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Large bending deformations of a cylindrical membrane with internal pressure
Author(s) -
Kolesnikov A.M.,
Zubov L.M.
Publication year - 2009
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800182
Subject(s) - bending moment , curvature , cylinder , bending , internal pressure , pure bending , nonlinear system , plastic bending , moment (physics) , mechanics , ordinary differential equation , physics , classical mechanics , differential equation , mathematical analysis , mathematics , geometry , bending stiffness , thermodynamics , quantum mechanics
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.