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.
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
\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://mathscinet.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}
Linking options:
https://www.mathnet.ru/eng/sjim641
https://www.mathnet.ru/eng/sjim/v13/i4/p97
This publication is cited in the following 6 articles:
Khudayarov B.A., Turaev F.Zh., “Mathematical Simulation of Nonlinear Oscillations of Viscoelastic Pipelines Conveying Fluid”, Appl. Math. Model., 66 (2019), 662–679
Rukavishnikov V.A., Tkachenko O.P., “Dynamics of a Fluid-Filled Curvilinear Pipeline”, Appl. Math. Mech.-Engl. Ed., 39:6 (2018), 905–922
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
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
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
Citation in format AMSBIB
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