 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| P.E. Tovstik and T.P. Tovstik, "One-Dimensional Models of a Beam Made of an Anisotropic Material with Oblique Anisotropy," Mech. Solids. 46 (6), 888-897 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
6 |
Pages |
888-897 |
| DOI |
10.3103/S0025654411060082 |
| Title |
One-Dimensional Models of a Beam Made of an Anisotropic Material with Oblique Anisotropy |
| Author(s) |
P.E. Tovstik (St. Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia, peter.tovstik@mail.ru)
T.P. Tovstik (St. Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia) |
| Abstract |
One-dimensional equations of the statics and free vibration of a strip beam made of an anisotropic material of general form (oblique anisotropy) are derived. It is shown that neither the Kirchhoff-Love hypotheses nor the classical Timoshenko-Reissner hypotheses lead to well-posed one-dimensional equations. A variant of the generalized Timoshenko-Reissner model is proposed that permits one to satisfy the boundary conditions on the beam surface exactly and leads to an asymptotically correct one-dimensional model. The solutions of the one- and two-dimensional equations of the statics and free vibration problems are compared and the dispersion equation is analyzed. |
| Keywords |
beams, oblique anisotropy, approximate models, vibration, dispersion equation |
| References |
| 1. | L. H. Donnell,
Beams, Plates, and Shells
(McGraw-Hill, New York, 1976; Nauka, Moscow, 1982). |
| 2. | L. A. Agalovyan,
Asymptotic Theory of Anisotropic Plates and Shells
(Nauka, Moscow, 1997)
[in Russian]. |
| 3. | V. A. Rodionova, B. F. Titaev, and K. F. Chernykh,
Applied Theory of Anisotropic Plates and Shells
(Izd. SPbGU, St. Petersburg, 1996)
[in Russian]. |
| 4. | P. E. Tovstik,
"On the Asymptotic Nature of Approximate Models of Beams, Plates, and Shells,"
Vestnik Sankt-Peterburgskogo Univ. Ser. 1. Mat. Mekh. Astr.,
No. 3, 49-54 (2007)
[Vestnik St. Petersburg Univ. Math. (Engl. Transl.)
40 (3), 188-192 (2007)] |
| 5. | P. E. Tovstik and T. P. Tovstik,
"On the 2D Models of Plates and Shells Including the Transversal Shear,"
ZAMM
87 (2), 160-171 (2007). |
| 6. | P. E. Tovstik and T. P. Tovstik,
"Two-Dimensional Models of Plates Made of an Anisotropic Material,"
in Proc. Seminar "Computer Methods in Continuum Mechanics, No. 3
(Izd. SPbGU, St. Petersburg, 2008),
pp. 4-16
[in Russian]. |
| 7. | R. V. Goldstein, V. A. Gorodtsov, and D. S. Lisovenko,
"To the Description of Multi-Layered Nanotubes in Models of Cylindrically Anisotropic Elasticity,"
Fizich. Mezomekh.
12 (5), 5-14 (2009)
[Phys. Mesomech. (Engl. Transl.)
13 (1-2), 12-20 (2010)]. |
| 8. | P. E. Tovstik,
"Models of Plates Made of an Anisotropic Material,"
Dokl. Ross. Akad. Nauk
425 (4), 487-491 (2009).
[Dokl. Phys. (Engl. Transl.)
54 (4), 205-209 (2009)]. |
|
| Received |
04 March 2010 |
| Link to Fulltext |
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