DETERMINATION OF THE BOUNDARY CONDITIONS OF THE STRESS FUNCTION WITH UNKNOWN COEFFICIENTS OF AN ELASTIC HALF-PLANE WITH CIRCULAR CAVITIES

Abstract

In this paper, discusses the solution of the first fundamental boundary value problem for an elastic half-space with a circular space.In the article, the definition of an analytical function with an unknown coefficient given in the inner contour is not related to the separations by the contour variable of the boundary condition, but to a system of infinite linear algebraic equations obtained in the process of orthogonalization of this boundary condition.The coefficients of a system of algebraic equations are expressed in terms of integrals along a circular contour, that is, it is obtained from comparing the coefficients of the same overhead forces satisfying the contour conditions.In order for the resulting infinite system of algebraic linear equations to have a solution, they must be regular.The rapid attenuation (approaching zero) of the coefficients that make up the system of algebraic linear equations as a result of the calculations carried out confirms this condition.The problem under consideration is a special case of the classical Bussinex problem. The coefficients of the system of algebraic equations are expressed by integrals over a circular contour.