Abstract:
Under study is some problem concerning the equilibrium of a two-layer structure
whose layers are some elastic plates.
The upper layer is glued to the lower one along a part of the edge.
The behavior of the plates is modelled
in the framework of the plane theory of elasticity.
Along the gluing line in the lower layer,
there is a crack crossing the external boundary at zero angle.
On the crack faces, the nonlinear boundary conditions are imposed
that exclude their mutual penetration.
The solvability of the equilibrium problem is considered
as well as the behavior of the solution in the case
when the elasticity moduli of upper plate tend to zero or to infinity.
Citation:
I. V. Frankina, “On the equilibrium of a two-layer elastic structure with a crack”, Sib. Zh. Ind. Mat., 22:4 (2019), 107–120; J. Appl. Industr. Math., 13:4 (2019), 629–641
\Bibitem{Fan19}
\by I.~V.~Frankina
\paper On the equilibrium of a two-layer elastic structure with a crack
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 4
\pages 107--120
\mathnet{http://mi.mathnet.ru/sjim1070}
\crossref{https://doi.org/10.33048/sibjim.2019.22.411}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 4
\pages 629--641
\crossref{https://doi.org/10.1134/S1990478919040069}
Linking options:
https://www.mathnet.ru/eng/sjim1070
https://www.mathnet.ru/eng/sjim/v22/i4/p107
This publication is cited in the following 4 articles:
Alexander Khludnev, “On equilibrium of a two-layer elastic structure with a crack in non-coercive case”, Z. Angew. Math. Phys., 75:3 (2024)
E. V. Pyatkina, “Ravnovesie trekhsloinoi plastiny s treschinoi”, Sib. zhurn. industr. matem., 25:1 (2022), 105–120
E. V. Pyatkina, “Equilibrium of a Three-Layer Plate with a Crack”, J. Appl. Ind. Math., 16:1 (2022), 122
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
Citation in format AMSBIB
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