Contact Problem for Elastic Bodies of Different Dimensions
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 4, pp. 60-75 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper a variational problem describing a contact between an elastic plate and a thin elastic beam is investigated. It is assumed that the contact zone is a priori unknown and is to be defined. The given model is described by the energy functional minimization problem over a set of admissible displacements or by the equivalent variational inequality for the fourth order operator. Various formulations of problem and their equivalence are investigated. Boundary conditions, fulfilled on a set of possible contact and their exact interpretation are found.
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N. V. Neustroeva. Contact Problem for Elastic Bodies of Different Dimensions. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 4, pp. 60-75. http://geodesic.mathdoc.fr/item/VNGU_2008_8_4_a6/

[1] Fikera G., Teoremy suschestvovaniya v teorii uprugosti, Mir, M., 1974

[2] Kinderlerer D., Stampakkya G., Vvedenie v variatsionnye neravenstva i ikh prilozheniya, Mir, M., 1983

[3] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972

[4] Kravchuk A. S., Variatsionnye i kvazivariatsionnye neravenstva v mekhanike, Izd-vo MGAPI, M., 1997

[5] Khludnev A. M., Khoffmann K.-Kh., Botkin N. D., “Variatsionnaya zadacha o kontakte uprugikh ob'ektov raznykh razmernostei”, Sib. mat. zhurn., 47:3 (2006), 707–717

[6] Glavachek I., Gaslinger Ya., Nechas I. i dr., Reshenie variatsionnykh neravenstv v mekhanike, Mir, M., 1986

[7] Khludnev A. M., “Metod gladkikh oblastei v zadache o ravnovesii plastiny s treschinoi”, Sib. mat. zhurn., 43:6 (2002), 1388–1400

[8] Khludnev A. M., “Teoriya treschin s vozmozhnym kontaktom beregov”, Uspekhi matematiki, 3:4 (2005), 41–82

[9] Khludnev A. M., “Regulyarizatsiya i suschestvovanie reshenii”, Sib. mat. zhurn., 39:3 (1998), 670–682

[10] Khludnev A. M., Kovtunenko V. A., Analysis of Cracks in Solids, WIT Press, Southampton–Boston, 2000

[11] Khludnev A. M., Sokolowski J., Modelling and Control in Solid Mechanics, Birkhauser, Basel–Boston–Berlin, 1997

[12] Schild B., “On the Coincidence Set in Biharmonic Variational Inequalities with Thin Obstacles”, Ann. Sc. Norm. Super. Pisa. Cl. Sci. IV. Ser. 13, 4 (1986), 559–616