ДОСЛІДЖЕННЯ НАПРУЖЕНОГО СТАНУ БАГАТОШАРОВОГО СЕРЕДОВИЩА, ЩО СКЛАДАЄТЬСЯ З ШАРУ І ПІВПРОСТОРУ З ЦИЛІНДРИЧНИМ ВКЛЮЧЕННЯМ

Abstract

The spatial problem of the theory of elasticity for a half-space is solved, which is rigidly connected by a free surface with an elastic layer and has a longitudinal circular infinite cylindrical inclusion. Layer, half-space and cylindrical inclusion are elastic homogeneous isotropic materials that are different from each other. The spatial problem of the theory of elasticity for a
half-space is solved, which is rigidly connected by a free surface with an elastic layer and has a longitudinal circular infinite cylindrical inclusion. Layer, halfspace and cylindrical inclusion are elastic homogeneous isotropic materials that are different from each other. The solution to the spatial problem of the theory of elasticity is obtained using the generalized Fourier
method, with respect to the Lame equations in cylindrical coordinates associated with a cylindrical inclusion and Cartesian oordinates associated with a layer and half-space. Satisfying the boundary and coupling conditions, we obtain infinite systems of linear algebraic equations that are solved by the truncation method. As a result, displacements and stresses were obtained at various points of the layer, half-space, and inclusion. A numerical analysis of the stress state of the composite body, which consists of a half-space (material - plastic), reinforced with a round steel rod, and has a protective layer of steel. The layer is ideally connected to the half-space, and the half-space is ideally connected to the elastic cylindrical inclusion. The proposed method can be used to calculate machine parts, tunnels in rocks and other spatial structures, the design schemes of which coincide with the statement of the problem of this work.