BENDING OF AN ELASTIC ENDLESS PLATE CONSIDERING THE CONTACT WITH AN ELASTIC SUBGRADE

Abstract

In recent decades, we have witnessed an extraordinary progress in tasks related to the problems of the interaction of building structures with the subsoil. The transition from low-rise buildings to high-ones, the design of more subtle structures hand in hand with the full use of building materials, places increasing demands on the methods of foundation of building objects. These tendencies might result in some problems when the issues of the interaction between the upper structure and the subsoil assume a dominant role. It concerns building constructions, industrial, water and road constructions. The problems of the interaction of the upper structure with the subsoil on which the structure is placed are primarily problems of foundation structures and foundations in general. Foundation structures are the connecting element between the superstructure and the subsoil and are supposed to transfer the load of the superstructure to the subsoil without failures. It is obvious that the knowledge of the actual foundation parameters, the appropriate choice of the foundation structure and its dimensions, the calculation of the actual stresses and deformations in the foundation gap leads to a significant economic effect. Solutions for contact tasks have undergone a long development. Winkler was a pioneer in the analysis of bending of plates on an elastic subsoil loaded with concentrated force and a moment. Later, other subsoil models came into use, too. Currently, contact tasks can be solved using FEM. The presented article deals with the bending of a plate of infinite length placed on an elastic foundation. The bending of the plate of infinite length is characterized by a differential equation, while the subsoil is characterized by the integral equation of the displacement of the edge of the half-space. Contact stresses originate at the contact between the plate and the subsoil. The contact stresses of the symmetrically loaded plate strip are assumed in the form of multiples of unknown coefficients and Legendre polynomials of the first kind. The equations have been solved using an indirect method. The effects of the individual function members of the function on the plate strip and on the subsoil are determined separately, thereafter their most suitable combination is calculated from the condition of the equal deformation on the subsoil and on the plate. The effectiveness of the presented procedure is demonstrated on a particular example.