# Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution

Jaroslav Haslinger; Tomáš Ligurský

Applications of Mathematics (2009)

- Volume: 54, Issue: 5, page 391-416
- ISSN: 0862-7940

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topHaslinger, Jaroslav, and Ligurský, Tomáš. "Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution." Applications of Mathematics 54.5 (2009): 391-416. <http://eudml.org/doc/37829>.

@article{Haslinger2009,

abstract = {The paper presents the analysis, approximation and numerical realization of 3D contact problems for an elastic body unilaterally supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model (a slip bound is given a priori) but with a coefficient of friction $\mathcal \{F\}$ which depends on a solution. It is shown that a solution exists for a large class of $\mathcal \{F\}$ and is unique provided that $\mathcal \{F\}$ is Lipschitz continuous with a sufficiently small modulus of the Lipschitz continuity. The problem is discretized by finite elements, and convergence of discrete solutions is established. Finally, methods for numerical realization are described and several model examples illustrate the efficiency of the proposed approach.},

author = {Haslinger, Jaroslav, Ligurský, Tomáš},

journal = {Applications of Mathematics},

keywords = {unilateral contact and friction; solution-dependent coefficient of friction; unilateral contact and friction; solution-dependent coefficient of friction},

language = {eng},

number = {5},

pages = {391-416},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution},

url = {http://eudml.org/doc/37829},

volume = {54},

year = {2009},

}

TY - JOUR

AU - Haslinger, Jaroslav

AU - Ligurský, Tomáš

TI - Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution

JO - Applications of Mathematics

PY - 2009

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 54

IS - 5

SP - 391

EP - 416

AB - The paper presents the analysis, approximation and numerical realization of 3D contact problems for an elastic body unilaterally supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model (a slip bound is given a priori) but with a coefficient of friction $\mathcal {F}$ which depends on a solution. It is shown that a solution exists for a large class of $\mathcal {F}$ and is unique provided that $\mathcal {F}$ is Lipschitz continuous with a sufficiently small modulus of the Lipschitz continuity. The problem is discretized by finite elements, and convergence of discrete solutions is established. Finally, methods for numerical realization are described and several model examples illustrate the efficiency of the proposed approach.

LA - eng

KW - unilateral contact and friction; solution-dependent coefficient of friction; unilateral contact and friction; solution-dependent coefficient of friction

UR - http://eudml.org/doc/37829

ER -

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- Ligurský, T., Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution. Diploma thesis MFF UK, 2007 (http://artax.karlin.mff.cuni.cz/ {ligut2am/tl21.pdf}), .

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