Compression of an elastic roller between two rigid plates

A closed solution - exact within two-dimensional linear elastostatics - is deduced for the problem appropriate to the compression of an elastic circular cylinder between two smooth, flat and parallel, rigid plates. The boundary displacements obtained for the cylinder involve elliptic integrals, whereas its stress field is given in terms of elementary functions exclusively. The results found for the distribution of the contact pressure and for the width of the contact zone are compared with the corresponding predictions of Hertz's approximate theory, for which elementary corrections are determined by asymptotic means. Analogous corrections are established for a previously available approximate estimate of the diametral compression undergone by the roller, which remains indeterminate in the Hertz treatment of this two-dimensional contact problem.