Finite element analysis of a static contact problem with Coulomb friction

Ivan Hlaváček

Applications of Mathematics (2000)

  • Volume: 45, Issue: 5, page 357-379
  • ISSN: 0862-7940

Abstract

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A unilateral contact problem with a variable coefficient of friction is solved by a simplest variant of the finite element technique. The coefficient of friction may depend on the magnitude of the tangential displacement. The existence of an approximate solution and some a priori estimates are proved.

How to cite

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Hlaváček, Ivan. "Finite element analysis of a static contact problem with Coulomb friction." Applications of Mathematics 45.5 (2000): 357-379. <http://eudml.org/doc/33065>.

@article{Hlaváček2000,
abstract = {A unilateral contact problem with a variable coefficient of friction is solved by a simplest variant of the finite element technique. The coefficient of friction may depend on the magnitude of the tangential displacement. The existence of an approximate solution and some a priori estimates are proved.},
author = {Hlaváček, Ivan},
journal = {Applications of Mathematics},
keywords = {unilateral contact; Coulomb friction; finite elements; existence proofs; unilateral contact; finite element method; existence; discrete contact problems; Coulomb friction; fixed point technique; uniqueness; penalty; regularization},
language = {eng},
number = {5},
pages = {357-379},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite element analysis of a static contact problem with Coulomb friction},
url = {http://eudml.org/doc/33065},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Finite element analysis of a static contact problem with Coulomb friction
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 5
SP - 357
EP - 379
AB - A unilateral contact problem with a variable coefficient of friction is solved by a simplest variant of the finite element technique. The coefficient of friction may depend on the magnitude of the tangential displacement. The existence of an approximate solution and some a priori estimates are proved.
LA - eng
KW - unilateral contact; Coulomb friction; finite elements; existence proofs; unilateral contact; finite element method; existence; discrete contact problems; Coulomb friction; fixed point technique; uniqueness; penalty; regularization
UR - http://eudml.org/doc/33065
ER -

References

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  1. Basic Error Estimates for Elliptic Problems, In: Handbook of Numerical Analysis, vol. II, P. G. Ciarlet, J. L. Lions (eds.), North-Holland, Amsterdam, 1991. (1991) Zbl0875.65086MR1115237
  2. Existenz und Regularität der Lösungen für Kontaktprobleme mit Reibung. Dissertation Thesis, Univ. Stuttgart, 1996. (1996) MR1466960
  3. 10.1142/S0218202598000196, Math. Models Methods Appl. Sci. 8 (1998), 445–468. (1998) MR1624879DOI10.1142/S0218202598000196
  4. Monotone operators. A survey directed to applications to differential equations, Appl. Math. 35 (1990), 257–301. (1990) MR1065003
  5. Least square method for solving contact problems with friction obeying the Coulomb law, Appl. Math. 29 (1984), 212–224. (1984) Zbl0557.73100MR0747213
  6. 10.1002/mma.1670050127, Math. Methods Appl. Sci. 5 (1983), 422–437. (1983) MR0716664DOI10.1002/mma.1670050127
  7. Remarks on a numerical method for unilateral contact including friction, In: Unilateral Problems in Structural Analysis, Birkhäuser, Basel, 1991, pp. 129–144. (1991) MR1169548

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