Signorini problem with a solution dependent coefficient of friction (model with given friction): Approximation and numerical realization

Jaroslav Haslinger; Oldřich Vlach

Applications of Mathematics (2005)

  • Volume: 50, Issue: 2, page 153-171
  • ISSN: 0862-7940

Abstract

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Contact problems with given friction and the coefficient of friction depending on their solutions are studied. We prove the existence of at least one solution; uniqueness is obtained under additional assumptions on the coefficient of friction. The method of successive approximations combined with the dual formulation of each iterative step is used for numerical realization. Numerical results of model examples are shown.

How to cite

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Haslinger, Jaroslav, and Vlach, Oldřich. "Signorini problem with a solution dependent coefficient of friction (model with given friction): Approximation and numerical realization." Applications of Mathematics 50.2 (2005): 153-171. <http://eudml.org/doc/33213>.

@article{Haslinger2005,
abstract = {Contact problems with given friction and the coefficient of friction depending on their solutions are studied. We prove the existence of at least one solution; uniqueness is obtained under additional assumptions on the coefficient of friction. The method of successive approximations combined with the dual formulation of each iterative step is used for numerical realization. Numerical results of model examples are shown.},
author = {Haslinger, Jaroslav, Vlach, Oldřich},
journal = {Applications of Mathematics},
keywords = {contact problems with given friction; unilateral contact and friction; solution dependent coefficient of friction; contact problems with given friction; unilateral contact and friction; solution dependent coefficient of friction},
language = {eng},
number = {2},
pages = {153-171},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Signorini problem with a solution dependent coefficient of friction (model with given friction): Approximation and numerical realization},
url = {http://eudml.org/doc/33213},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Vlach, Oldřich
TI - Signorini problem with a solution dependent coefficient of friction (model with given friction): Approximation and numerical realization
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 153
EP - 171
AB - Contact problems with given friction and the coefficient of friction depending on their solutions are studied. We prove the existence of at least one solution; uniqueness is obtained under additional assumptions on the coefficient of friction. The method of successive approximations combined with the dual formulation of each iterative step is used for numerical realization. Numerical results of model examples are shown.
LA - eng
KW - contact problems with given friction; unilateral contact and friction; solution dependent coefficient of friction; contact problems with given friction; unilateral contact and friction; solution dependent coefficient of friction
UR - http://eudml.org/doc/33213
ER -

References

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  5. Numerical Solution of Variational Inequalities. Springer Series in Applied Mathematical Sciences 66, Springer-Verlag, New York, 1988. (1988) MR0952855
  6. 10.1023/A:1022220711369, Appl. Math. 45 (2000), 357–379. (2000) MR1777018DOI10.1023/A:1022220711369
  7. 10.1017/S0308210500013536, Proc. R. Soc. Edinb. Sect. A 98 (1984), 365–383. (1984) MR0768357DOI10.1017/S0308210500013536
  8. Contact Problems in Elasticity. A Study of Variational Inequalities and Finite Element Methods, Mathematics and Computer Science for Engineers, SIAM, Philadelphia, 1988. (1988) MR0961258
  9. On the solution of the variational inequality to the Signorini problem with small friction, Boll. Unione Mat. Ital. V. Ser., 17 (1980), 796–811. (1980) MR0580559

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