Geodesic
On Finite Element Uniqueness Studies for Coulomb's Frictional Contact Model
International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) no. 1, pp. 41-50 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

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.
Keywords: Coulomb's friction law, finite elements, mesh-size dependent uniqueness conditions, non-uniqueness example
Mots-clés : element skończony 
@article{IJAMCS_2002_12_1_a3,
     author = {Hild, P.},
     title = {On {Finite} {Element} {Uniqueness} {Studies} for {Coulomb's} {Frictional} {Contact} {Model}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {41--50},
     year = {2002},
     volume = {12},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2002_12_1_a3/}
}
TY  - JOUR
AU  - Hild, P.
TI  - On Finite Element Uniqueness Studies for Coulomb's Frictional Contact Model
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2002
SP  - 41
EP  - 50
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2002_12_1_a3/
LA  - en
ID  - IJAMCS_2002_12_1_a3
ER  - 
%0 Journal Article
%A Hild, P.
%T On Finite Element Uniqueness Studies for Coulomb's Frictional Contact Model
%J International Journal of Applied Mathematics and Computer Science
%D 2002
%P 41-50
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/IJAMCS_2002_12_1_a3/
%G en
%F IJAMCS_2002_12_1_a3
Hild, P. On Finite Element Uniqueness Studies for Coulomb's Frictional Contact Model. International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) no. 1, pp. 41-50. http://geodesic.mathdoc.fr/item/IJAMCS_2002_12_1_a3/