Eigenvalue analysis for a frictional punch problem of concave notch

A numerical solution for the eigenvalue in a frictional punch problem is One edge of a concave notch is assumed to be traction free, 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 delta is assumed within the range - 0.3 <= delta <= 0.3. The notch angle beta between two edges is varying within the range pi <= beta <= 2 pi . The target function method is used to evaluate the eigenvalue lambda, in the stress expression sigma(ij) approximate to O(1/r(lambda 1)). Finally, the obtained eigenvalues are expressed in the form of lambda(1), = s(delta,beta) . The pressure under punch and the stresses at the corner points are singular in general.