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IssuesArchive of Issues2006-1pp.65-75

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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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