Determination of contact pressure distribution on frictionless rough surfaces using an optimisation approach: a one-dimensional study

Determining pressures and stresses that arise when mechanical components come into contact is crucial for analysis of surface-related failures. In real situations, determining contact pressure and stress distributions is challenging and depends on several factors, such as load, material properties and surface characteristics. This paper describes the determination of contact pressure on rough surfaces using a one-dimensional approach. Elastic, frictionless, unilateral, normal contact between a rough surface and a smooth surface is considered. Linear elastic half-space theory is used, and the contact pressure distribution is obtained by solving an associated optimisation problem. Results are given for a virtual wavy profile and two engineering roughness profiles.