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.

Voir la notice de l'article provenant de la source Library of Science

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},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2002},
     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
PB  - mathdoc
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
%I mathdoc
%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/