Symmetrical contact problem of a thick transversely isotropic plate

The symmetrical problem of the contact between a spherical indenter and a thick transversely isotropic plate is solved using the techniques of the Hankel transform. Solutions are written as the sums of the associated half-space solution and plate thickness effect terms. The normalized normal contact stress and the surface radial stress are obtained and calculated numerically for both composite materials and metallic substances. The example materials give both real and complex characteristic roots. A general method of calculation is described to determine the maximum tensile radial stress and the maximum compressive normal contact stress.The plate thickness effects on the contact stress and on the tensile radial stress are shown to be increasingly important with decreasing thickness. The effects that the material anisotropy has on the magnification of the contact stress and the maximum tensile radial stress are clearly revealed in the numerical results presented. The effects of material anisotropy for the composite are compared to those for the metallic substances.