Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
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IssuesArchive of Issues2009-6pp.673-687

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

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G.V. Kostin and V.V. Saurin, "Variational approaches to solving initial-boundary-value problems in the dynamics of linear elastic systems," J. Appl. Math. Mech. 73 (6), 673-687 (2009)
Year 2009 Volume 73 Issue 6 Pages 673-687
Title Variational approaches to solving initial-boundary-value problems in the dynamics of linear elastic systems
Author(s) G.V. Kostin (Moscow, Russia,
V.V. Saurin (Moscow, Russia,
Abstract Problems of the controlled motion of an elastic body are considered in the linear theory. Using the method of integrodifferential relations, a family of quadratic functionals is introduced, which define the state of the elastic body, and variational formulations of the initial-boundary-value problem of dynamics are given. Euler's equations and boundary and terminal relations corresponding to them are obtained from the condition for the functionals to be stationary. It is shown that there is a relation between the proposed formulations and the Hamilton variational principle in the case of boundary-value and time-periodic problems of dynamics. A numerical algorithm is developed for finding the motions of an elastic body, based on piecewise-polynomial approximations and a criterion is proposed for estimating the quality of the approximate solutions. An example of the calculation and analysis of the forced transverse motions of a rectilinear beam with a square cross section is given for the three-dimensional model.
Received 17 March 2009
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