Investigation of Stress State of the Layered Composite with a Longitudinal Cylindrical Cavity

The article presents the study of the stress state of a two-layer composite with a cylindrical cavity located parallel to the surfaces of the layers. Displacements are set on the cavity and the upper and lower boundaries of the upper and lower layers, respectively. The three-dimensional elasticity solution has been obtained by the analytical-numerical generalized Fourier method with respect to the system of Lame equations in local cylindrical coordinates associated with cavity and Cartesian coordinates associated with boundaries of the layers. The infinite systems of linear algebraic equations resulting from satisfying the boundary conditions are solved by the reduction method. As a result, displacements and stresses have been obtained at various points of the elastic body. We have compared the stress-strain state of a two-layer structure with a cylindrical cavity located in either of the layers. The analysis included various geometrical parameters and boundary functions; the results obtained were compared with a single-layer holed structure.