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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ISSN 0021-8928
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IssuesArchive of Issues2013-1pp.57-69

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G.V. Kostin, "Modelling of the forced motions of an elastic beam using the method of integrodifferential relations," J. Appl. Math. Mech. 77 (1), 57-69 (2013)
Year 2013 Volume 77 Issue 1 Pages 57-69
Title Modelling of the forced motions of an elastic beam using the method of integrodifferential relations
Author(s) G.V. Kostin (Moscow, Russia,
Abstract A variational approach to the numerical modelling of forced lateral motions of an Euler-Bernoulli elastic beam is developed for a number of linear boundary conditions using the method of integrodifferential relations. A class of linear boundary actions is considered. A family of quadratic functionals, connecting the displacement field of points of the beam with the bending-moment functions in the cross section and the momentum density is proposed. Variational formulations of the original initial-boundary value problem on the motion of the beam are given and the necessary conditions for the functionals introduced to be stationary are analysed. The integral and local quality characteristics of the admissible approximate solutions are determined. The relation between the variational problems, formulated for the beam model, with the classical Hamilton-Ostrogradskii variational principles is demonstrated. An algorithm for constructing approximate systems of ordinary differential equations is developed, the solution of which yields stationary (minimum) values of the functionals introduced on a specified set of displacement fields, moments and momenta. Examples of calculations of the displacements for an elastic beam and an analysis of the quality of the numerical solutions obtained are presented.
Received 16 July 2011
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