CONTACT OF ISOTROPIC SQUARE PLATES WITH RIGID SPHERICAL INDENTORS

The contact problem of an isotropic square plate indented by a rigid spherical indentor was studied. Employing an exact solution method with a simple discretization technique, the numerical sensitivity due to the ill-posed nature of the problem was precluded by enhancing the numerical procedure with a least square technique. For small indentations, the results were compared with the published solutions for a circular plate and good agreement was obtained. Depending upon the size of contact, the contact area was found to be either a circle or a hypotrocoid of four lobes featuring a shorter length of contact along the through-the-corner directions of the plate. The range of applicability of Hertz's theory was found to be limited to very small indentations. The distributions of the contact stresses over the plane of the plate were presented to illustrate the difference of contact behavior between a square plate and a circular plate. The load-indentor displacement relation was presented which showed that a square plate was stiffer than a circular plate under indentation.