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Sibirskii Zhurnal Industrial'noi Matematiki, 2011, Volume 14, Number 1, Pages 114–126 (Mi sjim656)  

This article is cited in 28 scientific papers (total in 28 papers)

On bending an elastic plate with a delaminated thin rigid inclusion

A. M. Khludnevab

a Lavrent'ev Institute of Hydrodynamics SB RAS, Novosibirsk, RUSSIA
b Novosibirsk State University, Novosibirsk, RUSSIA
References:
Abstract: Under study is the problem of bending an elastic plate with a thin rigid inclusion which may delaminate and form a crack. We find a system of boundary conditions valid on the faces of the crack and prove the existence of a solution. The problem of bending a plate with a volume rigid inclusion is also considered. We establish the convergence of solutions of this problem to a solution to the original problem as the size of the volume rigid inclusion tends to zero.
Keywords: plate, bending, rigid inclusion, crack, delamination.
Received: 30.03.2010
English version:
Journal of Applied and Industrial Mathematics, 2011, Volume 5, Issue 4, Pages 582–594
DOI: https://doi.org/10.1134/S1990478911040132
Bibliographic databases:
Document Type: Article
UDC: 539.3+517.958
Language: Russian
Citation: A. M. Khludnev, “On bending an elastic plate with a delaminated thin rigid inclusion”, Sib. Zh. Ind. Mat., 14:1 (2011), 114–126; J. Appl. Industr. Math., 5:4 (2011), 582–594
Citation in format AMSBIB
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\by A.~M.~Khludnev
\paper On bending an elastic plate with a~delaminated thin rigid inclusion
\jour Sib. Zh. Ind. Mat.
\yr 2011
\vol 14
\issue 1
\pages 114--126
\mathnet{http://mi.mathnet.ru/sjim656}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2951449}
\transl
\jour J. Appl. Industr. Math.
\yr 2011
\vol 5
\issue 4
\pages 582--594
\crossref{https://doi.org/10.1134/S1990478911040132}
Linking options:
  • https://www.mathnet.ru/eng/sjim656
  • https://www.mathnet.ru/eng/sjim/v14/i1/p114
  • This publication is cited in the following 28 articles:
    1. N. A. Nikolaeva, “Plastina Kirkhgofa — Lyava s ploskim zhestkim vklyucheniem”, Chelyab. fiz.-matem. zhurn., 8:1 (2023), 29–46  mathnet  crossref
    2. 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  crossref
    3. N. P. Lazarev, V. A. Kovtunenko, “Asymptotic analysis of the problem of equilibrium of an inhomogeneous body with hinged rigid inclusions of various widths”, J. Appl. Mech. Tech. Phys., 64:5 (2024), 911–920  mathnet  mathnet  crossref  crossref
    4. Zhen-Liang Hu, Ying Yang, Xian-Fang Li, “Singular elastic field induced by a rigid line adhering to a micro/nanoscale plate during bending”, Applied Mathematical Modelling, 108 (2022), 567  crossref
    5. Lazarev N., “Inverse Problem For Cracked Inhomogeneous Kirchhoff-Love Plate With Two Hinged Rigid Inclusions”, Bound. Value Probl., 2021:1 (2021), 88  crossref  mathscinet  isi  scopus
    6. Hu Zh.-L., Yang Y., Li X.-F., “Singular Elastic Field Induced By a Rigid Line Inclusion in a Thin Nanoplate With Surface Elasticity”, Int. J. Mech. Sci., 198 (2021), 106386  crossref  isi  scopus
    7. Lazarev N.P. Semenova G.M. Romanova N.A., “On a Limiting Passage as the Thickness of a Rigid Inclusions in An Equilibrium Problem For a Kirchhoff Love Plate With a Crack”, J. Sib. Fed. Univ.-Math. Phys., 14:1 (2021), 28–41  mathnet  crossref  mathscinet  isi  scopus
    8. Rudoy E., “Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions”, Technologies, 8:4 (2020), 59  crossref  isi
    9. Furtsev A. Rudoy E., “Variational Approach to Modeling Soft and Stiff Interfaces in the Kirchhoff-Love Theory of Plates”, Int. J. Solids Struct., 202 (2020), 562–574  crossref  isi  scopus
    10. Pyatkina V E., “a Contact of Two Elastic Plates Connected Along a Thin Rigid Inclusion”, Sib. Electron. Math. Rep., 17 (2020), 1797–1815  mathnet  crossref  mathscinet  zmath  isi  scopus
    11. G E Semenova, N P Lazarev, “Unique solvability of an equilibrium problem for a Kirchhoff-Love plate with a crack along the boundary of a flat rigid inclusion”, J. Phys.: Conf. Ser., 1666:1 (2020), 012046  crossref
    12. N. A. Nikolaeva, “On equilibrium of the elastic bodies with cracks crossing thin inclusions”, J. Appl. Industr. Math., 13:4 (2019), 685–697  mathnet  crossref  crossref
    13. A. I. Furtsev, “On Contact Between a Thin Obstacle and a Plate Containing a Thin Inclusion”, J Math Sci, 237:4 (2019), 530  crossref
    14. Konstantin A. Shishmarev, Alexander A. Papin, “Uniqueness of a solution of an ice plate oscillation problem in a channel”, Zhurn. SFU. Ser. Matem. i fiz., 11:4 (2018), 449–458  mathnet  crossref
    15. 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  mathnet  crossref  crossref  elib
    16. V. V. Shcherbakov, “Shape derivative of the energy functional for the bending of elastic plates with thin defects”, All-Russian Conference With International Participation Modern Problems of Continuum Mechanics and Explosion Physics Dedicated to the 60th Anniversary of Lavrentyev Institute of Hydrodynamics SB RAS, Journal of Physics Conference Series, 894, eds. Chesnokov A., Pruuel E., Shelukhin V., IOP Publishing Ltd, 2017, UNSP 012084  crossref  isi  scopus
    17. I. V. Frankina, “A contact problem for an elastic plate with a thin rigid inclusion”, J. Appl. Industr. Math., 10:3 (2016), 333–340  mathnet  crossref  crossref  mathscinet  elib
    18. N. P. Lazarev, “Optimal control of the size of rigid inclusion in equilibrium problem for inhomogeneous Timoshenko-type plate with crack”, J. Math. Sci., 228:4 (2018), 409–420  mathnet  crossref  crossref
    19. N. P. Lazarev, “Optimalnoe upravlenie razmerom zhestkogo vklyucheniya v zadache o ravnovesii neodnorodnogo trekhmernogo tela s treschinoi”, Matematicheskie zametki SVFU, 23:2 (2016), 51–64  mathnet  elib
    20. T. Popova, G. A. Rogerson, “On the problem of a thin rigid inclusion embedded in a Maxwell material”, ZAMM Z. Angew. Math. Phys., 67:4 (2016), 105  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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