Contact problems in elasticity: A study of Variational Inequalities and Finite Element methods

Abstract

We review the classical Hertz contact theory under normal load and formulate a new unified method valid for the Hertz contact theory and a variety of frictionless elliptic contact problem with an elliptic contact connection both for a rigid punch and a conical indenter. We also give a direct way to evaluate the stress and displacement field in the medium. As a limiting case, we derive the results for circular connection as well as line contact problems in the two-dimensional case. Relations of the contact stresses of the wheel of a locomotive rolling on the rails of straight and curved railway with failure of the rail are discussed. Use of such study in hardness testing is discussed.