Geodesic
Theoretical analysis of discrete contact problems with Coulomb friction
Applications of Mathematics, Tome 57 (2012) no. 3, pp. 263-295.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction $\mathcal {F}$ depending on the spatial variable is analysed. It is shown that a solution exists for any $\mathcal {F}$ and is globally unique if $\mathcal {F}$ is sufficiently small. The Lipschitz continuity of this unique solution as a function of $\mathcal {F}$ as well as a function of the load vector $\boldsymbol {f}$ is obtained. Furthermore, local uniqueness of solutions for arbitrary $\mathcal {F} > 0$ is studied. The question of existence of locally Lipschitz-continuous branches of solutions with respect to the coefficient $\mathcal {F}$ is converted to the question of existence of locally Lipschitz-continuous branches of solutions with respect to the load vector $\boldsymbol {f}$. A condition guaranteeing the existence of locally Lipschitz-continuous branches of solutions in the latter case and results for determining their directional derivatives are given. Finally, the general approach is illustrated on an elementary example, whose solutions are calculated exactly.
DOI : 10.1007/s10492-012-0016-9
Classification : 74G20, 74G55, 74M10, 74M15, 74S05
Keywords: unilateral contact; Coulomb friction; local uniqueness; qualitative behaviour 
@article{10_1007_s10492_012_0016_9,
     author = {Ligursk\'y, Tom\'a\v{s}},
     title = {Theoretical analysis of discrete contact problems with {Coulomb} friction},
     journal = {Applications of Mathematics},
     pages = {263--295},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2012},
     doi = {10.1007/s10492-012-0016-9},
     mrnumber = {2984603},
     zbl = {1265.74069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0016-9/}
}
TY  - JOUR
AU  - Ligurský, Tomáš
TI  - Theoretical analysis of discrete contact problems with Coulomb friction
JO  - Applications of Mathematics
PY  - 2012
SP  - 263
EP  - 295
VL  - 57
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0016-9/
DO  - 10.1007/s10492-012-0016-9
LA  - en
ID  - 10_1007_s10492_012_0016_9
ER  - 
%0 Journal Article
%A Ligurský, Tomáš
%T Theoretical analysis of discrete contact problems with Coulomb friction
%J Applications of Mathematics
%D 2012
%P 263-295
%V 57
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0016-9/
%R 10.1007/s10492-012-0016-9
%G en
%F 10_1007_s10492_012_0016_9
Ligurský, Tomáš. Theoretical analysis of discrete contact problems with Coulomb friction. Applications of Mathematics, Tome 57 (2012) no. 3, pp. 263-295. doi : 10.1007/s10492-012-0016-9. http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0016-9/

Cité par Sources :