Application of the Variational Method of Homogeneous Solutions in the Axisymmetric Problem of the Theory of Elasticity for a Finite Cylinder with Regard for Its Own Weight

We use the variational method of homogeneous solutions to investigate the stress-strain state of a solid finite cylinder with regard for its own weight. The lateral surface of the cylinder is fixed and the end faces are free of loads. The general solution is represented in the form of superposition of the solutions of the problems for an inhomogeneous system of equations with homogeneous conditions imposed on the end faces of the cylinder (principal state) and a homogeneous system of equations with inhomogeneous conditions on the end faces of the cylinder (perturbed state). The problem of determination of the perturbed state is reduced to infinite systems of linear algebraic equations solved by the method of reduction. Examples of numerical realization of the solution are presented.