On the Contact Problem for a Wavy Cylinder and an Elastic Half-Plane

Based on the solution to plane contact problems for one and two contact zones, the influence of the geometry of a wavy cylinder on the length of the actual contact region when it is introduced into an elastic half-plane is studied. Analytical expressions are obtained to determine the boundaries of two contact zones and the total load for an arbitrary gap function between the surfaces. The study establishes a relationship between the boundaries of the contact zone and the fictitious zone of negative (tensile) contact stresses that arise when the solution for a simply connected region is used. It is shown that the waviness of the cylinder surface has a significant effect on the load dependence of the length of the real contact area . A nonmonotonic behavior of this dependence is revealed in the transition from a doubly connected contact region to a simply connected one.