 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| G. Z. Sharafutdinov, "Axisymmetric strain of a thick-walled pipe made of a highly elastic material," Mech. Solids. 44 (2), 257-268 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
2 |
Pages |
257-268 |
| DOI |
10.3103/S0025654409020113 |
| Title |
Axisymmetric strain of a thick-walled pipe made of a highly elastic material |
| Author(s) |
G. Z. Sharafutdinov (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia, sharaf@imec.msu.ru) |
| Abstract |
We reduce the plane strain problem to a nonlinear elasticity problem for inhomogeneous bodies by choosing a new form of the elastic potential, whose parameters are determined from the data known in the literature. By using the geometric linearization method, we reduce that problem to a sequence of linear elasticity problems for inhomogeneous bodies. We obtain an analytic solution of the corresponding linear elasticity problem in the case of an arbitrary continuously differentiable dependence of the shear modulus on the radial coordinate. We determine the pipe stress-strain state and parameters in the case of finite and large strains for given sets of initial data and estimate the accuracy of the solution thus obtained. |
| References |
| 1. | A. Green and J. Adkins, Large Elastic Deformations and Nonlinear Continuum Mechanics (Clarendon Press, Oxford, 1960; Mir,Moscow, 1965). |
| 2. | J. Oden, Finite Elements of Nonlinear Continua (McGraw-Hill, New York, 1972; Mir,Moscow, 1976). |
| 3. | A. A. Pozdeev, P. V. Trusov, and Yu. I. Nyashin, Large Elastoplastic Deformations: Theory, Algorithms, and Applications (Nauka, Moscow, 1986) [in Russian]. |
| 4. | R. S. Rivlin, Rheology: Theory and Applications (Academic Press, New York, 1956; Izd-vo Inostr. Lit., Moscow, 1962). |
| 5. | A. Green and W. Zerna, Theoretical Elasticity (Clarendon Press, Oxford, 1968). |
| 6. | L. Treloar, The Physics of Rubber Elasticity (Clarendon Press, Oxford, 1949; Mir, Moscow, 1953). |
| 7. | G. Z. Sharafutdinov and V. A. Demin, "Geometric Linearization Method in Technological Problems of Nonlinear Deformation," in Elasticity and Inelasticity (Izd-vo MGU, Moscow, 2001), pp. 452–453 [in Russian]. |
| 8. | V. A. Demin and G. Z. Sharafutdinov, "Geometric Linearization Method in Problems of Nonlinear Deformation," in Mechanics, No. 24 (Dzial Wydawnictw i Poligrafi, Bialystok, 2001), pp. 123–127. |
| 9. | L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 7, Theory of Elasticity (Nauka, Moscow, 1967, 1987; Pergamon Press, Oxford, 1970). |
| 10. | I. I. Goldenblat, Several Problems of Mechanics of Deformable Media (Gostekhizdat, Moscow, 1955) [in Russian]. |
| 11. | G. Z. Sharafutdinov, "On Lamé Constants and the Constitutive Relations of Mechanics of Deformable Bodies," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 1, 55–58 (2004) [Moscow Univ. Math. Bull. (Engl. Transl.)]. |
| 12. | A. I. Lurie, The Theory of Elasticity (Nauka, Moscow, 1970) [in Russian]. |
|
| Received |
07 April 2006 |
| Link to Fulltext |
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