Eigenvalue analysis for a frictional punch problem of a concave notch with a fixed edge

Abstract

A numerical solution for the eigenvalue in a frictional punch problem is presented. One edge of a concave notch is assumed to be fixed, and the other edge is in contact with the frictional punch (Fig. 1). In addition to the normal pressure, the friction force is also applied along the contact edge of punch. The friction coefficient is assumed within the range (−0.3, 0.3). The notch angle between two edges is varying within the range 180 to 360 degrees. The target function method is used to evaluate the eigenvalue which is an exponent in the stress expression near the crack tip. Finally, the obtained eigenvalues are expressed in the form of a function of the friction coefficient and the angle of the concave notch. The pressure under the punch and the stresses at the corner points are singular, in general.