Equivalence Theory Applied to Anisotropic Thin Plates
Madjid Haddad, Yves Gourinat, Miguel Charlotte
DOI: 10.4236/eng.2011.37080   PDF    HTML     6,587 Downloads   10,979 Views   Citations


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.

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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.


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[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.
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[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.
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[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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