 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A. N. Danilin, N. N. Zuev, A. B. Kostrichenko, and V. I. Shalashilin, "Various versions of geometrically nonlinear relations for large deformations," Mech. Solids. 39 (3), 40-48 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
3 |
Pages |
40-48 |
| Title |
Various versions of geometrically nonlinear relations for large deformations |
| Author(s) |
A. N. Danilin (Moscow)
N. N. Zuev (Moscow)
A. B. Kostrichenko (Moscow)
V. I. Shalashilin (Moscow) |
| Abstract |
When modeling nonlinear deformation of elastic systems, various versions of displacement/strain geometrically nonlinear relations (GNR) are utilized [1-4]. Three kinds of the GNR-exact, complete quadratic, and incomplete quadratic ones-are compared and analyzed. The quadratic (complete and incomplete) relations are approximate ones. They result from the expansions of the exact relations in power series, with a certain number of terms being preserved. We show that the utilization of the approximate GNR can lead to a considerable error in the calculation and that it is impossible to determine beforehand which of the approximate versions should be preferred. The accuracy of the calculations on the basis of various GNR versions is estimated on the basis of simple case problems. Comparative examples are given. A finite-element formulation of the problem of strong geometrically nonlinear deformation of a cantilever beam, with the best parameterization procedure being involved, is considered. |
| References |
| 1. | V. V. Novozhilov, Fundamentals of Nonlinear Theory of Elasticity [in Russian], Gostekhizdat, Moscow, Leningrad, 1948. |
| 2. | A. I. Lur'e, Theory of Elasticity [in Russian],
Nauka, Moscow, 1970. |
| 3. | L. H. Donnel, Beams, Plates, and Shells [Russian translation],
Nauka, Moscow, 1982. |
| 4. | F. N. Shklyarchuk, "Analysis of the strain state and stability of geometrically nonlinear elastic systems," Izv. AN. MTT [Mechanics of Solids],
No. 1, pp. 140-146, 1998. |
| 5. | E. I. Grigolyuk and V. I. Shalashilin, Issues of Nonlinear Deformation. Continuation with Respect to a Parameter in Nonlinear Problems of Solid Mechanics [Russian], Nauka, Moscow, 1988. |
| 6. | V. I. Shalashilin and E. B. Kuznetsov, Continuation with Respect to a Parameter and the Best Parameterization [in Russian], Editorial URRS, Moscow,
1999. |
|
| Received |
17 September 2003 |
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