On a Contact Problem of an Elastic Half-Plane with a Circular Hole : 2nd Report, The Case of Frictionless Contact

Abstract

An analytical solution is presented for the stresses produced by the indentation of the straight boundary of a semi-infinite elastic plate with a circular hole by a flat-ended rigid stamp. It is supposed that the stamp is placed on the segment of the straight boundary, just above the hole, and pressed into the plate by a given force, perpendicular to the boundary, and that the coefficient of friction between the stamp and the plate is zero. The complex potentials, which have poles at the center of the hole and disturb the boundary conditions neither along the straight edge nor at the infinity, are added to the solution of the contact problem of a half-plane without hole and the parametric coefficients included in the complex potentials are then determined, so that the conditions at the rim of the hole may be satisfied. Numerical results obtained are shown in graphs and compared with those available.