| Popis: |
A substantially spatial problem of elasticity theory for a layer with a longitudinal circular cylindrical tube solved in it is solved. The layer and tube are rigidly fixed together. It is necessary to study the stress-strain state of the elastic bodies of both the layer and tube. On the lower boundary of the layer, displacements are given; on the upper boundary of the layer and the inner surface of the tube, stresses; on the boundary of the layer and tube, conjugation conditions. The solution to the spatial problem of the theory of elasticity is obtained using the generalized Fourier method in relation to the system of Lamé's equations in the cylindrical coordinates associated with the tube, and the Cartesian coordinates associated with the boundaries of the layer. By satisfying both the boundary and conjugation conditions, we obtain infinite systems of linear algebraic equations that are solved by the truncation method. As a result, we obtain displacements and stresses at different points of both the elastic layer and elastic tube. A numerical analysis of the stress-strain state of the elastic body of the layer and tube is carried out. Graphs of the normal stresses on the inner and outer surfaces of the tube are presented. |
