Domain Decomposition Schemes for Frictionless Multibody Contact Problems of Elasticity

  • Ivan I. DyyakEmail author
  • Ihor I. Prokopyshyn
Conference paper


The class of parallel Robin (Poincaré) domain decomposition schemes which are based on the penalty method and the simple iteration method for variational equations is proposed for solution of frictionless multibody contact problems of elasticity. The convergence of these schemes is proved. The numerical analysis is made for 2D contact problems using FEM approximations.


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  1. 1.
    Céa, J.: Optimisation. Théorie et algorithmes. Dunod, Paris (1971)zbMATHGoogle Scholar
  2. 2.
    Dyyak, I. I., Prokopyshyn, I. I.: The convergence of parallel Neumann domain decomposition scheme for frictionless multibody contact problems of elasticity. Mat. Met. Fiz.-Mekh. Polya. 52(3), 78–89 (2009) [In Ukrainian]Google Scholar
  3. 3.
    Glowinski, R., Lions, J. L., Trémolières, R.: Analyse numérique des inéquations variationnelles. Dunod, Paris (1976)zbMATHGoogle Scholar
  4. 4.
    Hüeber, S., Wohlmuth, B. I.: A primal-dual active set strategy for non-linear multibody contact problems. Comput. Meth. Appl. Mech. Engrg. 194(27–29), 3147–3166 (2005)zbMATHCrossRefGoogle Scholar
  5. 5.
    Kikuchi, N., Oden, J. T.: Contact Problem in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM, Philadelphia (1988)Google Scholar
  6. 6.
    Kravchuk, A. S.: The formulation of the contact problem for several deformable bodies as the nonlinear programming problem. PMM. 42(3), 466–474 (1978) [In Russian]Google Scholar
  7. 7.
    Kuzmenko, V. I.: On variational approach to the theory of contact problems for nonlinear elastic multilayer bodies. PMM. 43(5), 893–901 (1979) [In Russian]Google Scholar
  8. 8.
    Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaire. Dunod, Gauthier-Villars, Paris (1969)Google Scholar
  9. 9.
    Prokopyshyn, I.: Parallel domain decomposition schemes for frictionless contact problems of elasticity. Visnyk Lviv Univ. Ser. Appl. Math. Comp. Sci. 14, 123–133 (2008) [In Ukrainian]Google Scholar
  10. 10.
    Wriggers, P.: Computational Contact Mechanics, second ed. Springer, Heidelberg (2006)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Ivan Franko National University of LvivLvivUkraine

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