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Sib. Zh. Ind. Mat., 2010, Volume 13, Number 4, Pages 97–108 (Mi sjim641)  

This article is cited in 6 scientific papers (total in 6 papers)

Approximate solution to the nonlinear problem of an underground pipeline deformation

V. A. Rukavishnikov, O. P. Tkachenko

Computing Center, FEB RAS, Khabarovsk

Abstract: Some geometrically nonlinear mathematical model is constructed of a pipeline as a shell in a strongly viscous medium. We find a universal procedure for reducing the two-dimensional equations of motion to the one-dimensional equations for long bent pipes. We also constructed a difference scheme and propose a software omplex for numerical analysis of the equations under study. Some numerical experiments are conducted for a particular case of a bent pipeline, the deformations of the pipe wall are found, and the displacement of its centerline is calculated.

Keywords: curvilinear pipeline, finite deformation, difference scheme, numerical experiment.

Full text: PDF file (368 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2012, 6:1, 100–110

Bibliographic databases:

UDC: 532.595+519.633
Received: 25.02.2010

Citation: V. A. Rukavishnikov, O. P. Tkachenko, “Approximate solution to the nonlinear problem of an underground pipeline deformation”, Sib. Zh. Ind. Mat., 13:4 (2010), 97–108; J. Appl. Industr. Math., 6:1 (2012), 100–110

Citation in format AMSBIB
\Bibitem{RukTka10}
\by V.~A.~Rukavishnikov, O.~P.~Tkachenko
\paper Approximate solution to the nonlinear problem of an underground pipeline deformation
\jour Sib. Zh. Ind. Mat.
\yr 2010
\vol 13
\issue 4
\pages 97--108
\mathnet{http://mi.mathnet.ru/sjim641}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2841217}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 1
\pages 100--110
\crossref{https://doi.org/10.1134/S1990478912010115}


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

    This publication is cited in the following articles:
    1. Tkachenko O.P., “Chislennyi analiz dinamiki krivolineinogo truboprovoda”, Vychislitelnaya mekhanika sploshnykh sred, 5:3 (2012), 345–353  crossref  elib
    2. Tkachenko O., “Construction of the Mathematical Model of Complex Pipeline With Variable Geometry”, 15Th International Scientific Conference Underground Urbanisation as a Prerequisite For Sustainable Development, Procedia Engineering, 165, eds. Alpatov S., Prentkovskis O., Sterling R., Kaliampakos D., Elsevier Science BV, 2016, 1261–1274  crossref  isi
    3. Rukavishnikov V.A., Tkachenko O.P., “Numerical Modeling of the Fluid-Filled Pipelines in Viscous Medium”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 (Icnaam-2015), AIP Conference Proceedings, 1738, eds. Simos T., Tsitouras C., Amer Inst Physics, 2016, 030036  crossref  isi
    4. V. V. Karpov, A. A. Semenov, “Mathematical models and algorithms for studying the strength and stability of shell structures”, J. Appl. Industr. Math., 11:1 (2017), 70–81  mathnet  crossref  crossref  mathscinet  elib
    5. Rukavishnikov V.A., Tkachenko O.P., “Dynamics of a Fluid-Filled Curvilinear Pipeline”, Appl. Math. Mech.-Engl. Ed., 39:6 (2018), 905–922  crossref  mathscinet  isi  scopus
    6. Khudayarov B.A., Turaev F.Zh., “Mathematical Simulation of Nonlinear Oscillations of Viscoelastic Pipelines Conveying Fluid”, Appl. Math. Model., 66 (2019), 662–679  crossref  mathscinet  zmath  isi  scopus
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