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Approximated Calculation of the Kirchhoff Plate Resting on the Vlasov Foundation with Selected Boundary Conditions

Abstract The paper presents the problem of bending of the Kirchhoff plate resting freely on the elastic Vlasov subsoil with additional external load g to the subsoil applied near the transverse edge of the plate. The presented example is a special case of a plate resting freely on an elastic subsoil, it is common in construction industry. It was considered approximately, how an additional soil load g applied along the y-axis affects the deflection of a plate resting freely on the Vlasov foundation. Deflection diagrams of the plate and the surface of the elastic foundation outside the plate boundaries have been obtained. The diagrams of deflection of the plate middle surface and the displacements of the soil surface beyond the plate boundaries (in the transverse and longitudinal directions, taking into account the additional load g beyond the plate boundary) depending on the distance in the x-axis direction of this load were calculated.