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On The Two-Step Iterative Method of Solving Frictional Contact Problems in Elasticity

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
197--203
Opis fizyczny
Bibliogr. 18 poz., rys., wykr.
Twórcy
  • Institute of Mechanics, Bulgarian Academy of Sciences, “Acad. G. Bonchev” street, block 4, 11–13 Sofia, Bulgaria
  • Department of Civil Engineering, Democritus University of Thrace, 67–100 Xanti, Greece
Bibliografia
  • [1] 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.
  • [2] 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.
  • [3] Čapǎtinǎ A.R. and Cocu M. (1991): Internal approximation of quasi-variational inequalities. — Num. Math., Vol. 59, No. 4, pp. 385–398.
  • [4] Cocu M. (1984): Existence of solutions of Signorini problems with friction.—Int. J. Eng. Sci., Vol. 22, No. 10, pp. 567–575.
  • [5] 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.
  • [6] Duvaut G. and Lions J.-L. (1976): Inequalities in Mechanics and Physics. — Berlin: Springer.
  • [7] Glowinski R. (1984): Numerical Methods for Nonlinear Variational Problems.— New York: Springer.
  • [8] Hlavaček I., Haslinger J., Nečas J. and Lovišek J. (1988): Solution of Variational Inequalities in Mechanics. — New York: Springer.
  • [9] Kikuchi N. and Oden J.T. (1988): Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. — Philadelphia: SIAM.
  • [10] Klarbring A., Mikelič A. and Shillor M. (1989): On friction problems with normal compliance. — Nonlin. Anal., Vol. TMA 13, No. 8, pp. 935–955.
  • [11] 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.
  • [12] Lee C.Y. and Oden J.T. (1993b): A priori error estimation of hpfinite element approximations of frictional contact problems with normal compliance. — Int. J. Eng. Sci., Vol. 31, No. 6, pp. 927–952.
  • [13] Nečas J., Jarušek J. and Haslinger J. (1980): On the solution of the variational inequality to the Signorini problem with small friction. — Bull. Unione Math. Italiana, Vol. 17-B(5), pp. 796–811.
  • [14] Oden J.T. and Carey G.F. (1984): Finite Elements: Special Problems in Solid Mechanics, Vol. 5,—Englewood Cliffs, N.J.: Prentice-Hall.
  • [15] 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.
  • [16] Panagiotopoulos P.D. (1985): Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions. —Boston: Birkhäuser.
  • [17] Rabier P.J. and Oden J.T. (1987): Solution to Signorini-like contact problems through interface models. I. Preliminaries and formulation of a variational equality. — Nonlin. Anal., Vol. TMA 11, No. 12, pp. 1325–1350.
  • [18] Rabier P.J. and Oden J.T. (1988): Solution to Signorini-like contact problems through interface models. II. Existence and uniqueness theorems. —Nonlin. Anal., Vol. TMA 12, No. 1, pp. 1–17.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0016-0009
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