Article
MSC:
65N30,
73T05,
74A55,
74M15,
74S30,
74S99 | MR 0747213 | Zbl 0557.73100 | DOI: 10.21136/AM.1984.104086
Full entry |
PDF
(1.6 MB)
Feedback
PDF
(1.6 MB)
Feedback
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
Summary:
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.
References:
[1] I. Hlaváček J. Haslinger J. Nečas J. Lovíšek: Solution of Variation Inequalities in Mechanics. (in Slovak), ALFA, SNTL, Bratislava, Praha, 1982. MR 0755152
[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. MR 0580559
[3] J. Jarušek: Contact problems with bounded friction. Coercive case. Czech. Math. J. 33 (108) (1983), 237-261. MR 0699024
[4] J. Haslinger: Approximation of the Signorini problem with friction, obeying the Coulomb law. Math. Meth. in the Appl. Sci 5 (1983), 422-437. DOI 10.1002/mma.1670050127 | MR 0716664 | Zbl 0525.73130
[5] G. Duvaut J. L. Lions: Les inéquations en mécanique et en physique. Dunod, Paris 1972. MR 0464857
Search
Partner of
