Geodesic
Approximate solution to the nonlinear problem of an underground pipeline deformation
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 97-108

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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. 
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     author = {V. A. Rukavishnikov and O. P. Tkachenko},
     title = {Approximate solution to the nonlinear problem of an underground pipeline deformation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {97--108},
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     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2010_13_4_a8/}
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V. A. Rukavishnikov; O. P. Tkachenko. Approximate solution to the nonlinear problem of an underground pipeline deformation. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 97-108. http://geodesic.mathdoc.fr/item/SJIM_2010_13_4_a8/