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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2015, Volume 56, Issue 2, Pages 178–187
DOI: https://doi.org/10.15372/PMTF20150218 (Mi pmtf976) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Choosing an optimal shape of thin rigid inclusions in elastic bodies

V. V. Shcherbakovab

a Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
b Novosibirsk State University, Novosibirsk, 630090, Russia
Full-text PDF (264 kB) Citations (10)
DOI: https://doi.org/10.15372/PMTF20150218
Abstract: The optimal control problem for a three-dimensional elastic body containing a thin rigid inclusion as a surface is studied. It is assumed that the inclusion delaminates, which is why there is a crack between the elastic domain and the inclusion. The boundary conditions on the crack faces that exclude mutual penetration of the points of the body and inclusion are considered. The cost functional that characterizes the deviation of the surface force vector from the function prescribed on the external boundary is used; in this case, the inclusion shape is considered as a control function. It is proven that a solution of the described problem exists.
Keywords: thin rigid inclusion, crack, nonlinear boundary conditions, variational inequality, optimal control.
Received: 15.03.2013
Revised: 27.02.2014
English version:
Journal of Applied Mechanics and Technical Physics, 2015, Volume 56, Issue 2, Pages 321–329
DOI: https://doi.org/10.1134/S0021894415020182
Bibliographic databases:
Document Type: Article
UDC: 539.3+517.977
Language: Russian
Citation: V. V. Shcherbakov, “Choosing an optimal shape of thin rigid inclusions in elastic bodies”, Prikl. Mekh. Tekh. Fiz., 56:2 (2015), 178–187; J. Appl. Mech. Tech. Phys., 56:2 (2015), 321–329
Citation in format AMSBIB
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\by V.~V.~Shcherbakov
\paper Choosing an optimal shape of thin rigid inclusions in elastic bodies
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2015
\vol 56
\issue 2
\pages 178--187
\mathnet{http://mi.mathnet.ru/pmtf976}
\crossref{https://doi.org/10.15372/PMTF20150218}
\elib{https://elibrary.ru/item.asp?id=23592083}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2015
\vol 56
\issue 2
\pages 321--329
\crossref{https://doi.org/10.1134/S0021894415020182}
Linking options:
  • https://www.mathnet.ru/eng/pmtf976
  • https://www.mathnet.ru/eng/pmtf/v56/i2/p178
    • This publication is cited in the following 10 articles:
    1. A. I. Furtsev, E. M. Rudoy, S. A. Sazhenkov, “On hyperelastic solid with thin rigid inclusion and crack subjected to global injectivity condition”, Phil. Trans. R. Soc. A., 382:2277 (2024)  crossref
    2. Nyurgun P. Lazarev, Galina M. Semenova, Natalya A. Romanova, “On a limiting passage as the thickness of a rigid inclusions in an equilibrium problem for a Kirchhoff-Love plate with a crack”, Zhurn. SFU. Ser. Matem. i fiz., 14:1 (2021), 28–41  mathnet  crossref
    3. Victor A. Kovtunenko, Kohji Ohtsuka, “Inverse problem of shape identification from boundary measurement for Stokes equations: Shape differentiability of Lagrangian”, Journal of Inverse and Ill-posed Problems, 2020  crossref
    4. A. M. Khludnev, T. S. Popova, “The junction problem for two weakly curved inclusions in an elastic body”, Siberian Math. J., 61:4 (2020), 743–754  mathnet  mathnet  crossref  crossref  isi  scopus
    5. Alexander Khludnev, Tatyana Popova, “Equilibrium problem for elastic body with delaminated T-shape inclusion”, Journal of Computational and Applied Mathematics, 376 (2020), 112870  crossref
    6. A. I. Furtsev, “On Contact Between a Thin Obstacle and a Plate Containing a Thin Inclusion”, J Math Sci, 237:4 (2019), 530  crossref
    7. A. M. Khludnev, “On modeling thin inclusions in elastic bodies with a damage parameter”, Mathematics and Mechanics of Solids, 24:9 (2019), 2742  crossref
    8. Alexander Khludnev, Tatiana Popova, “Semirigid inclusions in elastic bodies: Mechanical interplay and optimal control”, Computers & Mathematics with Applications, 77:1 (2019), 253  crossref
    9. A. M. Khludnev, “Inverse problems for elastic body with closely located thin inclusions”, Z. Angew. Math. Phys., 70:5 (2019)  crossref
    10. Evgeny Rudoy, “On numerical solving a rigid inclusions problem in 2D elasticity”, Z. Angew. Math. Phys., 68:1 (2017)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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