The development of a linear influence function for an elastic half-space

The determination of stresses induced in mechanical contacts arising in such components as gears, indenters and roller bearings is an important factor in the design procedure. In most cases the geometry of the contact problem is too complex to allow a full analytical solution. Some form of numerical method or semi-analytical method must then be employed. The influence function method has so far been useful but limited due to the nature of the influence functions employed. Piecewise constant elements have been used where piecewise linear elements would give a more sophisticated solution. In this paper the influence functions for a hexagonal-based pyramid of pressure (the shape needed for a piecewise linear function) are derived and some of their asymptotic properties considered.