 | | 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, "Two-Dimensional Model of a Plate Made of an Anisotropic Inhomogeneous Material," Mech. Solids. 52 (2), 144-154 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
2 |
Pages |
144-154 |
| DOI |
10.3103/S0025654417020042 |
| Title |
Two-Dimensional Model of a Plate Made of an Anisotropic Inhomogeneous Material |
| Author(s) |
P.E. Tovstik (St.-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia; Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia)
T.P. Tovstik (Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia, tovstik_t@mail.ru) |
| Abstract |
We present an asymptotic derivation of the two-dimensional equations of equilibrium of a thin elastic inhomogeneous plate manufactured of an anisotropic material of general form with 21 moduli of elasticity. We also consider simplified models obtained under special assumptions on the moduli. We use test examples to illustrate the error estimate of the proposed model and discuss its scope. The model is compared with the classical Kirchhoff-Love and Timoshenko-Reissner models. |
| Keywords |
plate, anisotropy, inhomogeneity, asymptotics |
| References |
| 1. | L. H. Donnell,
Beams, Plates, and Shells
(McGraw-Hill, New York, 1976; Nauka, Moscow, 1982). |
| 2. | V. A. Rodionova, B. F. Titaev, and K. F. Chernykh,
Applied Theory of Anisotropic Plates and Shells
(Izdat. SPbGU, St. Petersburg, 1996)
[in Russian]. |
| 3. | L. A. Agalovyan,
Asymptotic Theory of Anisotropic Plates and Shells
(Nauka, Moscow, 1997)
[in Russian]. |
| 4. | J. N. Reddy,
Mechanics of Laminated Composite Plates and Shells
(CRC Press, 2004). |
| 5. | 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)] |
| 6. | 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). |
| 7. | 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
(Izdat. SPbGU, St. Petersburg, 2008),
pp. 4-16
[in Russian]. |
| 8. | 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)]. |
| 9. | 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)]. |
| 10. | P. E. Tovstik and T. P. Tovstik,
"Two-Dimensional Linear Model of Elastic Shell
Accounting for General Anisotropy of Material,"
Acta Mechanica
225 (3), 647-661 (2014). |
| 11. | P. E. Tovstik and T. P. Tovstik,
"Two-Dimensional Linear Model of Anisotropic Shells,"
in SSTA. 2013. Gdansk, Vol. 3,
pp. 153-156. |
| 12. | Y. Vetukov, A. Kuzin, and M. Krommer,
"Asymptotic Splitting of the Three-Dimensional Problem of Elasticity
for Non-Homogeneous Piezoelectric Plates,"
Int. J. Solids Struct.
40, 12-23 (2011). |
| 13. | P. Schnieder and R. Kienzler,
"An algorithm for the Automatization of Pseudo Reductions of PDE Systems
Arising from the Uniform-Approximation Technique,"
in Shell-Like Structures. Non-Classical Theories and Applications
(Springer, Berlin, 2011),
pp. 377-390. |
| 14. | N. F. Morozov and P. E. Tovstik,
"Bending of a Two-Layer Beam with Non-Rigid Contact between the Layers,"
Prikl. Mat. Mekh.
75 (1), 112-121 (2011)
[J. Appl. Math. Mech. (Engl. Transl.)
75 (1), 77-84 (2011)]. |
| 15. | P. E. Tovstik and T. P. Tovstik,
"Two-Dimensional Model of Plate Made of Anisotropic Inhomogeneous Material,"
in AIP Conference Proceedings, Vol. 1648
(2015),
p. 300011. |
|
| Received |
15 July 2014 |
| Link to Fulltext |
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