Journal
APPLICATIONS OF MATHEMATICS
Volume 57, Issue 3, Pages 263-295Publisher
ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS
DOI: 10.1007/s10492-012-0016-9
Keywords
unilateral contact; Coulomb friction; local uniqueness; qualitative behaviour
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Funding
- Charles University Grant Agency [18008]
- Grant Agency of the Czech Republic [201/07/0294]
- Necas Center for Mathematical Modeling
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A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction F depending on the spatial variable is analysed. It is shown that a solution exists for any F and is globally unique if F is sufficiently small. The Lipschitz continuity of this unique solution as a function of F as well as a function of the load vector f is obtained. Furthermore, local uniqueness of solutions for arbitrary F > 0 is studied. The question of existence of locally Lipschitz-continuous branches of solutions with respect to the coefficient F is converted to the question of existence of locally Lipschitz-continuous branches of solutions with respect to the load vector 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.
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