Formulation of axisymmetric boundary value problems of the linear theory of elasticity for canonical bodies in harmonic potentials
The paper is based on the representation of the fundamental solution of the linear elasticity theory of the mechanics of a deformable solid in the J. Dougall’s form through spatial harmonic functions. The axisymmetric problem of the elasticity theory in a cylindrical coordinate system for bodies bounded by a canonical surface is formulated. As a case, the boundary value problem of pure torsion is formulated and the elastic characteristics and structure of the corresponding external loads on the side surface of a given isotropic elastic body in the above-mentioned harmonic potentials are presented. This approach makes it possible to obtain and extend the set of exact analytical solutions of boundary value problems of the spatial elasticity theory and is the theoretical basis for calculating the strength parameters of mechanical systems.