Mixed finite element analysis of semi-coercive unilateral contact problems with given friction

Ivan Hlaváček

Applications of Mathematics (2007)

  • Volume: 52, Issue: 1, page 25-58
  • ISSN: 0862-7940

Abstract

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A unilateral contact 2D-problem is considered provided one of two elastic bodies can shift in a given direction as a rigid body. Using Lagrange multipliers for both normal and tangential constraints on the contact interface, we introduce a saddle point problem and prove its unique solvability. We discretize the problem by a standard finite element method and prove a convergence of approximations. We propose a numerical realization on the basis of an auxiliary “bolted” problem and the algorithm of Uzawa.

How to cite

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Hlaváček, Ivan. "Mixed finite element analysis of semi-coercive unilateral contact problems with given friction." Applications of Mathematics 52.1 (2007): 25-58. <http://eudml.org/doc/33275>.

@article{Hlaváček2007,
abstract = {A unilateral contact 2D-problem is considered provided one of two elastic bodies can shift in a given direction as a rigid body. Using Lagrange multipliers for both normal and tangential constraints on the contact interface, we introduce a saddle point problem and prove its unique solvability. We discretize the problem by a standard finite element method and prove a convergence of approximations. We propose a numerical realization on the basis of an auxiliary “bolted” problem and the algorithm of Uzawa.},
author = {Hlaváček, Ivan},
journal = {Applications of Mathematics},
keywords = {unilateral contact; Tresca’s model of friction; mixed variational formulation; Uzawa algorithm; unilateral contact; Tresca's model of friction; mixed variational formulation; Uzawa algorithm},
language = {eng},
number = {1},
pages = {25-58},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Mixed finite element analysis of semi-coercive unilateral contact problems with given friction},
url = {http://eudml.org/doc/33275},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Mixed finite element analysis of semi-coercive unilateral contact problems with given friction
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 1
SP - 25
EP - 58
AB - A unilateral contact 2D-problem is considered provided one of two elastic bodies can shift in a given direction as a rigid body. Using Lagrange multipliers for both normal and tangential constraints on the contact interface, we introduce a saddle point problem and prove its unique solvability. We discretize the problem by a standard finite element method and prove a convergence of approximations. We propose a numerical realization on the basis of an auxiliary “bolted” problem and the algorithm of Uzawa.
LA - eng
KW - unilateral contact; Tresca’s model of friction; mixed variational formulation; Uzawa algorithm; unilateral contact; Tresca's model of friction; mixed variational formulation; Uzawa algorithm
UR - http://eudml.org/doc/33275
ER -

References

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