Geodesic
Mathematical modeling of critical states of thin-walled cylindrical shells under internal pressure and axial compression
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 11 (2019) no. 4, pp. 39-46

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The loading conditions of a thin-walled cylindrical shell, including large-diameter pipes, under compressive (negative) axial stresses and tensile (positive) ring stresses are considered. The purpose of the article is to specify the dependences of critical deformations, stresses, pressures, and axis loads on the shell on the parameters and loading conditions. The research method is based on the application of the loss in stability of the plastic deformation process Swift–Marciniak criterion. The material of the shell is assumed to be isotropic with exponential-power deformation diagram. Explicit analytical expressions for the target values were obtained. Considering the given parameters of the shell and loading conditions, the results allow to determine critical pressures, critical axial loads and wall thickness at a given working pressure.
Keywords: thin-walled cylindrical shell, large-diameter pipe, plastic stability, Swift criterion, critical deformations, critical stresses, critical pressures, localization of plastic deformation. 
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     author = {V. L. Dilman},
     title = {Mathematical modeling of critical states of thin-walled cylindrical shells under internal pressure and axial compression},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {39--46},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2019_11_4_a4/}
}
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V. L. Dilman. Mathematical modeling of critical states of thin-walled cylindrical shells under internal pressure and axial compression. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 11 (2019) no. 4, pp. 39-46. http://geodesic.mathdoc.fr/item/VYURM_2019_11_4_a4/