Contact problem for a plane containing a slit of variable width : PMM vol. 38, n 6, 1974, pp. 1084–1089

The problem of compression of an elastic plane with a slit of variable width commensurate to the elastic strains is considered. The case of the origination of several contact sections of the slit edges is investigated. Adhesion of the edges hence occurs at some part of the contact area, while slip is possible at the rest of this area. A solution of the problem is obtained in quadratures by the Muskhelishvili method using the apparatus of linear conjugates of analytic functions. The stress and displacement potentials are found, the magnitudes of the contact sections and the adhesion zones are determined. A specific example is analyzed and numerical computations are carried out.The contact problem for a plane weakened by a constant-width rectilinear slit has been considered in 1 – 3].