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Опубликовано 2011-06-05 Опубликовано на SciPeople2011-06-05 11:25:55 ЖурналWILEY-VCH Verlag GmbH & Co. KGaA

Large bending deformations of a cylindrical membrane with internal pressure
Kolesnikov A. M., Zubov L. M. / Алексей Колесников
ZAMM (Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik). 2009. Volume 89. Issue 4. P.288–305
Аннотация We consider the large bending of a thin-walled cylinder made of a rubberlike material. It is loaded by internal pressure and bending moments at the ends. The exact formulation of the problem is given within the framework of the nonlinear membrane theory taking into account large strains of the cylinder. Using the special substitution describing the pure bending of the cylinder, the problem is reduced to the system of nonlinear ordinary differential equations. The latter is solved numerically. We establish that there exists the limit value of the bending moment, which depends essentially upon the internal pressure. As an example, the Mooney–Rivlin material is considered. On the base of the calculations we propose the approximate formulae describing the bending moment dependence on the axis curvature of the cylinder and the ultimate bending moment dependence on the internal pressure.
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