An approximate solution of the contact problem for the hard disk and plane with a circular hole without application of singular equations

Abstract

For the first time the contact problem of elasticity theory for the rigid (not deformable) disk and elastic plane with a hole was approximately solved using the method of analytic functions without the application of singular equations. It is assumed that the stress distribution in the area of contact is represented by the Fourier series. The coefficients of the series expansion of analytic functions are expressed in terms of the coefficients of the Fourier series of contact stress. At the end of the solution the Fourier series and, respectively, series of analytic functions is truncated to the lowest possible number of members. The familiar Lewin-Reshetova expression for the contact displacements was used as a boundary condition for this problem. The quadrature formula of solution allowing engineers to perform calculations of interfaces such as shaft – bush was obtained. The proposed method allows authors to develop the applied theory of wear resistance of sliding bearings taking into consideration microgeometrical parameters of their surfaces.