On Finite Element Uniqueness Studies for Coulomb's Frictional Contact Model

• Autorzy: Hild P.
• 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 C varepsilon2 |log(h)|{-1}, where h and varepsilon 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; finite elements; mesh-size dependent uniqueness conditions; non-uniqueness example

PL

prawo Coulomba; element skończony; niepowtarzalność

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2002
• Tom: Vol. 12, no 1
• Strony: 41--50
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Hild P.

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

Bibliografia

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