Theoretical analysis of discrete contact problems with Coulomb friction

Tomáš Ligurský

Applications of Mathematics (2012)

  • Volume: 57, Issue: 3, page 263-295
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Ligurský, Tomáš. "Theoretical analysis of discrete contact problems with Coulomb friction." Applications of Mathematics 57.3 (2012): 263-295. <http://eudml.org/doc/247097>.

@article{Ligurský2012,
abstract = {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 $f$ 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 $f$. 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.},
author = {Ligurský, Tomáš},
journal = {Applications of Mathematics},
keywords = {unilateral contact; Coulomb friction; local uniqueness; qualitative behaviour; unilateral contact; Coulomb friction; local uniqueness; qualitative behaviour},
language = {eng},
number = {3},
pages = {263-295},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Theoretical analysis of discrete contact problems with Coulomb friction},
url = {http://eudml.org/doc/247097},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Ligurský, Tomáš
TI - Theoretical analysis of discrete contact problems with Coulomb friction
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 263
EP - 295
AB - 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 $f$ 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 $f$. 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.
LA - eng
KW - unilateral contact; Coulomb friction; local uniqueness; qualitative behaviour; unilateral contact; Coulomb friction; local uniqueness; qualitative behaviour
UR - http://eudml.org/doc/247097
ER -

References

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