The solution of the problem of elasticity theory for a half-space with a longitudinal cylindrical pipe andan elastic layer linked to the half-space, with displacements given on the boundary surfaces

Abstract

A solution to the spatial problem of the theory of elasticity is proposed for a composite in the form of a half-space with a longitudinal thick-walled circular cylindrical tube and a layer rigidly attached to the surface of the halfspace. Layer, half-space and pipe elastic homogeneous isotropic materials different from each other. On the free surface of the layer and the inner surface of the pipe, displacements are specified. At the boundary of the layer and half-space, as well as at the boundary of half-space and the outer surface of the pipe, the matching conditions are coupling. It is necessary to evaluate the stress state of the multilayer medium. The solution of the spatial problem of the theory of elasticity is obtained on the basis of the generalized Fourier method in cylindrical coordinates associated with the pipe and Cartesian coordinates associated with the layer and half-space. Satisfying the boundary and conjugation coupling, we obtain infinite systems of linear algebraic equations that are solved by the reduction method. As a result, displacements and stresses were obtained at various points of the layer, half-space, and.