On a method of solution of the axisymmetric contact problem of the theory of elasticity

In a paper by Korenev [1] the problem of the indentation of a general-type elastic foundation by a circular planar stamp was reduced to a pair of integral equations for a certain auxiliary function. In the case of the contact stress this problem is directly reduced in the present paper to a Fredholm integral equation of the first kind. Further, for certain types of elastic foundations, in particular a homogeneous elastic half-space, this integral equation is simply transformed into a Wiener-Hopf equation which admits an exact solution. It is shown that in certain cases the method presented allows one to obtain an exact solution of the axisymmetric contact problem, with the surface structure of the contacting bodies taken into account [2].