Eigenvalue Analysis for a Frictional Punch Problem of Concave Notch

A numerical solution for the eigenvalue in a frictional punch problem is presented, 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 δ is assumed within the range – 0.3 ⩾ 6 ⩾ 0,3. The notch angle β between two edges is varying within the range π ⩾ β ⩾ 2π. The target function method is used to evaluate the eigenvalue λ1 in the stress expression σij ≈ O(1/rλ1). Finally, the obtained eigenvalues are expressed in the form of λ1 = s(δ, β). The pressure under punch and the stresses at the corner points are singular in general.