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A nonlinear model of a turbine blade by asymptotic analysis

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EN
Abstrakty
EN
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.
Twórcy
  • Departamento de Métodos Matemáticos y de Representación, E.T.S. de Arquitectura, Universidade da Coruña, Campus da Zapateira, s/n. 15071 A Coruña, Spain
Bibliografia
  • [1] Bernadou M., Fayolle S. and Léné F. (1989): Numerical analysis of junctions between plates. - Comp. Meth. Appl. Mech. Eng., Vol. 74, No. 3, pp. 307-326.
  • [2] Bernadou M. and Lalanne B. (1987): Calcul de déplacements, contraintes, modes propes de pales tournantes. - Rapport final de l’opération n0 83/322. Contrat DRET/INRIA n0 15/84.01.1103.1.
  • [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.
  • [4] Ciarlet P.G. (1988): Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity. - Amsterdam: North-Holland.
  • [5] Ciarlet P.G. (1990): Plates and Junctions in Elastic Multi-structures. - Paris: Masson.
  • [6] Ciarlet P.G. (1997): Mathematical Elasticity, Vol. II: Theory of Plates. - Amsterdam: North-Holland.
  • [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.
  • [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.
  • [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.
  • [11] Ciarlet P.G. and Paumier J.C. (1986): A justification of the Marguerre-von Kármán equations. - Comp. Mech., Vol. 1, pp. 177-202.
  • [12] Destuynder P. (1986): Une Théorie Asymptotique des Plaques Minces en Élasticité Linéaire. - Paris: Masson.
  • [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.
  • [14] Le Dret H. (1989): Folded plates revisited. - Comp. Mech., Vol. 5, No. 5, pp. 345-365.
  • [15] Le Dret H. (1990): Modeling of a folded plate. - Comp. Mech., Vol. 5, No. 6, pp. 401-416.
  • [16] Le Dret H. (1991): Problèmes Variationnels dans les Multi-Domaines: Modélisation 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, Université Paris 6, Paris.
  • [18] Rodriguez J.M. (1999): Asymptotic analysis of a turbine blade. - Asympt. Anal., Vol. 21, No. 3-4, pp. 239-273.
  • [19] Trabucho L. and Viaño 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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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0001-0010
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