Numerical Solution of Geometrically Non-linear Problem of Contact of Automobile Tire with Solid Supporting Surface

Statements and solutions of the following contact problems are given: compression of the stationary automobile tire and slow rolling of the compressed tire along the solid supporting surface and also a model of the orthotropic three-layer shell. The problems are solved by the finite element method. To satisfy the contact conditions the penalty method is applied which is realized by modification of the rigidity matrix and vector of nodal loads. A general case of existence of sliding and gripping areas is considered. It is shown that in case of sliding the contact rigidity matrix looses its symmetry. Results of calculations ofthe radial automobile tire 175/70R13 of the Belotserkovsky tire factory are given as an example.