On the two-step iterative method of solving frictional contact problems in elasticity

Angelov, Todor ; Liolios, Asterios

International Journal of Applied Mathematics and Computer Science, Tome 15 (2005), p. 197-203 / Harvested from The Polish Digital Mathematics Library

Résumé

A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.

Détail

Publié le : 2005-01-01

Zbl 1156.74357

EUDML-ID : urn:eudml:doc:207735

Bibliographie

[000] Andersson L.-E. and Klarbring A. (2001): A review of the theory of static and quasi-static frictional contact problems in elasticity. - Phil. Trans. Roy. Soc.London, Vol. A 359, No. 1789, pp. 2519-2539. | Zbl 1097.74574

[001] Angelov T.A. and Liolios A.A. (2004): An iterative solution procedure for Winkler-type contact problems with friction. -Z. Angew. Math. Mech., Vol. 84, No. 2, pp. 136-143. | Zbl 1254.74104

[002] Cvapvatinva A.R. and Cocu M. (1991): Internal approximation of quasi-variational inequalities. - Num. Math., Vol. 59, No. 4, pp. 385-398. | Zbl 0742.65055

[003] Cocu M. (1984): Existence of solutions of Signorini problems with friction.- Int. J. Eng. Sci., Vol. 22, No. 10, pp. 567-575. | Zbl 0554.73096

[004] Demkowicz L. and Oden J.T. (1982): On some existence and uniqueness results in contact problems with nonlocal friction. - Nonlin. Anal., Vol. TMA 6,pp. 1075-1093. | Zbl 0511.73122

[005] Duvaut G. and Lions J.-L. (1976): Inequalities in Mechanics and Physics.- Berlin: Springer. | Zbl 0331.35002

[006] Glowinski R. (1984): Numerical Methods for Nonlinear Variational Problems.- New York: Springer. | Zbl 0536.65054

[007] Hlavaček I., Haslinger J., Nečas J. and Lovišek J. (1988): Solution of Variational Inequalities in Mechanics. - New York: Springer. | Zbl 0654.73019

[008] Kikuchi N. and Oden J.T. (1988): Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. -Philadelphia: SIAM. | Zbl 0685.73002

[009] Klarbring A., Mikelič A. and Shillor M. (1989): On friction problems with normal compliance. - Nonlin. Anal., Vol. TMA 13, No. 8,pp. 935-955. | Zbl 0707.73068

[010] Lee C.Y. and Oden J.T. (1993a): Theory and approximation of quasistatic frictional contact problems. - Comp. Math. Appl. Mech.Eng., Vol. 106, No. 3, pp. 407-429. | Zbl 0783.73083

[011] Lee C.Y. and Oden J.T. (1993b): A priori error estimation of hp-finite element approximations of frictional contact problems with normal compliance. - Int. J.Eng. Sci., Vol. 31, No. 6, pp. 927-952. | Zbl 0772.73078

[012] Nečas J., Jarušek J. and Haslinger J. (1980): On the solutionof the variational inequality to the Signorini problem with small friction.- Bull. Unione Math. Italiana, Vol. 17-B(5), pp. 796-811. | Zbl 0445.49011

[013] Oden J.T. and Carey G.F. (1984): Finite Elements: Special Problems in Solid Mechanics, Vol. 5, - Englewood Cliffs, N.J.: Prentice-Hall. | Zbl 0535.73050

[014] Panagiotopoulos P.D. (1975): A Nonlinear Programming Approach to the Unilateral Contact and Friction Boundary Value Problem in the Theory of Elasticity. - Ing. Archiv., Vol. 44, No. 6, pp. 421-432. | Zbl 0332.73018

[015] Panagiotopoulos P.D. (1985): Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions. - Boston: Birkhuser. | Zbl 0579.73014

[016] Rabier P.J. and Oden J.T. (1987): Solution to Signorini-like contact problemsthrough interface models. I. Preliminaries and formulation of a variational equality. - Nonlin. Anal., Vol. TMA 11, No. 12, pp. 1325-1350.

[017] Rabier P.J. and Oden J.T. (1988): Solution to Signorini-like contact problemsthrough interface models. II. Existence and uniqueness theorems. -Nonlin. Anal., Vol. TMA 12, No. 1, pp. 1-17.