A NUMERICAL-ANALYSIS OF ROLLING-CONTACT PROBLEMS USING QUASI-STATIC VARIATIONAL FORMULATION

This paper deals with the numerical solution of a class of the rolling contact problems. We shall consider the contact of the perfectly rigid wheel with an elastic rail on a rigid foundation. We propose a quasistatic approach to solve this contact problem. This approach is based on an assumption that for the observer moving with the rolling body the displacement of the supporting foundation is independent on time. The elliptic variational inequality formulation of this contact problem is provided. Using duality theory and the regularized relation between tangent and normal components of the contact stress we formulate this problem as an optimization problem with respect to the normal contact stress. The finite element method is used as a discretization method. The Pschenichnyj method combined with Newtonian method is used to solve numerically this discretized optimization problem. Numerical examples are given.