CONTACT PROBLEM FOR A RECTANGULAR PLATE ON ELASTIC SEEDING IN POLAR COORDINATES

Abstract

In this paper, the problem of calculating a rectangular plate on an elastic base in polar coordinates by the Zhemochkin method is considered for the first time. Such problems arise, for example, when metal columns of circular cross-section are supported on rectangular bases lying on a concrete base. When solving this problem, several types of Zhemochkin plots in polar form were used. The Saint-Venant principle was widely used to determine the displacements of the elastic base from a single force distributed over a complex-shaped Zhemochkin section. Two examples are considered: a square plate on an elastic base and a rectangular plate also on an elastic base. In the last example, along with the Zhemochkin sections, rectangular sections were used in polar coordinates. Numerical results are obtained showing the phenomenon of decreasing contact stresses in places near the corners of the plate.