Surface normal deformation in elastic quarter-space

An efficient and explicit solution for the surface deformation of quarter-space under normal load is developed using the concept of flexibility matrix, which serves like springs in response to loads. Quarter-space is characterized by the unbounded side surface, such as in roller bearings and gears. The solution method is verified using a typical case. The edge effect on surface deformation under three load types namely, Hertzian point, flat cylindrical punch and Hertzian line, are evaluated. The effect can be considerable if the applied load is close to edge. The flexibility matrix is constant for a given case. Hence, the solution method is highly efficient, and particularly suitable for quarter-space problems which require iterative calculations, such as elasto-hydrodynamic lubrication analyses.