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

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

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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:3, 435–443

Bibliographic databases:

UDC: 539.3+517.97

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
\Bibitem{Pya16} \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 \vol 19 \issue 3 \pages 75--84 \mathnet{http://mi.mathnet.ru/sjim930} \crossref{https://doi.org/10.17377/sibjim.2016.19.307} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3588955} \elib{https://elibrary.ru/item.asp?id=26477435} \transl \jour J. Appl. Industr. Math. \yr 2016 \vol 10 \issue 3 \pages 435--443 \crossref{https://doi.org/10.1134/S1990478916030145} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84983541752} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. I. V. Fankina, “Optimalnoe upravlenie razmerom zhestkogo sloya konstruktsii”, Sib. zhurn. chist. i prikl. matem., 17:3 (2017), 86–97
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
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
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
6. I. V. Fankina, “O ravnovesii dvusloinoi uprugoi konstruktsii pri nalichii treschiny”, Sib. zhurn. industr. matem., 22:4 (2019), 107–120
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
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
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
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