Axisymmetric Problem of the Theory of Elasticity for a Hollow Cylinder of Finite Length with Regard for Its Weight

Abstract

We consider a hollow elastic cylinder of finite length subjected to the action of its own weight and an axisymmetric normal load applied to the upper base. The lower base of the cylinder is immovably fixed. The inner cylindrical surface is under the conditions of sliding restraint and its outer surface is immovably fixed. The problem is reduced to an integral equation of the first kind for normal stresses on the fixed lateral surface. We determine the character of singularity of the required function and propose an efficient algorithm for the solution of the obtained equation based on the expansion of the required function in a series in Jacobi polynomials. We present the results of calculations of normal stresses on the lateral surfaces of the cylinder, which show that, in the case of rigid fixing, the influence of the weight of the cylinder is much weaker than in the case of sliding restraint.