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Sibirskii Zhurnal Industrial'noi Matematiki, 2011, Volume 14, Number 4, Pages 32–43 (Mi sjim695)  

This article is cited in 9 scientific papers (total in 9 papers)

An equilibrium problem for a Timoshenko plate with a through crack

N. P. Lazarevab

a Mathematics Research Institute, Northeastern Federal University, Yakutsk, RUSSIA
b Lavrent'ev Institute of Hydrodynamics, Siberian Division of the RAS, Novosibirsk, RUSSIA
Full-text PDF (305 kB) Citations (9)
References:
Abstract: We study the equilibrium problem for an elastic plate (Timoshenko model) with a vertical crack. On the curve defining the through crack we impose a boundary condition as an inequality describing the nonpenetration of the opposite crack edges. We prove the unique solvability of the variational statement of the problem. From the variational statement we deduce a complete system of boundary conditions, which we use to obtain an equivalent differential statement. We establish additional smoothness of the solution in comparison with that given in the variational statement. We prove that the solution functions are infinitely smooth under additional assumptions on the function of external loads and the functions of displacements near the curve describing the through crack.
Received: 12.07.2010
Bibliographic databases:
Document Type: Article
UDC: 539.311
Language: Russian
Citation: N. P. Lazarev, “An equilibrium problem for a Timoshenko plate with a through crack”, Sib. Zh. Ind. Mat., 14:4 (2011), 32–43
Citation in format AMSBIB
\Bibitem{Laz11}
\by N.~P.~Lazarev
\paper An equilibrium problem for a~Timoshenko plate with a~through crack
\jour Sib. Zh. Ind. Mat.
\yr 2011
\vol 14
\issue 4
\pages 32--43
\mathnet{http://mi.mathnet.ru/sjim695}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2954005}
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  • https://www.mathnet.ru/eng/sjim/v14/i4/p32
  • This publication is cited in the following 9 articles:
    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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    Abstract page:513
    Full-text PDF :184
    References:90
    First page:10
     
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