V. V. Shcherbakov, “On an optimal control problem of thin inclusions shapes in elastic bodies”, Sib. Zh. Ind. Mat., 16:1 (2013), 138–147; J. Appl. Industr. Math., 7:3 (2013), 435

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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 1, Pages 138–147 (Mi sjim774)

This article is cited in 32 scientific papers (total in 32 papers)

On an optimal control problem of thin inclusions shapes in elastic bodies

V. V. Shcherbakov

Lavrentiev Institute of Hydrodynamics of the SDRAS, Novosibirsk, Russia

Full-text PDF (260 kB) Citations (32)

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Abstract: The paper concerns an optimal control problem for a 2D elastic body with a thin rigid inclusion and a crack. The thin rigid inclusion is supposed to delaminate and contain a kink. Inequality type boundary conditions are imposed at the crack faces to provide a mutual nonpenetration between the crack faces. The cost functional characterizes the derivative of the energy function with respect to the crack length. The position of the kink is considered as a control function. The main result is the existence of a solution to the optimal control problem.

Keywords: crack, thin rigid inclusion, nonlinear boundary conditions, optimal control, derivative of energy functional.

Received: 20.09.2012

English version:
Journal of Applied and Industrial Mathematics, 2013, Volume 7, Issue 3, Pages 435–443
DOI: https://doi.org/10.1134/S1990478913030174

Bibliographic databases:

Document Type: Article

UDC: 539.375+517.977

Language: Russian

Citation: V. V. Shcherbakov, “On an optimal control problem of thin inclusions shapes in elastic bodies”, Sib. Zh. Ind. Mat., 16:1 (2013), 138–147; J. Appl. Industr. Math., 7:3 (2013), 435–443

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sjim774

https://www.mathnet.ru/eng/sjim/v16/i1/p138

This publication is cited in the following 32 articles:

N. A. Nikolaeva, “Zadacha o ravnovesii uprugogo tela s treschinoi i tonkimi vklyucheniyami, kotorye sopryazheny mezhdu soboi”, Dalnevost. matem. zhurn., 24:1 (2024), 73–95
E. V. Pyatkina, “Ravnovesie trekhsloinoi plastiny s treschinoi”, Sib. zhurn. industr. matem., 25:1 (2022), 105–120
Natalia Nikolaeva, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 020030
E. V. Pyatkina, “Equilibrium of a Three-Layer Plate with a Crack”, J. Appl. Ind. Math., 16:1 (2022), 122
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
Khludnev A.M., “On Modeling Thin Inclusions in Elastic Bodies With a Damage Parameter”, Math. Mech. Solids, 24:9 (2019), 2742–2753
A. M. Khludnev, T. S. Popova, “Zadacha sopryazheniya uprugogo vklyucheniya Timoshenko i poluzhestkogo vklyucheniya”, Matematicheskie zametki SVFU, 25:1 (2018), 73–89
A. M. Khludnev, “Equilibrium of an elastic body with closely spaced thin inclusions”, Comput. Math. Math. Phys., 58:10 (2018), 1660–1672
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
A. M. Khludnev, “On modeling elastic bodies with defects”, Sib. Electron. Math. Rep., 15 (2018), 153–166
A. M. Khludnev, “Asymptotics of anisotropic weakly curved inclusions in an elastic body”, J. Appl. Industr. Math., 11:1 (2017), 88–98
V. A. Puris, “The conjugation problem for thin elastic and rigid inclusions in an elastic body”, J. Appl. Industr. Math., 11:3 (2017), 444–452
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
E. Rudoy, “On numerical solving a rigid inclusions problem in 2D elasticity”, ZAMM Z. Angew. Math. Phys., 68:1 (2017), 19
A. M. Khludnev, T. S. Popova, “On Crack Propagations in Elastic Bodies With Thin Inclusions”, Sib. Electron. Math. Rep., 14 (2017), 586–599
A. Khludnev, “Rigidity parameter identification for thin inclusions located inside elastic bodies”, J. Optim. Theory Appl., 172:1 (2017), 281–297
I. V. Frankina, “Optimal control of the rigid layer size of the construction”, J. Math. Sci., 237:4 (2019), 521–529
E. M. Rudoy, “Numerical solution of an equilibrium problem for an elastic body with a delaminated thin rigid inclusion”, J. Appl. Industr. Math., 10:2 (2016), 264–276
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
N. P. Lazarev, “Optimalnoe upravlenie razmerom zhestkogo vklyucheniya v zadache o ravnovesii neodnorodnogo trekhmernogo tela s treschinoi”, Matematicheskie zametki SVFU, 23:2 (2016), 51–64

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

Сибирский журнал индустриальной математики

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