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Equivalence Theory Applied to Anisotropic Thin Plates

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 modeling may be substituted by another one that, even though it may possibly have material constitutive laws and geomet- ric 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. [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 Bâtiment 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.
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Madjid Haddad, Yves Gourinat, M. Charlotte. Equivalence Theory Applied to Anisotropic Thin Plates. Engineering, Scientific Research, 2011, 3 (7), pp.669-679. ⟨10.4236/eng.2011.37080⟩. ⟨hal-01852516⟩



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