STATIC ANALYSIS OF A PLATE ON ELASTIC FOUNDATION WITH THE MODELING IN PC “LIRA” AND WITH THE CALCULATION BY VARIATIONAL-DIFFERENCE METHOD

Abstract

Static analysis of a plate on elastic foundation is made in two ways on the example of a reinforced concrete road plate 2PP30.18-30 series B3.503.1-1 intended for temporary roads. The plate are calculated on the PC «LIRA». Also the plate are calculated by the variational-difference method like a construction on linearly elastic inhomogeneous foundation (in the form of criss-crossed reinforced concrete tapes). When setting up a contact problem, hypotheses and assumptions of the theory of elasticity and structural mechanics are used. The hypotheses of the theory of bending are valid for a plate. When the deformation energy functional is compiled, the work of the forces of the intrinsic weight of the elastic foundation is not taken into account. In the contact zone, the equality of the displacements of the foundation to the deflections of the plate is valid. When calculating a layered elastic medium is replaced by a rectangular design area, which is approximated by a rectangular grid of finite dimensions. For unknowns are accepted vertical and horizontal movements of the nodes of the calculation area and reactive pressures (contact stresses) in the contact zone of the plate with the base. Based on the calculated values of nodal displacements the intensity of deformations and the intensity of stresses are identifying. When calculating in a PC «LIRA», 6 loading options are considered (central and edge). When calculating the variational-difference method, only central loading is considered. There are given the results of numerical studies in comparison to the two variants of calculations in this article.