The axisymmetric contact problem of an elastic layer subjected to a tensile stress applied over a circular region

An analytical solution is presented for an axisymmetric contact problem of an elastic layer subjected to a tensile stress applied over a circular region. This mixed boundary-value problem is effectively reduced to an exact solution of an infinite system of simultaneous equations in which the normal displacement in the circular region is expressed as an appropriate series. The normal contact stress between the elastic layer and the rigid plate and the normal displacement in the circular region, as well as the stress singularity factor, are shown in curves calculated numerically. The effects of the layer thickness and Poisson's ratio on stress and displacement distributions are discussed.