Axisymmetric problem for a finite length elastic cylinder with a fixed lateral surface with allowance for its self-weight (Q2808378)

The authors study an elastic cylinder with allowance for its self-weight. Sliding restraint conditions are given on the cylinder bottom base, normal axisymmetric loading is applied to the cylinder upper base and its lateral surface is fixed. By means of the integral Hankel transform the problem is reduced to a first kind integral equation with respect to normal stresses on the fixed cylindrical surface. After singularities of the unknown function are found, the solution of the integral equation is expressed in the form of a series in terms of Jacobi polynomials. Results of normal stress calculations for the fixed surface are obtained with and without allowance for the cylinder self-weight.