A simple relation in elastic contact problems

In this paper, a new relation is introduced that simplifies the determination of the Muskhelishviliʹs potential function in plane contact problems. The relation is Φ ( z ) = 1 / 2 [ p ( z ) - i q ( z ) ] , which is correct for all uncoupled contact problems. The new relation is proved in a mathematical way and utilized to obtain the potential function in several contact problems. A complete agreement has been observed between our results and the potential functions that have been obtained from complicated methods in the past. Utilization of the new relation simplifies the solution of contact problems and analytical calculation of the stress and displacement fields, which may lead to the design of better cutting tools or fretting fatigue test pads.