 | | 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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| G. M. Kulikov, "Strain-displacement relationships that exactly represent large rigid displacements of a shell," Mech. Solids. 39 (5), 105-113 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
5 |
Pages |
105-113 |
| Title |
Strain-displacement relationships that exactly represent large rigid displacements of a shell |
| Author(s) |
G. M. Kulikov (Tambov) |
| Abstract |
The finite element method (FEM) has become the most powerful numerical method that is utilized currently for solving problems in mechanics of shells. At the same time, the problem of the construction of curved finite elements for thin shells subject to large displacements and arbitrarily large rotations is still far from being solved [1-3]. This is for that reason that the representation provided by the strain-displacement relationships for rigid displacements of the shell element is inadequate. Therefore, no wonder that since the strain relationships that would be able to represent an arbitrary strain state in local curvilinear coordinates are not available in the literature, the degenerate (isoparametric) element concept [4] has been mostly developed. This concept enables one to represent rigid displacements of the element in the global Cartesian reference frame but requires considerable increase in the computational time [3, 5].
In the literature, there are a lot of versions of both the classical (Kirchhoff-Love) theory of shells and the theory refined on the basis of Timoshenko's hypothesis. However, only some of these theories (e.g., those of [6-9]) provide adequate approximations for rigid displacements of the shell. This observation is validated in [7, 10, 11] for the geometrically linear Kirchhoff-Love theory of shells and in [12] for the refined theory of shells. In the present paper, the results of [12] are extended to shells subject to large displacements and arbitrarily large rotations. |
| References |
| 1. | A. S. Sakharov and N. Altenbach (Editors), Finite Element Method in
Solid Mechanics [in Russian],
Vishcha Shkola, Kiev, 1982. |
| 2. | A. I. Golovanov and M. S. Kornishin,
Introduction to Finite Element Method for Statics of Thin Shells
[in Russian], KFTI AN SSSR, Kazan, 1989. |
| 3. | K. J. Bathe, Finite Element Procedures. Englewood Cliffs,
Prentice Hall, New York, 1996. |
| 4. | S. Ahmad, B. M. Irons, and O. C. Zienkiewicz,
"Analysis of thick and thin shell structures by curved elements,"
Intern. J. Numer. Meth. Eng., Vol. 2, No. 3, pp. 419-451, 1970. |
| 5. | A. K. Noor, "Bibliography of books and monographs
on finite element technology,"
Appl. Mech. Rev., Vol. 44, No. 6, pp. 307-317, 1991. |
| 6. | V. V. Novozhilov, Theory of Thin Shells
[in Russian], Sudpromgiz, Leningrad, 1962. |
| 7. | A. L. Goldenveizer, Theory of Elastic Thin Shells
[in Russian], Nauka, Moscow, 1976. |
| 8. | G. M. Kulikov and S. V. Plotnikova, "Comparative analysis of two
algorithms for numerical solution of nonlinear static problems for laminate
anisotropic shells of revolution. Pt. 2. Account for transverse
reduction," Mekhanika Komposit. Materialov, Vol. 35, No. 4, pp. 425-446,
1999. |
| 9. | G. M. Kulikov, "Refined global approximation theory of mulilayered
plates and shells,"
J. Eng. Mech., Vol. 127, No. 2, pp. 119-125, 2001. |
| 10. | D. Kantin, "The strain-displacement relationships
for cylindrical shells,"
Raketnaya Tekhnika i Kosmonavtika, Vol. 6, No. 9, pp. 219-220, 1968. |
| 11. | D. J. Dawe, Rigid-body motions and strain-displacement equations
of curved shell finite elements,"
Intern. J. Mech. Sci., Vol. 14, No. 9, pp. 569-578, 1972. |
| 12. | G. M. Kulikov and S. V. Plotnikova, "Simple and effective
elements based upon Timoshenko-Mindlin shell theory," Comput. Meth. Appl.
Mech. Eng., Vol. 191, No. 11-12, pp. 1173-1187, 2002. |
| 13. | V. V. Novozhilov, Theory of Elasticity
[in Russian], Sudpromgiz, Leningrad, 1958. |
| 14. | A. Yu. Ishlinskii, Orientation, Gyroscopes, and Inertial Navigation
[in Russian], Nauka, Moscow, 1976. |
| 15. | G. M. Kulikov, "Non-linear analysis of multilayered shells
under initial stress,"
Intern. J. Non-linear Mech., Vol. 36, No. 2, pp. 323-334, 2001. |
|
| Received |
06 May 2002 |
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