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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 1, Pages 294–304 (Mi timm1165)  
This article is cited in 3 scientific papers (total in 3 papers)

Optimal shapes of cracks in a viscoelastic body

V. V. Shcherbakova, O. I. Krivorot'kob

a Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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Abstract: We consider an optimal control problem for equations describing the quasistatic deformation of a linear viscoelastic body. There is a crack in the body, and displacements of opposite faces of the crack are constrained by the nonpenetration condition. The continuous dependence of the solution to the equilibrium problem on the shape of the crack is established. In particular, we prove the existence of a shape for which the crack opening is minimal
Keywords: viscoelasticity; crack; nonpenetration condition; optimal control; fictitious domain method.
Received: 17.09.2014
Bibliographic databases:
Document Type: Article
UDC: 517.97+539.3
Language: Russian
Citation: V. V. Shcherbakov, O. I. Krivorot'ko, “Optimal shapes of cracks in a viscoelastic body”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 1, 2015, 294–304
Citation in format AMSBIB
\Bibitem{ShcKri15}
\by V.~V.~Shcherbakov, O.~I.~Krivorot'ko
\paper Optimal shapes of cracks in a viscoelastic body
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 1
\pages 294--304
\mathnet{http://mi.mathnet.ru/timm1165}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3407902}
\elib{https://elibrary.ru/item.asp?id=23137999}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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