Geodesic
Rigid Switching on in the Contact Problem for Elastic Plates
Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 4, pp. 92-105.

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We consider a family of problems describing the contact of elastic plates located at a fixed angle to each other and, in the natural state, touching along a line. The plates are subjected only to bending. We study passage to the limit from elastic switching on to rigid switching on. We show that the limiting problems describe exactly the contact of an elastic plate with a rigid bar and the problem of the equilibrium of an elastic plate with rigid switching on. We establish the solvability of the problems, find the boundary conditions holding on the possible contact set and their precise interpretation.
Mots-clés : Kirghoff–Lyav model
Keywords: contact problem, rigid switching on. 
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N. V. Neustroeva. Rigid Switching on in the Contact Problem for Elastic Plates. Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 4, pp. 92-105. http://geodesic.mathdoc.fr/item/SJIM_2009_12_4_a8/

[1] Khludnev A. M., “Ob odnostoronnem kontakte dvukh plastin, raspolozhennykh pod uglom drug k drugu”, Prikl. mekhanika i tekhn. fizika, 49:4 (2008), 42–58 | MR

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

[3] Caffarelli L. A., Friedman A., “The obstacle problem for the biharmonic operator”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 6:1 (1979), 151–184 | MR | Zbl

[4] Caffarelli L. A., Friedman A., Torelli A., “The two-obstacle problem for the biharmonic operator”, Pacific J. Math., 103:2 (1982), 325–335 | MR | Zbl

[5] Schild B., “On the coincidence set in biharmonic variational inequalities with thin obstacles”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 13:4 (1986), 559–616 | MR | Zbl

[6] Dal Maso G., Paderni G., “Variational inequalities for the biharmonic operator with varying obstacles”, Ann. Mat. Pura Appl., 153 (1988), 203–227 | DOI | MR | Zbl

[7] Khludnev A. M., Sokolowski J., Modelling and Control in Solid Mechanics, Birkhäuser, Basel–Boston–Berlin, 1997 | MR | Zbl

[8] Glavachek I., Gaslinger Ya., Nechas I., Lovishek Ya., Reshenie variatsionnykh neravenstv v mekhanike, Mir, M., 1986 | MR

[9] Khludnev A. M., Zadacha o treschine na granitse zhestkogo vklyucheniya v uprugoi plastine, Preprint No 1–2009, In-t gidrodinamiki SO RAN, Novosibirsk, 2009, 18 pp.

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

[11] Khludnev A. M., Leugering G., “Unilateral contact problems for two perpendicular elastic structures”, J. Anal. Appl., 27:2 (2008), 157–177 | MR | Zbl

[12] Khludnev A. M., Tani A., “Unilateral contact problem for two inclined elastic bodies”, European J. Mech. A Solids, 27:3 (2008), 365–377 | DOI | MR | Zbl

[13] 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 | MR | Zbl

[14] Neustroeva N. V., “Kontaktnaya zadacha dlya uprugikh tel raznykh razmernostei”, Vestnik NGU. Ser. Matematika, mekhanika, informatika, 8:4 (2008), 60–75