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Sib. Zh. Ind. Mat., 2013, Volume 16, Number 4, Pages 142–151 (Mi sjim812)  

This article is cited in 24 scientific papers (total in 24 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

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.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:1, 97–105

Bibliographic databases:

UDC: 539.95+517.977
Received: 17.07.2013

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
\Bibitem{Shc13}
\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://www.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}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Khludnev, “Optimalnoe upravlenie vklyucheniyami v uprugom tele, peresekayuschimi vneshnyuyu granitsu”, Sib. zhurn. industr. matem., 18:4 (2015), 75–87  mathnet  crossref  mathscinet  elib
    2. N. A. Nikolaeva, “Method of fictitious areas in a task about balance of a plate of Kirchhoff–Lyava”, J. Math. Sci., 221:6 (2017), 872–882  mathnet  crossref  crossref
    3. Lazarev N., “Existence of An Optimal Size of a Delaminated Rigid Inclusion Embedded in the Kirchhoff-Love Plate”, Bound. Value Probl., 2015, 180  crossref  isi
    4. Khludnev A.M., “Optimal Control of a Thin Rigid Inclusion Intersecting the Boundary of An Elastic Body”, Pmm-J. Appl. Math. Mech., 79:5 (2015), 493–499  crossref  isi
    5. E. V. Pyatkina, “Optimal control of the shape of a layer shape in the equilibrium problem of elastic bodies with overlapping domains”, J. Appl. Industr. Math., 10:3 (2016), 435–443  mathnet  crossref  crossref  mathscinet  elib
    6. 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
    7. 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
    8. A. M. Khludnev, T. S. Popova, “Ob ierarkhii tonkikh vklyuchenii v uprugikh telakh”, Matematicheskie zametki SVFU, 23:1 (2016), 87–107  mathnet  elib
    9. A. Khludnev, T. Popova, “Junction problem for rigid and semirigid inclusions in elastic bodies”, Arch. Appl. Mech., 86:9 (2016), 1565–1577  crossref  isi
    10. V. Shcherbakov, “Shape optimization of rigid inclusions for elastic plates with cracks”, ZAMM Z. Angew. Math. Phys., 67:3 (2016), 71  crossref  isi
    11. N. P. Lazarev, “Optimal control of the thickness of a rigid inclusion in equilibrium problems for inhomogeneous two-dimensional bodies with a crack”, ZAMM Z. Angew. Math. Mech., 96:4 (2016), 509–518  crossref  isi
    12. N. P. Lazarev, H. Itou, N. V. Neustroeva, “Fictitious domain method for an equilibrium problem of the Timoshenko-type plate with a crack crossing the external boundary at zero angle”, Jpn. J. Ind. Appl. Math., 33:1 (2016), 63–80  crossref  isi
    13. N. Lazarev, T. Popova, G. Semenova, “Existence of an optimal size of a rigid inclusion for an equilibrium problem of a Timoshenko plate with Signorini-type boundary condition”, J. Inequal. Appl., 2016, 18  crossref  isi
    14. E. V. Pyatkina, “On control problem for two-layers elastic body with a crack”, J. Math. Sci., 230:1 (2018), 159–166  mathnet  crossref  crossref
    15. 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
    16. 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
    17. 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
    18. 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
    19. 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
    20. A. Khludnev, “Rigidity parameter identification for thin inclusions located inside elastic bodies”, J. Optim. Theory Appl., 172:1 (2017), 281–297  crossref  mathscinet  zmath  isi  scopus
    21. 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
    22. 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
    23. 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
    24. Khludnev A., “On Thin Timoshenko Inclusions in Elastic Bodies With Defects”, Arch. Appl. Mech., 89:8 (2019), 1691–1704  crossref  mathscinet  isi  scopus
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