Abstract:
This paper deals with the unilateral contact problem for two elastic plates located at a given angle to each other. One of the plates contains a rigid inclusion and is deformed in its plane with the other one being vertically deformed. Assuming that the solution is smooth, the differential statement being equivalent to the variational formulation is justified. We analyse different configurations of the rigid inclusion. The problem with rigid inclusion is shown to be obtained as the limiting one of the family of elastic problems.
Citation:
T. A. Rotanova, “The Unilateral Contact Problem for Two Plates One of them Containing a Rigid Inclusion”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 11:1 (2011), 87–98; J. Math. Sci., 188:4 (2013), 452–462
\Bibitem{Rot11}
\by T.~A.~Rotanova
\paper The Unilateral Contact Problem for Two Plates One of them Containing a~Rigid Inclusion
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2011
\vol 11
\issue 1
\pages 87--98
\mathnet{http://mi.mathnet.ru/vngu72}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 188
\issue 4
\pages 452--462
\crossref{https://doi.org/10.1007/s10958-012-1142-3}
Linking options:
https://www.mathnet.ru/eng/vngu72
https://www.mathnet.ru/eng/vngu/v11/i1/p87
This publication is cited in the following 15 articles:
Alexander Khludnev, “T-shape inclusion in elastic body with a damage parameter”, Journal of Computational and Applied Mathematics, 393 (2021), 113540
Alexander Khludnev, Tatyana Popova, “Equilibrium problem for elastic body with delaminated T-shape inclusion”, Journal of Computational and Applied Mathematics, 376 (2020), 112870
V.A. Krysko, J. Awrejcewicz, I.V. Papkova, O.A. Saltykova, A.V. Krysko, “Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses”, International Journal of Nonlinear Sciences and Numerical Simulation, 20:3-4 (2019), 373
A. I. Furtsev, “A contact problem for a plate and a beam in presence of adhesion”, J. Appl. Industr. Math., 13:2 (2019), 208–218
V. A. Puris, “The conjugation problem for thin elastic and rigid inclusions in an elastic body”, J. Appl. Industr. Math., 11:3 (2017), 444–452
A. M. Khludnev, T. S. Popova, “On the mechanical interplay between Timoshenko and semirigid inclusions embedded in elastic bodies”, Z Angew Math Mech, 97:11 (2017), 1406
AM Khludnev, L Faella, TS Popova, “Junction problem for rigid and Timoshenko elastic inclusions in elastic bodies”, Mathematics and Mechanics of Solids, 22:4 (2017), 737
A.M. Khludnev, T.S. Popova, “Timoshenko inclusions in elastic bodies crossing an external boundary at zero angle”, Acta Mechanica Solida Sinica, 30:3 (2017), 327
Luisa Faella, Alexander Khludnev, “Junction problem for elastic and rigid inclusions in elastic bodies”, Math Methods in App Sciences, 39:12 (2016), 3381
Alexander Khludnev, Tatiana Popova, “Junction problem for rigid and semirigid inclusions in elastic bodies”, Arch Appl Mech, 86:9 (2016), 1565
A. M. Khludnev, “Optimalnoe upravlenie vklyucheniyami v uprugom tele, peresekayuschimi vneshnyuyu granitsu”, Sib. zhurn. industr. matem., 18:4 (2015), 75–87
A.M. Khludnev, “Optimal control of a thin rigid inclusion intersecting the boundary of an elastic body”, Journal of Applied Mathematics and Mechanics, 79:5 (2015), 493
A. M. Khludnev, “On an equilibrium problem for a two-layer elastic body with a crack”, J. Appl. Industr. Math., 7:3 (2013), 370–379
Khludnev A., “Contact problems for elastic bodies with rigid inclusions”, Quart. Appl. Math., 70:2 (2012), 269–284
Khludnev A., “Thin rigid inclusions with delaminations in elastic plates”, Eur. J. Mech. A Solids, 32 (2012), 69–75
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