Axisymmetric Contact Problem for a Half Space with Nonspecified Zones of Interaction

We propose a numerical algorithm for solving the axisymmetric problem of the theory of elasticity on the interaction of an elastic half space with a rigid punch whose surface has a complex shape. Under the action of this punch, contact occurs in certain isolated zones unknown in advance. The contact problem is formulated in the form of the Signorini integral equations/inequalities transformed into a system of linear algebraic equations/inequalities by using quadrature formulas for singular integrals. The solution of this system is reduced to finding the minimum of a quadratic form under linear constraints for the unknown contact pressure. By using the developed algorithm, we investigate the axisymmetric problem of interaction of an elastic half space with paraboloidal punch with a shallow notch or a system of notches.