On finite element uniqueness studies for Coulombs frictional contact model

• Autorzy: Patrick Hild
• Języki publikacji: EN

Abstrakty

EN

We are interested in the finite element approximation of Coulomb's frictional unilateral contact problem in linear elasticity. Using a mixed finite element method and an appropriate regularization, it becomes possible to prove existence and uniqueness when the friction coefficient is less than Cε^{2}|log(h)|^{-1}, where h and ε denote the discretization and regularization parameters, respectively. This bound converging very slowly towards 0 when h decreases (in comparison with the already known results of the non-regularized case) suggests a minor dependence of the mesh size on the uniqueness conditions, at least for practical engineering computations. Then we study the solutions of a simple finite element example in the non-regularized case. It can be shown that one, multiple or an infinity of solutions may occur and that, for a given loading, the number of solutions may eventually decrease when the friction coefficient increases.

Słowa kluczowe

EN

Coulomb's friction law; non-uniqueness example; mesh-size dependent uniqueness conditions; finite elements

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: 12
• Numer: 1
• Strony: 41-50

Daty

wydano

2002

otrzymano

2001-09-01

poprawiono

2002-01-01

Twórcy

autor

Patrick Hild

• Laboratoire de Mathématiques, Université de Savoie, CNRS UMR 5127, 73376 Le Bourget-du-Lac, France

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