On the contact of a rigid sphere and a plate S.K. Lucas, * P.G. Howlett † and J.M. Thredgold ‡ Centre for Industrial and Applied Mathematics, School of Mathematics and Statistics, University of South Australia, Mawson Lakes SA 5095, AUSTRALIA May, 2004 Abstract We consider the problem of the contact between a rigid sphere and a thin initially flat plate. After reviewing some plate theory, we establish that a defor- mation where a finite piece of the plate takes the shape of the sphere is physically unrealisable, and that the contact region must be a ring. However, for small de- flections using classical theory and looking at some typical parameter values, we find that the radius of the ring is so small that for practical purposes it should be considered as a point load. We also outline the case for large deflections. Keywords: thin plate, contact, deformation, ring load. 1 Introduction At the February 2000 meeting of the Mathematics in Industry Study Group (MISG) in Adelaide, South Australia, one of the problems presented involved a lens fracture test, where a spectacle lens is put under an applied load through a spherical indentor made of steel (see Lucas & Hill [1]). If the lens deflects too far, or breaks, then it fails the test. The purpose of this paper is to outline some results obtained for the idealised problem of contact between a rigid sphere and a thin flat plate. * To receive correspondence, Email: s.lucas@unisa.edu.au, Fax +61 8 83025785 † Email: p.howlett@unisa.edu.au, Fax +61 8 83025785 ‡ Email: jane.thredgold@postgrads.unisa.edu.au 1