 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
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| G. V. Kostin and V. V. Saurin, "Variational approaches in the beam theory," Mech. Solids. 41 (1), 65-75 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
1 |
Pages |
65-75 |
| Title |
Variational approaches in the beam theory |
| Author(s) |
G. V. Kostin (Moscow)
V. V. Saurin (Moscow) |
| Abstract |
Equations governing the stress-strain state of an elastic beam are derived on
the basis of the classical variational principles and on the basis of the
integro-differential relations. The influence of Poisson's ratio on the
stiffness characteristics of an elastic beam with a rectangular cross section
is investigated. Explicit expressions are obtained for the stress fields in an
isotropic or anisotropic beam for an arbitrary type of loading. A system of
differential equations for displacement fields in these beams is presented. The
solutions of case bending problems for a homogeneous beam subjected to various
boundary condition are given. |
| References |
| 1. | L. H. Donnell, Beams, Plates, and Shells [Russian translation], Nauka,
Moscow, 1982. |
| 2. | S. P. Timoshenko, Strength of Materials. Part 1. Elementary Theory
and Problems, D. Van Nostrand, Princeton, 1955. |
| 3. | J. W. Strutt (Baron Rayleigh) Theory of Sound. Volume 1, MacMillan,
London, 1926. |
| 4. | S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw, New
York, 1970. |
| 5. | H. G. Hahn, Elastizitatstheorie: Grundlagen der linearen Theorie und
Anwendungen auf eindimensionale, ebene und rauliche Probleme, B. G. Teubner,
Stuttgart, 1985. |
| 6. | K. Washizu, Variational Methods in Elasticity and Plasticity, Pergamon
Press, Oxford, 1982. |
| 7. | R. Kienzler, "On consistent plate theories," Archive of Applied
Mechanics, Vol. 72, pp. 229-247, 2002. |
| 8. | G. V. Kostin and V. V. Saurin, "Itegro-differential approach to
solving problems of linear elasticity," Doklady RAN, Vol. 404, No. 5,
pp. 628-631, 2005. |
| 9. | G. V. Kostin and V. V. Saurin, "Integro-differential formulation and
the variational method for solving linear elasticity problems," Problemy
Prochnosti i Plastichnosti, Vol. 67, pp. 190-198, 2005. |
|
| Received |
07 June 2005 |
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