Krokhmal' P. The second fundamental boundary-value problem of elasticity for a torus

An elastic toroidal body or an elastic space with a rigid toroidal inclusion. To find an exact analytical solution of the second fundamental boundary-value problem of elasticity for a torus and to investigate the problem of existence of a single-valued solution of elastostatics equations in spatial double-connected toroidal regions. The methods of investigation are the Fourier method of separation of variables, the method of using of the general solutions of the Lame equation. An exact solution of the displacement boundary-value problem of elasticity for a torus is found. An approach to construction of exact solutions of infinite systems of linear algebraic equations with banded matrices is suggested. The conditions of existence of the single-valued solutions of the elastostatics equations are found.