Geodesic
Finite element modelling for a beam on the Winckler type basis with variable rigidity
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 1, pp. 23-30.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study constructing a beam on the Winckler basis that is under the influence of a cross-force. This force rotates around the axis of the beam. The rigidity of this basis depends on the time variable. A general mathematical model is deduced for this type of constructions. Variational formulations of the boundary value problems in question are obtained. The finite element method is used to determine the stresses of a beam. We discuss the corresponding eigenvalue problems in order to apply the method of normal shapes. Finally, a`numerical result with practical application is presented. 
@article{SJVM_2005_8_1_a2,
     author = {A. B. Andreev and J. T. Maximov and M. R. Racheva},
     title = {Finite element modelling for a beam on the {Winckler} type basis with variable rigidity},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {23--30},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2005_8_1_a2/}
}
TY  - JOUR
AU  - A. B. Andreev
AU  - J. T. Maximov
AU  - M. R. Racheva
TI  - Finite element modelling for a beam on the Winckler type basis with variable rigidity
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2005
SP  - 23
EP  - 30
VL  - 8
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2005_8_1_a2/
LA  - en
ID  - SJVM_2005_8_1_a2
ER  - 
%0 Journal Article
%A A. B. Andreev
%A J. T. Maximov
%A M. R. Racheva
%T Finite element modelling for a beam on the Winckler type basis with variable rigidity
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2005
%P 23-30
%V 8
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2005_8_1_a2/
%G en
%F SJVM_2005_8_1_a2
A. B. Andreev; J. T. Maximov; M. R. Racheva. Finite element modelling for a beam on the Winckler type basis with variable rigidity. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 1, pp. 23-30. http://geodesic.mathdoc.fr/item/SJVM_2005_8_1_a2/

[1] Andreev A. B., Maximov J. T., Racheva M. R., “Finite element method for calculation of dynamic stresses in the continuous beam on elastic supports”, Siberian J. of Numer. Mathematics / Sib. Branch of Russ. — Novosibirsk, 6:2 (2003), 113–124 | Zbl

[2] Ciarlet P. G., The Finite Element Method for Elliptic Problems, Amsterdam – New York – Oxford, 1978 | MR

[3] Levina Z. M., Reshetov D. N., Contact Stiffness of Machines. Machinery Constraction, Mashinostroenie, Moscow, 1971 (in Russian)

[4] Timoshenko S. P., Goodier J. N., Theory of Elasticity, McGraw Hill Intern., London, 1982 | MR

[5] Timoshenko S. P., Young D. H., Weaver W., Vibration Problems in Engineering, John Wiley Sons, New York, 1977