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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2017, Volume 21, Number 3, Pages 496–506
DOI: https://doi.org/10.14498/vsgtu1555
(Mi vsgtu1555)
 

This article is cited in 2 scientific papers (total in 2 papers)

Mechanics of Solids

Integro-differential equations the second boundary value problem of linear elasticity theory. Message 1. Homogeneous isotropic body

V. V. Struzhanov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation
Full-text PDF (586 kB) Citations (2)
(published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: The system of equations of the second boundary value problem of the linear theory of elasticity for homogeneous isotropic bodies is reduced to two separate integro-differential equations of Fredholm type, which allowed to apply for their research the theorem of Fredholm. The spectral radii of the corresponding operators are determined and the existence and uniqueness of the solution of the second boundary value problem are proved. It is also established that the decision of the second integro-differential equation can be found by successive approximations and presented convergent with a geometric rate close to Neumann. The method application is illustrated on the example of calculation of residual stresses in a quenched cylinder.
Keywords: second boundary-value problem, homogeneous isotropic body, integro-differential equation, spectral radius, successive approximation.
Received: July 12, 2017
Revised: August 23, 2017
Accepted: September 18, 2017
First online: September 22, 2017
Bibliographic databases:
Document Type: Article
UDC: 539.3
MSC: 74C10
Language: Russian
Citation: V. V. Struzhanov, “Integro-differential equations the second boundary value problem of linear elasticity theory. Message 1. Homogeneous isotropic body”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:3 (2017), 496–506
Citation in format AMSBIB
\Bibitem{Str17}
\by V.~V.~Struzhanov
\paper Integro-differential equations the second boundary value problem of linear elasticity theory.
Message~1.~Homogeneous isotropic body
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 3
\pages 496--506
\mathnet{http://mi.mathnet.ru/vsgtu1555}
\crossref{https://doi.org/10.14498/vsgtu1555}
\zmath{https://zbmath.org/?q=an:06964800}
\elib{https://elibrary.ru/item.asp?id=32248393}
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  • https://www.mathnet.ru/eng/vsgtu/v221/i3/p496
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Full-text PDF :239
    References:67
     
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