Equivalence Theory Applied to Anisotropic Thin Plates

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DOI: 10.4236/eng.2011.37080    6,079 Downloads   9,996 Views   Citations

ABSTRACT

We extend the Equivalence Theory (ET) formulated by Absi [1] for the statics of isotropic materials to the statics and dynamics of orthotropic materials. That theory relies on the assumption that any real body mod- eling may be substituted by another one that, even though it may possibly have material constitutive laws and geometric properties with no physical sense (like negative cross sections or Young modulus), is intended to be more advantageous for calculus. In our approach, the equivalence is expressed by equating both the effective strain energies of the two models and the material structural weights in dynamics [2]. We provide a numerical analysis of the convergence properties of ET approach while comparing its numerical results with those predicted by the analytical theory and the Finite Elements Method for thin plates.

Cite this paper

M. Haddad, Y. Gourinat and M. Charlotte, "Equivalence Theory Applied to Anisotropic Thin Plates," Engineering, Vol. 3 No. 7, 2011, pp. 669-679. doi: 10.4236/eng.2011.37080.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] E. ABSI, “La Theorie des Equivalences et Son Application a l’Etude des Ouvrages d’Art,” Série: Théories et Méthodes de Calcul, Annales de l’Institut Technique du Batiment et des Travaux Publics, Supplément No. 298, Octobre 1972.
[2] M. Haddad, “Application de la Methode des Equivalences en Dynamique,” Rapport de Stage Master2 Recherche, l’Institut Supérieur de l’Aéronautique et de l’Espace (ISAE), Toulouse, 7 February 2010.
[3] S. Vegas, “Application de la Theorie des Equivalences a l’Etude d’Une Dalle Biaise,” PhD Thesis, University Paul Sabatier de Toulouse, 11 June 1976.
[4] G. M. Cucchi, “Elastic-Static Analysis of Shear Wall/Slab-Frame Systems Using the Framework Method,” Pergamon, 30 June 1993.
[5] S. Timochenko, S. W. Kreiger, “Théorie des Plaques et Coques,” Librairie Polytechnique CH, Beranger, 1961.
[6] S. Abrate, “Inpact in Composite Structures,” Cambridge University Press, Cambridge, 1998, pp. 59-61. doi:10.1017/CBO9780511574504
[7] W. Leissa, “Vibrations of Plates,” Ohio State University Columbus, Ohio, Edition Scientific and Technical Information Division, Office of Technology Utilization, National Aeronautics and Space Administration, Washinton, DC, 1969.

  
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