindrical surface. After finding the singularities of the unknown function, the solution of the integral equation is sought in the form of a series in Jacobi polynomials. The results of numerical evaluation of the normal stresses on the fixed surface of the cylinder are obtained both with regard for its weight and by neglecting its weight.