We show that the intrinsic equations of Koiter's model of a linearly elastic shell can be derived from the intrinsic formulation of the three-dimensional equations of a linearly elastic shell, by using an appropriate a priori assumption regarding the three-dimensional strain tensor fields appearing in these equations. To this end, we recast in particular the Dirichlet boundary conditions satisfied by any admissible displacement field as boundary conditions satisfied by the covariant components of the corresponding strain tensor field expressed in the natural curvilinear coordinates of the shell. Then we show that, when restricted to strain tensor fields satisfying a specific a priori assumption, these new boundary conditions reduce to those of the intrinsic equations of Koiter's model of a linearly elastic shell.
Nous établissons que les équations intrinsèques du modèle de coques linéairement élastiques de Koiter peuvent étre déduites de la formulation intrinsèque des équations tridimensionnelles d'une coque linéairement élastique en faisant une hypothèse a priori appropriée sur les champs de tenseurs de déformation tridimensionnels apparaissant dans ces équations. À cette fin, nous reformulons en particulier les conditions au bord de Dirichlet satisfaites par tout champ de déplacements admissible comme des conditions au bord satisfaites par les composantes covariantes du champ de tenseurs de déformations exprimées en fonction des coordonnées curvilignes naturelles de la coque. Nous montrons ensuite que, lorsqu'elles sont restreintes aux champs de tenseurs de déformations satisfaisant une hypothèse a priori spécifique, les nouvelles conditions au bord se ramènent à celles des équations intrinsèques du modèle de coques linéairement élastiques de Koiter.
Accepted:
Published online:
Philippe G. Ciarlet 1; Cristinel Mardare 2
@article{CRMATH_2019__357_1_99_0, author = {Philippe G. Ciarlet and Cristinel Mardare}, title = {Asymptotic justification of the intrinsic equations of {Koiter's} model of a linearly elastic shell}, journal = {Comptes Rendus. Math\'ematique}, pages = {99--110}, publisher = {Elsevier}, volume = {357}, number = {1}, year = {2019}, doi = {10.1016/j.crma.2018.10.008}, language = {en}, }
TY - JOUR AU - Philippe G. Ciarlet AU - Cristinel Mardare TI - Asymptotic justification of the intrinsic equations of Koiter's model of a linearly elastic shell JO - Comptes Rendus. Mathématique PY - 2019 SP - 99 EP - 110 VL - 357 IS - 1 PB - Elsevier DO - 10.1016/j.crma.2018.10.008 LA - en ID - CRMATH_2019__357_1_99_0 ER -
%0 Journal Article %A Philippe G. Ciarlet %A Cristinel Mardare %T Asymptotic justification of the intrinsic equations of Koiter's model of a linearly elastic shell %J Comptes Rendus. Mathématique %D 2019 %P 99-110 %V 357 %N 1 %I Elsevier %R 10.1016/j.crma.2018.10.008 %G en %F CRMATH_2019__357_1_99_0
Philippe G. Ciarlet; Cristinel Mardare. Asymptotic justification of the intrinsic equations of Koiter's model of a linearly elastic shell. Comptes Rendus. Mathématique, Volume 357 (2019) no. 1, pp. 99-110. doi : 10.1016/j.crma.2018.10.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.10.008/
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