Une justification du modèle de coques de Naghdi

A justification of Naghdi's shell model

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageFrench
Pages (from-to)951-954
Number of pages4
Journal / PublicationComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Issue number10
Publication statusPublished - 15 May 1999
Externally publishedYes


We consider a thin linearly elastic loaded shell allowing non-zero inextensional displacements. Under some assumptions on the loads, we prove that the tangential and normal parts of the stress tensor are small compared with the transverse part, when the thickness of the shell goes to zero. Besides, the displacement vector and the transverse part of the stress tensor are of the same order of magnitude with respect to the thickness when the material constituting the shell is isotropic and homogeneous. The limit model, which is a flexural model, can also be obtained from Naghdi's model but not from Koiter's model. In some cases of anisotropic materials, the displacement vector is of a larger order of magnitude than the stress tensor, when the thickness goes to zero.