zbMATH — the first resource for mathematics

Signorini problem with a solution dependent coefficient of friction (model with given friction): Approximation and numerical realization. (English) Zbl 1099.65109
Summary: 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.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
PDF BibTeX Cite
Full Text: DOI EuDML
[1] P. Bisegna, F. Lebon, and F. Maceri: D-PANA: a convergent block-relaxation solution method for the discretized dual formulation of the Signorini-Coulomb contact problem. C. R. Acad. Sci. Paris, Sér. I 333 (2001), 1053–1058. · Zbl 1106.74382
[2] Z. Dostál: Box constrained quadratic programming with proportioning and projections. SIAM J. Optim. 7 (1997), 871–887. · Zbl 0912.65052
[3] C. Eck, J. Jarušek: Existence results for the static contact problem with Coulomb friction. Math. Models Methods Appl. Sci. 8 (1998), 445–468. · Zbl 0907.73052
[4] J. Haslinger, Z. Dostál, and R. Kučera: On a splitting type algorithm for the numerical realization of contact problems with Coulomb friction. Comput. Methods Appl. Mech. Eng. 191 (2002), 2261–2881. · Zbl 1131.74344
[5] I. Hlaváček, J. Haslinger, J. Nečas, and J. Lovíšek: Numerical Solution of Variational Inequalities. Springer Series in Applied Mathematical Sciences 66. Springer-Verlag, New York, 1988.
[6] I. Hlaváček: Finite element analysis of a static contact problem with Coulomb friction. Appl. Math. 45 (2000), 357–379. · Zbl 1019.74035
[7] J. Haslinger, P. D. Panagiotopulos: The reciprocal variational approach to the Signorini problem with friction. Approximation results. Proc. R. Soc. Edinb. Sect. A 98 (1984), 365–383. · Zbl 0547.73096
[8] N. Kikuchi, J. T. Oden: Contact Problems in Elasticity. A Study of Variational Inequalities and Finite Element Methods, Mathematics and Computer Science for Engineers. SIAM, Philadelphia, 1988. · Zbl 0685.73002
[9] J. Nečas, J. Jarušek, and J. Haslinger: On the solution of the variational inequality to the Signorini problem with small friction. Boll. Unione Mat. Ital. V. Ser., 17 (1980), 796–811. · Zbl 0445.49011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.