An approximate solution of the axisymmetric contact problem for an elastic sphere

An axisymmetric, fractionally non-linear contact problem for an elastic sphere with a priori unknown boundary of the contactarea is considered. An integral equation for determining the density of the contact pressures is constructed taking account of the shear displacements of the boundary points of the elastic body. An approximate solution, which refines the equations of Hertz' theory, is constructed in the case of a small contact area.