Previous |  Up |  Next


contact problems with given friction; unilateral contact and friction; solution dependent coefficient of friction
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.
[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. DOI 10.1016/S0764-4442(01)02153-X | MR 1872471
[2] Z.  Dostál: Box constrained quadratic programming with proportioning and projections. SIAM J.  Optim. 7 (1997), 871–887. DOI 10.1137/S1052623494266250 | MR 1462070
[3] C.  Eck, J.  Jarušek: Existence results for the static contact problem with Coulomb friction. Math. Models Methods Appl. Sci. 8 (1998), 445–468. DOI 10.1142/S0218202598000196 | MR 1624879
[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. DOI 10.1016/S0045-7825(01)00378-4 | MR 1903144
[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. MR 0952855
[6] I.  Hlaváček: Finite element analysis of a static contact problem with Coulomb friction. Appl. Math. 45 (2000), 357–379. DOI 10.1023/A:1022220711369 | MR 1777018
[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. DOI 10.1017/S0308210500013536 | MR 0768357
[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. MR 0961258
[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. MR 0580559
Partner of
EuDML logo