Axisymmetrical boundary-value problems of elasticity theory for finite-length cylinders and cones

摘要

The axisymmetrical boundary-value problems of elasticity theory for finite-length cylinders and cones are presented. It should be noted that the construction of exact solutions is based on the fact that the boundary conditions are homogeneous on the variable on which the integral transform is performed. The integral transform can be applied in the case when the boundary conditions are inhomogeneous in the initial boundary-value problem. The inversion formulas are presented by conditionally convergent series, and the operations with them can be carried out only after improving their convergence. The formulated problem is reduced to the one-dimensional boundary-value problem. The particular solutions of the inhomogeneous equations should be constructed after the integral transforms.