Abstract:
Under study is the equilibrium problem for two plates with possible contact between them. It is assumed that the plates of the same shape and size are located in parallel without a gap. The clamped edge condition is stated on their lateral boundaries. The deflections of the plates satisfy the nonpenetration condition. There is a vertical crack in the lower layer. Along one edge of the crack, the plates are rigidly glued with each other. The three cases are studied in the paper: In the first case, the both layers are elastic, whereas in the second and third cases, the lower or upper layer respectively is rigid. To describe the displacement of the points of elastic plates, the Kirchhoff–Love model is used. Variational and differential formulations of the problems are derived and the unique solvability of the problems is established.
Keywords:
Kirchhoff–Love plate, contact problem, crack with nonpenetration condition.
Citation:
E. V. Pyatkina, “A contact problem for two plates of the same shape glued along one edge of a crack”, Sib. Zh. Ind. Mat., 21:2 (2018), 79–92; J. Appl. Industr. Math., 12:2 (2018), 334–346
\Bibitem{Pya18}
\by E.~V.~Pyatkina
\paper A contact problem for two plates of the same shape glued along one edge of a~crack
\jour Sib. Zh. Ind. Mat.
\yr 2018
\vol 21
\issue 2
\pages 79--92
\mathnet{http://mi.mathnet.ru/sjim1001}
\crossref{https://doi.org/10.17377/sibjim.2018.21.207}
\elib{https://elibrary.ru/item.asp?id=35459103}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 2
\pages 334--346
\crossref{https://doi.org/10.1134/S1990478918020138}
\elib{https://elibrary.ru/item.asp?id=35536102}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047851771}
Linking options:
https://www.mathnet.ru/eng/sjim1001
https://www.mathnet.ru/eng/sjim/v21/i2/p79
This publication is cited in the following 8 articles:
N. P. Lazarev, G. M. Semenova, E. D. Fedotov, “Optimal Control of the Obstacle Inclination Angle in the Contact Problem for a Kirchhoff–Love Plate”, Lobachevskii J Math, 45:11 (2024), 5383
N. P. Lazarev, G. M. Semenova, E. D. Fedotov, “An Equilibrium Problem for a Kirchhoff–Love Plate, Contacting an Obstacle by Top and Bottom Edges”, Lobachevskii J Math, 44:2 (2023), 614
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
N. P. Lazarev, G. M. Semenova, “Equilibrium problem for a Timoshenko plate
with a geometrically nonlinear condition of nonpenetration
for a vertical crack”, J. Appl. Industr. Math., 14:3 (2020), 532–540
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
I. V. Frankina, “On the equilibrium of a two-layer elastic structure with a crack”, J. Appl. Industr. Math., 13:4 (2019), 629–641
E. V. Pyatkina, “A Problem of Glueing of Two Kirchhoff - Love Plates”, Sib. Electron. Math. Rep., 16 (2019), 1351–1374
I. V. Frankina, “The Equilibrium of a Two Layer Structure in the Presence of a Defect”, Sib. Electron. Math. Rep., 16 (2019), 959–974
Citation in format AMSBIB
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