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Sib. Zh. Ind. Mat., 2016, Volume 19, Number 3, Pages 75–84 (Mi sjim930)  

This article is cited in 9 scientific papers (total in 9 papers)

Optimal control of the shape of a layer shape in the equilibrium problem of elastic bodies with overlapping domains

E. V. Pyatkina

Lavrent'ev Institute of Hydrodynamics SB RAS, 15 Lavrent'ev av., 630090 Novosibirsk

Abstract: We consider the equilibrium problem for a two-layer elastic body. One of the plates contains a crack. The second is a disk centered at one of the crack tips. The spherical layer is glued by its edge to the first plate. The unique solvability is proved of the problem in the nonlinear setting. An optimal control problem is also considered. The radius of the second layer $a$ is chosen as the control function. It is assumed that $a$ is positive and takes values in a closed interval. We show that there exist a value of $a$ minimizing the functional that characterizes the change of the potential energy as the crack length increases and a value of $a$ that characterizes the opening of the crack.

Keywords: elastic plate, overlapping domain, crack with nonpenetration, optimal control problem.

DOI: https://doi.org/10.17377/sibjim.2016.19.307

Full text: PDF file (336 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:3, 435–443

Bibliographic databases:

UDC: 539.3+517.97
Received: 18.11.2015

Citation: E. V. Pyatkina, “Optimal control of the shape of a layer shape in the equilibrium problem of elastic bodies with overlapping domains”, Sib. Zh. Ind. Mat., 19:3 (2016), 75–84; J. Appl. Industr. Math., 10:3 (2016), 435–443

Citation in format AMSBIB
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\by E.~V.~Pyatkina
\paper Optimal control of the shape of a~layer shape in the equilibrium problem of elastic bodies with overlapping domains
\jour Sib. Zh. Ind. Mat.
\yr 2016
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\jour J. Appl. Industr. Math.
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\pages 435--443
\crossref{https://doi.org/10.1134/S1990478916030145}
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    This publication is cited in the following articles:
    1. N. P. Lazarev, E. M. Rudoy, “Optimal size of a rigid thin stiffener reinforcing an elastic plate on the outer edge”, ZAMM Z. Angew. Math. Mech., 97:9 (2017), 1120–1127  crossref  mathscinet  isi  scopus
    2. I. V. Fankina, “Optimalnoe upravlenie razmerom zhestkogo sloya konstruktsii”, Sib. zhurn. chist. i prikl. matem., 17:3 (2017), 86–97  mathnet  crossref
    3. N. Lazarev, G. Semenova, “An optimal size of a rigid thin stiffener reinforcing an elastic two-dimensional body on the outer edge”, J. Optim. Theory Appl., 178:2 (2018), 614–626  crossref  mathscinet  zmath  isi  scopus
    4. N. P. Lazarev, T. S. Popova, G. A. Rogerson, “Optimal control of the radius of a rigid circular inclusion in inhomogeneous two-dimensional bodies with cracks”, Z. Angew. Math. Phys., 69:3 (2018), 53  crossref  mathscinet  zmath  isi  scopus
    5. N. P. Lazarev, S. Das, M. P. Grigor'ev, “Optimal control of a thin rigid stiffener for a model describing equilibrium of a Timoshenko plate with a crack”, Sib. Electron. Math. Rep., 15 (2018), 1485–1497  mathnet  crossref  mathscinet  zmath  isi  scopus
    6. I. V. Fankina, “O ravnovesii dvusloinoi uprugoi konstruktsii pri nalichii treschiny”, Sib. zhurn. industr. matem., 22:4 (2019), 107–120  mathnet  crossref
    7. N. Lazarev, H. Itou, “Optimal location of a rigid inclusion in equilibrium problems for inhomogeneous Kirchhoff-Love plates with a crack”, Math. Mech. Solids, 24:12 (2019), 3743–3752  crossref  mathscinet  isi  scopus
    8. N. Lazarev, V. Everstov, “Optimal location of a rigid inclusion in equilibrium problems for inhomogeneous two-dimensional bodies with a crack”, ZAMM-Z. Angew. Math. Mech., 99:3 (2019), UNSP e201800268  crossref  mathscinet  isi  scopus
    9. I. V. Frankina, “The Equilibrium of a Two Layer Structure in the Presence of a Defect”, Sib. Electron. Math. Rep., 16 (2019), 959–974  mathnet  crossref  mathscinet  zmath  isi  scopus
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