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UDC 519.853.2 + 519.632

© N. N. Maksimova, 2013

NUMERICAL INVESTIGATION OF VARIATIONAL PROBLEM IN MECHANICS USING THE DUALITY METHODS

The article describes the duality methods for solving the variational problem corresponding to a model problem of mechanics with friction. Numerical implementation of the algorithms is performed with the finite element approximation of the problem. The results of the numerical calculations are presented.

Keywords: model problem of mechanics with friction, dual scheme with a modified Lagrangian functional, Uzawa algorithm, multiplier method, finite element method.

References:

  1. Glovinski, R. Chislennoe issledovanie variatsionnykh neravenstv / R. Glovinski, ZH.-L. Lions, R. Tremol`er. - M.: Mir, 1979. - 574 s.
  2. Kushniruk N.N., Namm R.V. Metod mnozhiteley Lagranzha dlya resheniya polu-koertsitivnoy model`noy zadachi s treniem // Sibirskiy zhurnal vychislitel`noy matematiki, 2009. - T. 12, № 4. - S. 409-420.
  3. Kushniruk N.N. Optimizatsionnye metody resheniya variatsionnykh nera-venstv // Diss. na soiskanie uch. st. kand. fiz.-mat. nauk. - Habarovsk, 2010. - 109 s.
  4. Bertsekas, D. Uslovnaya optimizatsiya i metody mnozhiteley Lagranzha / D. Bertsekas. - M.: Radio i svyaz`, 1987. - 400 s.
  5. Vasil`ev, F.P. Chislennye metody resheniya ekstremal`nykh zadach / F.P. Vasil`ev. - M.: Nauka, 1980. - 518 s.
  6. Gol`shteyn, E.G. Modifitsirovannye funktsii Lagranzha. Teoriya i metody optimizatsii / E.G. Gol`shteyn, N.V. Tret`yakov. - M.: Nauka, 1989. - 400 s.
  7. Grossman K. Nelineynoe programmirovanie na osnove bezuslovnoy minimi-zatsii / K. Grossman, A.A. Kaplan. - Novosibirsk: Nauka. Sibirskoe otdelenie, 1981. - 183 s.
  8. Kushniruk N.N. Metod Udzavy s modifitsirovannoy funktsiey Lagranzha dlya resheniya zadachi o dvizhenii zhidkosti v beskonechnoy trube s treniem na granitse // Informatika i sistemy upravleniya, 2009. - № 1(19). - S. 3-14.
  9. Maksimova (Kushniruk) N.N., Namm R.V. Iterativnaya proksimal`naya regulya-rizatsiya modifitsirovannogo funktsionala Lagranzha dlya resheniya polukoertsitiv-noy model`noy zadachi s treniem // Sibirskiy zhurnal vychislitel`noy matematiki, 2011. - T. 14, № 4. - S. 393-408.
  10. Kushniruk N.N., Namm R.V., Tkachenko A.S. Ob ustoychivom sglazhivayushchem me-tode resheniya model`noy zadachi mekhaniki s treniem // ZHurnal vychislitel`noy ma-tematiki i matematicheskoy fiziki, 2011. - T. 51. - № 6. - S. 1032-1042.
  11. Kushniruk N.N., Namm R.V. O konechno-elementnom reshenii model`noy zadachi mekhaniki s treniem na osnove sglazhivayushchego metoda mnozhiteley Lagranzha // ZHurnal vychislitel`noy matematiki i matematicheskoy fiziki, 2012. - T. 52. - № 1. - S. 24-34.
  12. Rokafellar, R.T. Vypuklyy analiz / Rokafellar R.T. - M.: Mir, 1973. - 469 s.

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