Abstract
In this work the effect of the unbending of a curved tube under a uniform normal pressure is investigated. The problem is considered within the framework of the nonlinear membrane theory. It is shown that the inflation of a curved tube is the special case of pure bending. The tube with a circular cross section made of a Mooney-Rivlin material is studied numerically. The dependencies between the curvature of the centerline of deformed curved tube and the internal pressure are obtained. It is found that there are the maximum pressures for the considered materials.
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References
Kabric, S.A. et al.: General Nonlinear Theory of Elastic Shells (in Russian). Saint Petersburg Univ. Press., Saint Petersburg (2002)
Kolesnikov, A.M.: Compression of nonlinear elastic membranes between rigid surfaces. In: Kreja, I., Pietraszkiewicz , W. (eds) Shell Structures: Theory and Applications, Vol.2, pp. 71–74. Taylor & Francis Group, London (2010)
Kolesnikov A.M. (2010) Straightening of hyperelastic curved tube by internal pressure (in Russian). Proceeding of the XIV conferrence <<Modern problems of continuum mechanics>>, vol. 1, pp. 182-186. Rostov-on-Don
Kolesnikov A.M., Zubov L.M. (2009) Large bending deformations of a cylindrical membrane with internal pressure. Z. Angew. Math. Mech. doi:10.1002/zamm.200800182.
Libai, A., Simmonds, J.G.: Nonlinear Theory of Elastic Shells. Cambridge Univ. Press., Cambridge (1998)
Zubov, L.M.: The Methods of Nonlinear Elasticity in Shell Theory (in Russian). Rostov Univ. Press., Rostov-on-Don (1982)
Zubov, L.M.: Semi-inverse solution in non-linear theory of elastic shells. Archives of Mechanics. 53(45), 599–610 (2001)
Acknowledgements
This research was supported by the President of the Russian Federation (grant MK-439.2011.1).
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© 2011 Springer-Verlag Berlin Heidelberg
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Kolesnikov, A.M. (2011). Unbending of Curved Tube by Internal Pressure. In: Altenbach, H., Eremeyev, V. (eds) Shell-like Structures. Advanced Structured Materials, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21855-2_31
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DOI: https://doi.org/10.1007/978-3-642-21855-2_31
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