Calculation of the beam on a combined base.

The article considers the issues of calculating beams on an elastic base consisting of an upper Winkler layer that allows structural deformations and a lower layer that represents an elastic half-plane. To determine the deformations of the lower layer, the Vlasov-Kantorovich variational method was used. A special case of using the first term in the decomposition of the function of vertical displacements of points of the lower layer is considered. The change of vertical displacements along the thickness of the layer is analyzed. The beam calculation is constructed in the form of the method of initial parameters. The expression for the deflection function of the beam is obtained and its calculation for the action of the concentrated force is performed. The value of the bending moment in the middle of the beam is analyzed depending on its rigidity and the parameters of the base. It was found that he values of the moments in the calculation of the beam on the elastic half-plane are higher than in the calculation using the proposed combined model. The approximate variational Vlasov-Kantorovich method allows us to construct various computational schemes of the elastic base. The proposed combined model of the elastic base has great computational flexibility and allows to obtain solutions in a wide range of internal forces in the beam. [ABSTRACT FROM AUTHOR]