Abstract:
Under consideration is the problem of contact between a plate and a beam. It is assumed that no mutual penetration between the plate and the beam can occur, and so an appropriate nonpenetration condition is used. On the other hand, the adhesion of the bodies is taken into account which is characterized by a numerical adhesion parameter. We study the existence and uniqueness of a solution for the contact problem as well as the passage to the limit with respect to the adhesion parameter. The accompanying optimal control problem is investigated in which the adhesion parameter acts as a control parameter.
Citation:
A. I. Furtsev, “A contact problem for a plate and a beam in presence of adhesion”, Sib. Zh. Ind. Mat., 22:2 (2019), 105–117; J. Appl. Industr. Math., 13:2 (2019), 208–218
\Bibitem{Fur19}
\by A.~I.~Furtsev
\paper A contact problem for a plate and a beam in presence of adhesion
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 2
\pages 105--117
\mathnet{http://mi.mathnet.ru/sjim1047}
\crossref{https://doi.org/10.33048/sibjim.2019.22.210}
\elib{https://elibrary.ru/item.asp?id=41637287}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 2
\pages 208--218
\crossref{https://doi.org/10.1134/S1990478919020030}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85067282632}
Linking options:
https://www.mathnet.ru/eng/sjim1047
https://www.mathnet.ru/eng/sjim/v22/i2/p105
This publication is cited in the following 7 articles:
N. P. Lazarev, G. M. Semenova, E. S. Efimova, “Optimalnoe upravlenie vneshnimi nagruzkami v zadache o ravnovesii sostavnogo tela, kontaktiruyuschego s zhestkim vklyucheniem s ostroi kromkoi”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody kraevykh zadach. Pontryaginskie chteniya—XXXIV», Voronezh, 3-9 maya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 230, VINITI RAN, M., 2023, 88–95
N. P. Lazarev, E. F. Sharin, E. S. Efimova, “Equilibrium Problem for an Inhomogeneous Kirchhoff–Love Plate Contacting with a Partially Delaminated Inclusion”, Lobachevskii J Math, 44:10 (2023), 4127
Nyurgun Lazarev, Galina Semenova, “Optimal control of loads for an equilibrium problem describing a point contact of an elastic body with a sharp-shaped stiffener”, Z. Angew. Math. Phys., 73:5 (2022)
E. M. Rudoy, H. Itou, N. P. Lazarev, “Asymptotic justification of the models of thin inclusions in an elastic body in the antiplane shear problem”, J. Appl. Industr. Math., 15:1 (2021), 129–140
E. Rudoy, “Asymptotic justification of models of plates containing inside hard thin inclusions”, Technologies, 8:4 (2020), 59
A. Furtsev, E. Rudoy, “Variational approach to modeling soft and stiff interfaces in the Kirchhoff-Love theory of plates”, Int. J. Solids Struct., 202 (2020), 562–574
A. I. Furtsev, “the Unilateral Contact Problem For a Timoshenko Plate and a Thin Elastic Obstacle”, Sib. Electron. Math. Rep., 17 (2020), 364–379
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