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

Aplikace matematiky (1984)

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

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topHaslinger, 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

top- I. Hlaváček J. Haslinger J. Nečas J. Lovíšek, Solution of Variation Inequalities in Mechanics, (in Slovak), ALFA, SNTL, Bratislava, Praha, 1982. (1982) MR0755152
- 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
- J. Jarušek, Contact problems with bounded friction. Coercive case, Czech. Math. J. 33 (108) (1983), 237-261. (1983) MR0699024
- J. Haslinger, 10.1002/mma.1670050127, Math. Meth. in the Appl. Sci 5 (1983), 422-437. (1983) Zbl0525.73130MR0716664DOI10.1002/mma.1670050127
- G. Duvaut J. L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris 1972. (1972) MR0464857

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