# A nonlinear model of a turbine blade by asymptotic analysis

• Volume: 12, Issue: 1, page 101-113
• ISSN: 1641-876X

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## Abstract

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In this paper we obtain a limit model for a turbine blade fixed to a 3D solid. This model is a three-dimensional linear elasticity problem in the 3D part of the piece (the rotor) and a two-dimensional problem (the nonlinear shallow shell equations) in the 2D part (the turbine blade), with junction conditions in the part of the turbine blade fixed to the rotor. To obtain this model, we perform an asymptotic analysis, starting with the nonlinear three-dimensional elasticity equations on all the pieces and taking as a small parameter the thickness of the blade.

## How to cite

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Rodríguez, José. "A nonlinear model of a turbine blade by asymptotic analysis." International Journal of Applied Mathematics and Computer Science 12.1 (2002): 101-113. <http://eudml.org/doc/207562>.

@article{Rodríguez2002,
abstract = {In this paper we obtain a limit model for a turbine blade fixed to a 3D solid. This model is a three-dimensional linear elasticity problem in the 3D part of the piece (the rotor) and a two-dimensional problem (the nonlinear shallow shell equations) in the 2D part (the turbine blade), with junction conditions in the part of the turbine blade fixed to the rotor. To obtain this model, we perform an asymptotic analysis, starting with the nonlinear three-dimensional elasticity equations on all the pieces and taking as a small parameter the thickness of the blade.},
author = {Rodríguez, José},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {multistructures; nonlinear elasticity; asymptotic analysis; shallow shells; junctions; limit model; three-dimensional linear elasticity; nonlinear shallow shell equations; junction conditions; small parameter},
language = {eng},
number = {1},
pages = {101-113},
title = {A nonlinear model of a turbine blade by asymptotic analysis},
url = {http://eudml.org/doc/207562},
volume = {12},
year = {2002},
}

TY - JOUR
AU - Rodríguez, José
TI - A nonlinear model of a turbine blade by asymptotic analysis
JO - International Journal of Applied Mathematics and Computer Science
PY - 2002
VL - 12
IS - 1
SP - 101
EP - 113
AB - In this paper we obtain a limit model for a turbine blade fixed to a 3D solid. This model is a three-dimensional linear elasticity problem in the 3D part of the piece (the rotor) and a two-dimensional problem (the nonlinear shallow shell equations) in the 2D part (the turbine blade), with junction conditions in the part of the turbine blade fixed to the rotor. To obtain this model, we perform an asymptotic analysis, starting with the nonlinear three-dimensional elasticity equations on all the pieces and taking as a small parameter the thickness of the blade.
LA - eng
KW - multistructures; nonlinear elasticity; asymptotic analysis; shallow shells; junctions; limit model; three-dimensional linear elasticity; nonlinear shallow shell equations; junction conditions; small parameter
UR - http://eudml.org/doc/207562
ER -

## References

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1. Bernadou M., Fayolle S. and Lene F. (1989): Numerical analysis of junctions between plates. - Comp. Meth. Appl. Mech. Eng., Vol. 74, No. 3, pp. 307-326. Zbl0687.73068
2. Bernadou M. and Lalanne B. (1987): Calcul de deplacements, contraintes, modes propes de pales tournantes. - Rapport final de l'operation n^0 83322. Contrat DRETINRIA 1584.01.1103.1.
3. Bernadou M. and Oden T. (1981): An existence theorem for a class of non linear shallow shells problems. - J. Math. Pures Appl., Vol. 60, No. 3, pp. 285-308. Zbl0424.35040
4. Ciarlet P.G. (1988): Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity. - Amsterdam: North-Holland. Zbl0648.73014
5. Ciarlet P.G. (1990): Plates and Junctions in Elastic Multistructures. - Paris: Masson. Zbl0706.73046
6. Ciarlet P.G. (1997): Mathematical Elasticity, Vol. II: Theory of Plates. - Amsterdam: North-Holland. Zbl0888.73001
7. Ciarlet P.G. (2000): Mathematical Elasticity, Vol. III: Theory of Shells. - Amsterdam: North-Holland.
8. Ciarlet P.G. and Le Dret H. (1989): Justification of the boundary conditions of a clamped plate by an asymptotic analysis. - Asympt. Anal., Vol. 2, No. 4, pp. 257-277. Zbl0699.73011
9. Ciarlet P.G., Le Dret H. and Nzengwa R. (1989): Junctions between three-dimensional and two-dimensional linearly elastic structures. - J. Math. Pures Appl., Vol. 68, No. 3, pp. 261-295. Zbl0661.73013
10. Ciarlet P.G. and Miara B. (1992): Justification of the Two-Dimensional Equations of a Linearly Elastic Shallow Shell. - Comm. Pure Appl. Math., Vol. 45, No. 3, pp. 327-360. Zbl0769.73050
11. Ciarlet P.G. and Paumier J.C. (1986): A justification of the Marguerre-von Karman equations. - Comp. Mech., Vol. 1, pp. 177-202. Zbl0633.73069
12. Destuynder P. (1986): Une Theorie Asymptotique des Plaques Minces en Elasticite Lineaire. - Paris: Masson. Zbl0627.73064
13. El Chazly N.M. (1993): Static and dynamic analysis of wind turbine blades using the finite element method. - Int. J. Num. Meth. Eng., Vol. 36, No. 16, pp. 2791-2804. Zbl0800.73464
14. Le Dret H. (1989): Folded plates revisited. - Comp. Mech., Vol. 5, No. 5, pp. 345-365. Zbl0741.73025
15. Le Dret H. (1990): Modeling of a folded plate. - Comp. Mech., Vol. 5, No. 6, pp. 401-416. Zbl0741.73026
16. Le Dret H. (1991): Problèmes Variationnels dans les Multi-Domaines: Modelisation des Jonctions et Applications. - Paris: Masson.
17. Rodriguez J.M. (1997): Analyse asymptotique des pales de turbines et des poutres à profil mince. - Ph.D. Thesis, Universite Paris 6, Paris.
18. Rodriguez J.M. (1999): Asymptotic analysis of a turbine blade. - Asympt. Anal., Vol. 21, No. 3-4, pp. 239-273. Zbl0969.74021
19. Trabucho L. and Via no J.M. (1996): Mathematical modelling of rods, In: Handbook of Numerical Analysis, Vol. IV (P.G. Ciarlet and J.L. Lions, Eds.). - Amsterdam: North-Holland, pp. 487-974.

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