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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 4, Pages 142–151 (Mi sjim812)  

This article is cited in 35 scientific papers (total in 35 papers)

Existence of an optimal shape for thin rigid inclusions in the Kirchhoff–Love plate

V. V. Shcherbakov

Lavrent'ev Institute of Hydrodynamics SB RAS, 15 Lavrent'ev av., 630090 Novosibirsk
References:
Abstract: The paper deals with an optimal control problem for the elliptic system of equations describing an equilibrium of a Kirchhoff–Love plate with delaminated thin rigid inclusion. It is required to minimize the mean square integral deviation of the bending moment from the function given on the exterior boundary. The inclusion shape is considered as the control function. The solvability of the problem is established.
Keywords: Kirchhoff–Love plate model, thin rigid inclusion, crack, nonlinear boundary conditions, optimal control.
Received: 17.07.2013
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 1, Pages 97–105
DOI: https://doi.org/10.1134/S1990478914010116
Bibliographic databases:
Document Type: Article
UDC: 539.95+517.977
Language: Russian
Citation: V. V. Shcherbakov, “Existence of an optimal shape for thin rigid inclusions in the Kirchhoff–Love plate”, Sib. Zh. Ind. Mat., 16:4 (2013), 142–151; J. Appl. Industr. Math., 8:1 (2014), 97–105
Citation in format AMSBIB
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\by V.~V.~Shcherbakov
\paper Existence of an optimal shape for thin rigid inclusions in the Kirchhoff--Love plate
\jour Sib. Zh. Ind. Mat.
\yr 2013
\vol 16
\issue 4
\pages 142--151
\mathnet{http://mi.mathnet.ru/sjim812}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3234800}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 1
\pages 97--105
\crossref{https://doi.org/10.1134/S1990478914010116}
Linking options:
  • https://www.mathnet.ru/eng/sjim812
  • https://www.mathnet.ru/eng/sjim/v16/i4/p142
  • This publication is cited in the following 35 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. Nyurgun P. Lazarev, “Equilibrium problem for a thermoelastic Kirchhoff–Love plate with a delaminated flat rigid inclusion”, Phil. Trans. R. Soc. A., 380:2236 (2022)  crossref
    4. Nyurgun Lazarev, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 020011  crossref
    5. 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
    6. Rudoy E., “Asymptotic Justification of Models of Plates Containing Inside Hard Thin Inclusions”, Technologies, 8:4 (2020), 59  crossref  isi
    7. 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
    8. Lazarev N.P., “Equilibrium Problem For An Thermoelastic Kirchhoff-Love Plate With a Nonpenetration Condition For Known Configurations of Crack Edges”, Sib. Electron. Math. Rep., 17 (2020), 2096–2104  mathnet  crossref  mathscinet  zmath  isi  scopus
    9. 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
    10. 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
    11. Khludnev A., “On Thin Timoshenko Inclusions in Elastic Bodies With Defects”, Arch. Appl. Mech., 89:8 (2019), 1691–1704  crossref  mathscinet  isi  scopus
    12. A. I. Furtsev, “On Contact Between a Thin Obstacle and a Plate Containing a Thin Inclusion”, J Math Sci, 237:4 (2019), 530  crossref
    13. A. M. Khludnev, T. S. Popova, “Zadacha sopryazheniya uprugogo vklyucheniya Timoshenko i poluzhestkogo vklyucheniya”, Matematicheskie zametki SVFU, 25:1 (2018), 73–89  mathnet  crossref  elib
    14. A. M. Khludnev, “Equilibrium of an elastic body with closely spaced thin inclusions”, Comput. Math. Math. Phys., 58:10 (2018), 1660–1672  mathnet  crossref  crossref  isi  elib
    15. N. Lazarev, N. Neustroeva, “Optimal control of rigidity parameter of elastic inclusions in composite plate with a crack”, Mathematics and Computing (ICMC 2018), Springer Proceedings in Mathematics & Statistics, 253, eds. D. Ghosh, D. Giri, R. Mohapatra, K. Sakurai, E. Savas, T. Som, Springer, 2018, 67–77  crossref  mathscinet  isi  scopus
    16. A. M. Khludnev, “Asymptotics of anisotropic weakly curved inclusions in an elastic body”, J. Appl. Industr. Math., 11:1 (2017), 88–98  mathnet  crossref  crossref  mathscinet  elib
    17. N. V. Neustroeva, N. P. Lazarev, “The derivative of the energy functional in an equilibrium problem for a Timoshenko plate with a crack on the boundary of an elastic inclusion”, J. Appl. Industr. Math., 11:2 (2017), 252–262  mathnet  crossref  crossref  elib
    18. A. M. Khludnev, T. S. Popova, “Timoshenko inclusions in elastic bodies crossing an external boundary at zero angle”, Acta Mech. Solida Sin., 30:3 (2017), 327–333  crossref  mathscinet  isi  scopus
    19. A. M. Khludnev, L. Faella, C. Perugia, “Optimal control of rigidity parameters of thin inclusions in composite materials”, ZAMM Z. Angew. Math. Phys., 68:2 (2017), 47  crossref  mathscinet  zmath  isi  scopus
    20. A. M. Khludnev, T. S. Popova, “On Crack Propagations in Elastic Bodies With Thin Inclusions”, Sib. Electron. Math. Rep., 14 (2017), 586–599  mathnet  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    Сибирский журнал индустриальной математики
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