Least square method for solving contact problems with friction obeying the Coulomb law

Jaroslav Haslinger

Aplikace matematiky (1984)

  • Volume: 29, Issue: 3, page 212-224
  • ISSN: 0862-7940

Abstract

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The paper deals with numerical realization of contact problems with friction obeying the Coulomb law. The original problem is formulated as the fixed-point problem for a certain operator generated by the variational inequality. This inequality is transformed to a system of variational nonlinear equations generating other operators, in a sense "close" to the above one. The fixed-point problem of these operators is solved by the least-square method in which equations and the corresponding quadratic error play the role of the state equations and the cost function, respectively.

How to cite

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Haslinger, Jaroslav. "Least square method for solving contact problems with friction obeying the Coulomb law." Aplikace matematiky 29.3 (1984): 212-224. <http://eudml.org/doc/15349>.

@article{Haslinger1984,
abstract = {The paper deals with numerical realization of contact problems with friction obeying the Coulomb law. The original problem is formulated as the fixed-point problem for a certain operator generated by the variational inequality. This inequality is transformed to a system of variational nonlinear equations generating other operators, in a sense "close" to the above one. The fixed-point problem of these operators is solved by the least-square method in which equations and the corresponding quadratic error play the role of the state equations and the cost function, respectively.},
author = {Haslinger, Jaroslav},
journal = {Aplikace matematiky},
keywords = {friction; Coulomb law; variational inequality formulation replaced; in finite dimension by family of nonlinear equations; simultaneous; penalization and regularization; continuous model; finite element discretisation; least squares method; friction; Coulomb law; variational inequality formulation replaced; in finite dimension by family of nonlinear equations; simultaneous; penalization and regularization; continuous model; finite element discretisation; least squares method},
language = {eng},
number = {3},
pages = {212-224},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Least square method for solving contact problems with friction obeying the Coulomb law},
url = {http://eudml.org/doc/15349},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Haslinger, Jaroslav
TI - Least square method for solving contact problems with friction obeying the Coulomb law
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 3
SP - 212
EP - 224
AB - The paper deals with numerical realization of contact problems with friction obeying the Coulomb law. The original problem is formulated as the fixed-point problem for a certain operator generated by the variational inequality. This inequality is transformed to a system of variational nonlinear equations generating other operators, in a sense "close" to the above one. The fixed-point problem of these operators is solved by the least-square method in which equations and the corresponding quadratic error play the role of the state equations and the cost function, respectively.
LA - eng
KW - friction; Coulomb law; variational inequality formulation replaced; in finite dimension by family of nonlinear equations; simultaneous; penalization and regularization; continuous model; finite element discretisation; least squares method; friction; Coulomb law; variational inequality formulation replaced; in finite dimension by family of nonlinear equations; simultaneous; penalization and regularization; continuous model; finite element discretisation; least squares method
UR - http://eudml.org/doc/15349
ER -

References

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  1. I. Hlaváček J. Haslinger J. Nečas J. Lovíšek, Solution of Variation Inequalities in Mechanics, (in Slovak), ALFA, SNTL, Bratislava, Praha, 1982. (1982) MR0755152
  2. J. Nečas J. Jarušek J. Haslinger, On the solution of the variational inequality to the Signorini problem with small friction, Bolletino U.M.I. (5), 17 - B (1980), 796-811. (1980) MR0580559
  3. J. Jarušek, Contact problems with bounded friction. Coercive case, Czech. Math. J. 33 (108) (1983), 237-261. (1983) MR0699024
  4. J. Haslinger, 10.1002/mma.1670050127, Math. Meth. in the Appl. Sci 5 (1983), 422-437. (1983) Zbl0525.73130MR0716664DOI10.1002/mma.1670050127
  5. G. Duvaut J. L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris 1972. (1972) MR0464857

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