The spatial contact problem for an elastic wedge with unknown contact area

Abstract

The contact problem of the indentation of an elliptic paraboloid into one side of a spatial wedge, the other side of which is free from stresses, is investigated without introducing any limitations on the remoteness of the punch from the edge of the wedge and on the aperture angle of the wedge. In the case when the punch approaches close to the edge, the method of non-linear boundary equations of the Hammerstein type is used [l, 2], which enables the normal contact pressures and the unknown contact area to be determined simultaneously. The kernel of the integral equation of the contact problem is then regularized both outside the edge and on the edge of the wedge. The solution obtained agrees well with that obtained in [3], constructed using the asymptotic “large λ” method, which is effective when the punch is sufficiently far from the edge of the wedge, when the contact area can be assumed to be an ellipse, and also with the exact solution of the corresponding contact problem for a half-space [4]. A numerical analysis of the asymmetry of the contact area, the dependence of the indenting force on the settling of the punch, and the effective stresses at the point of initial contact for different aperture angles of the wedge and two orientations of the elliptic paraboloid with respect to the edge is carried out for values of the parameters of the problem given in [5].