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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2012, Volume 53, Issue 2, Pages 175–185 (Mi pmtf1357)  
This article is cited in 5 scientific papers (total in 5 papers)

Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack

N. P. Lazarevab

a Research Institute of Mathematics, Ammosov North-East Federal University, Yakutsk, 677000, Russia
b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (280 kB) Citations (5)
Abstract: The variational formulation of the equilibrium problem for a Timoshenko plate containing a vertical plane crack is considered. Nonpenetration conditions in the form of inequalities (Signorini type conditions) are specified on the crack faces. The behavior of the solution and the corresponding energy functional of the plate with variation in the crack length is analyzed. A formula for the derivative of the energy functional along the crack length is obtained. The solutions are found to continuously depend on the parameter characterizing the crack length.
Keywords: crack, variational inequality, Timoshenko plate, energy functional, derivative of the energy functional.
Received: 02.02.2011
Accepted: 01.07.2011
English version:
Journal of Applied Mechanics and Technical Physics, 2012, Volume 53, Issue 2, Pages 299–307
DOI: https://doi.org/10.1134/S0021894412020198
Bibliographic databases:
Document Type: Article
UDC: 539.375
Language: Russian
Citation: N. P. Lazarev, “Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack”, Prikl. Mekh. Tekh. Fiz., 53:2 (2012), 175–185; J. Appl. Mech. Tech. Phys., 53:2 (2012), 299–307
Citation in format AMSBIB
\Bibitem{Laz12}
\by N.~P.~Lazarev
\paper Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2012
\vol 53
\issue 2
\pages 175--185
\mathnet{http://mi.mathnet.ru/pmtf1357}
\elib{https://elibrary.ru/item.asp?id=17651514}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2012
\vol 53
\issue 2
\pages 299--307
\crossref{https://doi.org/10.1134/S0021894412020198}
Linking options:
  • https://www.mathnet.ru/eng/pmtf1357
  • https://www.mathnet.ru/eng/pmtf/v53/i2/p175
    • This publication is cited in the following 5 articles:
    1. Nyurgun Lazarev, Galina Semenova, “On the connection between two equilibrium problems for cracked bodies in the cases of thin and volume rigid inclusions”, Bound Value Probl, 2019:1 (2019)  crossref
    2. Nyurgun Lazarev, Mark Grigoryev, AIP Conference Proceedings, 1903, 2017, 030033  crossref
    3. H. Itou, A. M. Khludnev, “On delaminated thin Timoshenko inclusions inside elastic bodies”, Math Methods in App Sciences, 39:17 (2016), 4980  crossref
    4. AM Khludnev, GR Leugering, “On Timoshenko thin elastic inclusions inside elastic bodies”, Mathematics and Mechanics of Solids, 20:5 (2015), 495  crossref
    5. N.P. Lazarev, E.M. Rudoy, “Shape sensitivity analysis of Timoshenko's plate with a crack under the nonpenetration condition”, Z Angew Math Mech, 94:9 (2014), 730  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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