Dynamic computations of nonlinear beams in contact with rough surfaces

We present computations of a two-dimensional nonlinear ring in contact with a rough surface for the analysis of tire dynamic behaviour at low frequencies in both non-rolling and rolling conditions. For the ring, the assumptions of a Timoshenko beam and finite displacements are considered to build the model. The analytical formulation is established successfully in linear/nonlinear static and dynamic states in non-rolling and rolling conditions using an Arbitrary Lagrangian Eulerian approach. Then, the contact with a real road is introduced. In particular, the calculation of the contact is divided into a non-linear stationary analysis followed by a linear dynamic calculation. The validation of this model is successfully done by comparisons with test results like rolling on simple shapes or with Abaqus computations.