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

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version)

Russian Russian English English About Journal | Issues | Editorial Board | Contact Us
 


ΘΟΜευ ΠΐΝWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2013-1pp.57-69

Archive of Issues

Total articles in the database: 2048
In Russian (ΟΜΜ): 1249
In English (J. Appl. Math. Mech.): 799

<< Previous article | Volume 77, Issue 1 / 2013 | Next article >>
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, kostin@ipmnet.ru)
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
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S0021892813000579
<< Previous article | Volume 77, Issue 1 / 2013 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 245, 119526 Moscow, Russia (+7 495) 434-2149 pmm@ipmnet.ru pmmedit@ipmnet.ru https://pmm.ipmnet.ru
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Journal of Applied Mathematics and Mechanics
webmaster
Rambler's Top100