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In this paper, the problem of large pure bending deformations of membrane is considered. The membrane is a sector of torus with a closed cross-section. This membrane is called a curved tube for short. We consider the homogenous, incompressible, isotropic and hyperelastic material. The external load is a constant pressure and bending couples acting at the edges. The equilibrium equations reduce to ordinary differential equations. As an example, the membrane with a constant thickness and with a circular cross-section is investigated.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
507--507
Opis fizyczny
–-516, Bibliogr. 11 poz.
Twórcy
autor
- Theory of Elasticity Department Southern Federal University Rostov-on-Don, 344010, Russian Federation, Alexei.M.Kolesnikov@gmail.com
Bibliografia
- 1. T. von Kármán, Ueber die Formänderung dünnwandiger Rohre, insbesondere federnder Ausgleichrohre, Z. Vereines Deutscher Ingenieure, 55, 45, 1889–1895, 1911.
- 2. R.A. Clark, E. Reissner, Bending of curved tubes, Adv. Appl. Mech., 2, 93–122, 1951.
- 3. E. Reissner, On finite pure bending of curved tubes. Int. J. Solids Struct., 17, 839–844, 1981.
- 4. E.L. Axelrad, Equations of deformation for shells of revolution and for bending of thinwalled tubes subjected to large elastic displacements, (translated from a 1960 article In Russian) Am. Rocket Soc. J., 32, 1147–1151, 1962.
- 5. E.L. Axelrad, Theory of Flexible Shells, North Holland, Amsterdam 1987.
- 6. K. Tatsuzo, Bending rigidity of an inflated circular cylindrical membrane of rubbery material, AIAA Journal. 10, 11, 1485–1491, 1972.
- 7. A. Libai, J.S. Simmonds, The Nonlinear Theory of Elastic and Shells, 2nd ed., Cambridge Univ. Press., Cambridge 1998.
- 8. L.M. Zubov, Semi-inverse solution in non-linear theory of elastic shells, Archives of Mechanics, 53, 4–5, 599–610, 2001.
- 9. A.M. Kolesnikov, L.M. Zubov, Large bending deformations of a cylindrical membrane with internal pressure, Z. Angew. Math. Mech., 89, 4, 288–305, 2009.
- 10. L.M. Zubov, The methods of nonlinear elasticity in the shell theory [in Russian], Rostov. Univ. Press, Rostov-on-Don 1982.
- 11. A.M. Kolesnikov, Straightening of hyperelastic curved tube by internal pressure [in Russian], Proceeding of the XIV conference: Modern Problems of Continua Mechanics, Azov– Rostov-on-Don, 1, 182–186, 2010.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0009-0054