Extending the Mossakovskii method to contacts supporting a moment

Abstract

In this article, we extend the Mossakovskii approach to half-plane contacts supporting a moment. Since the method relies on approximating the punch geometry by a series of flat punches, we choose the load path in (P, M)-space that fixes the body tilt, which allows us to reduce the standard Cauchy singular integral formulation to a non-symmetric Abel integral equation. We use the formulation to derive simple expressions for the applied normal force and necessary applied moment as functions of the contact extent and indenter tilt, while also deriving the coefficients of the square-root terms in the contact pressure expansion at the edges of the contact. These results are analysed in detail for two specific examples: the tilted wedge and the tilted flat-and-rounded punch. We conclude by briefly discussing the equivalent tangential problem when an applied shear force and differential bulk tensions are present.