A fast correction for traction-free surface of elastic quarter-space

Abstract

Applying the Hertz theory to some non-Hertzian contact problems can produce acceptable results. Nevertheless, including the influence of free surfaces requires numerical methods, many of which are based on the Boussinesq-Cerruti solution. This paper presents a new approach which is better capable of releasing quarter-space free surfaces from shear and normal internal stresses without any increase in calculation times. The mirrored pressure for shear correction is multiplied by a correction factor (ψ), which accounts for the normal load. The expression ψ is derived from the Hetényi correction process, and the resulting displacements show an enhanced correspondence with validation FEM models; with an imposed fluctuating pressure, the maximum edge displacement error was -21,90% for a shear load correction (Poisson coefficient ? = 0,3), and introducing the ψ factor reduced the deviation to -9,55%, while for μ of 0,15, the maximum error was -11,30%, which was reduced to +0,60% with the ψ factor. © 2010 WIT Press.