Boussinesq-Cerruti functions and a simple technique for substantial acceleration of subsurface stress computations in elastic half-spaces

Abstract

The Boussinesq-Cerruti potential functions for the calculation of subsurface stresses and displacements in elastic half-spaces are presented in full and in clear formulation. They were expanded and optimized for fast computational analysis of subsurface stress and displacement fields, including fatigue life computations. A simple technique was developed to accelerate the computations by omitting the stress contribution of parts of the loaded boundary if the said contribution is lower than a predetermined limit. The error of this approximation was defined and formulated for the comparison of various solutions. The technique was applied in a computationally intensive problem involving a rolling-sliding-spinning elastohydrody-namic, elliptical, heavily loaded contact, and three-dimensional subsurface stress and displacement fields were calculated with hundreds of thousands of surface gridpoints and tens of thousands of subsurface gridpoints, followed by the computation of fatigue lives of the contacting solids. Results are presented for a smooth contact, but the method has been applied and is particularly useful for rough contacts as well. The results show a two to ten-fold acceleration of computations, which reduces the computational times by 50-95 per cent for a negligible-to-small loss of accuracy. In real terms, this means reduction of computer time from days to hours or from hours to minutes.