Approximate contact solutions for non-axisymmetric homogeneous and power-law graded elastic bodies: A practical tool for design engineers and tribologists

Abstract

In two recent papers, approximate solutions for compact non-axisymmetric contact problems of homogeneous and power-law graded elastic bodies have been suggested, which provide explicit analytical relations for the force–approach relation, the size and the shape of the contact area, as well as for the pressure distribution therein. These solutions were derived for profiles, which only slightly deviate from the axisymmetric shape. In the present paper, they undergo an extensive testing and validation by comparison of solutions with a great variety of profile shapes with numerical solutions obtained by the fast Fourier transform (FFT)-assisted boundary element method (BEM). Examples are given with quite significant deviations from axial symmetry and show surprisingly good agreement with numerical solutions.

A General Approximate Solution for the Slightly Non-Axisymmetric Normal Contact Problem of Layered and Graded Elastic Materials

“…In the homogeneous case, we have d* = 1, and therefore, of course, the respective known results [25] are recovered.…”

“…Recently, Popov [24] published an approximate analytical solution for the slightly non-axisymmetric version of this contact problem, which has proven (by comparison with rigorous numerical solutions) to give very satisfactory results. In the follow-up publication [25], the authors thoroughly tested the quality of the suggested approximate analytical solution for contact geometries that are far from axial symmetry and found that it is even well-applicable to indenters with random three-dimensional shapes, e.g., a single asperity of a rough surface.…”