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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
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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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Linking options:
http://mi.mathnet.ru/eng/sjim930 http://mi.mathnet.ru/eng/sjim/v19/i3/p75
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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
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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
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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
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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
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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
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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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