A seminumerical method of solving three-dimensional frictionless contact problems between two elastic bodies subjected to a normal loading is presented. This method is a generalization of an existing one, the generality is relating to the contact type (conformal or antiformal) and to the contact geometry (arbitrary shape of the bodies). Based on the use of influence functions, this method requires the discretization of the different contact criteria over a candidate contact surface and the optimization of the solution to fulfill these criteria. It allows us the determination of the true contact surface, the pressure distribution, and the approach between the two bodies. The method has been implemented in a computer program called 'CONTELA', and has been applied for antiformal geometries (our results axe in close agreement with Hertz analytical model) and for closely conformal geometries (our calculations confirm the Hertz theory limitation to deal with this kind of contact geometry).
Sassi, M., & Desvignes, M. (1998). A seminumerical method for three-dimensional frictionless contact problems. Mathematical and Computer Modelling, 28(4–8), 413–425. https://doi.org/10.1016/S0895-7177(98)00131-9