Analysis and Numerical Approximation of an Electro-elastic Frictional Contact Problem

El. Essoufi; El. Benkhira; R. Fakhar

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 84-90
  • ISSN: 0973-5348

Abstract

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We consider the problem of frictional contact between an piezoelectric body and a conductive foundation. The electro-elastic constitutive law is assumed to be nonlinear and the contact is modelled with the Signorini condition, nonlocal Coulomb friction law and a regularized electrical conductivity condition. The existence of a unique weak solution of the model is established. The finite elements approximation for the problem is presented, and error estimates on the solutions are derived

How to cite

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Essoufi, El., Benkhira, El., and Fakhar, R.. Taik, A., ed. "Analysis and Numerical Approximation of an Electro-elastic Frictional Contact Problem." Mathematical Modelling of Natural Phenomena 5.7 (2010): 84-90. <http://eudml.org/doc/197671>.

@article{Essoufi2010,
abstract = {We consider the problem of frictional contact between an piezoelectric body and a conductive foundation. The electro-elastic constitutive law is assumed to be nonlinear and the contact is modelled with the Signorini condition, nonlocal Coulomb friction law and a regularized electrical conductivity condition. The existence of a unique weak solution of the model is established. The finite elements approximation for the problem is presented, and error estimates on the solutions are derived},
author = {Essoufi, El., Benkhira, El., Fakhar, R.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {piezoelectric; Coulomb’s law; Signorini condition; fixed point process; finite element approximation; error estimates; electro-elastic static problem; piezoelectric materials; unilateral contact; nonlocal Coulomb's friction; variational inequality; fixed point; iterative method},
language = {eng},
month = {8},
number = {7},
pages = {84-90},
publisher = {EDP Sciences},
title = {Analysis and Numerical Approximation of an Electro-elastic Frictional Contact Problem},
url = {http://eudml.org/doc/197671},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Essoufi, El.
AU - Benkhira, El.
AU - Fakhar, R.
AU - Taik, A.
TI - Analysis and Numerical Approximation of an Electro-elastic Frictional Contact Problem
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 84
EP - 90
AB - We consider the problem of frictional contact between an piezoelectric body and a conductive foundation. The electro-elastic constitutive law is assumed to be nonlinear and the contact is modelled with the Signorini condition, nonlocal Coulomb friction law and a regularized electrical conductivity condition. The existence of a unique weak solution of the model is established. The finite elements approximation for the problem is presented, and error estimates on the solutions are derived
LA - eng
KW - piezoelectric; Coulomb’s law; Signorini condition; fixed point process; finite element approximation; error estimates; electro-elastic static problem; piezoelectric materials; unilateral contact; nonlocal Coulomb's friction; variational inequality; fixed point; iterative method
UR - http://eudml.org/doc/197671
ER -

References

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  1. H. Brezis. Equations et inéquations non linéaires dans les espaces vectoriels en dualité. Annales Inst. Fourier, 18 (1968), 115-175. Zbl0169.18602
  2. P. G. Ciarlet. The finite element method for elliptic problems. North-Holland, Amsterdam, 1978.  Zbl0383.65058
  3. M. Sofonea, EL-H. Essoufi. A Piezoelectric contact problem with slip dependent coefficient of friction. Math. Model. Anal., 9 (2004), 229-242. Zbl1092.74029
  4. Z. Lerguet, M. Shillor, M. Sofonea. A frictional contact problem for an electro-viscoelastic body. Electronic journal of differential equations, 2007 (2007), No. 170, 1-16. Zbl1139.74041
  5. A. Touzaline. A Quasistatic unilateral contact problem with slip-dependent coefficient of friction for nonlinear elastic materials. Electronic journal of differential equations, 2006 (2006), No. 144, 1-14. Zbl1128.74322

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