Justification asymptotique des hypothèses de Kirchhoff-Love pour une coque encastrée linéairement élastique

The displacement vector of a linearly elastic shell can be computed by using the two-dimensional Koiter's model, based on the a priori Kirchhoff-Love assumptions. These hypotheses imply that the displacement of any point of the shell is an affine function of the transverse variable x₃. The term independent of x₃ of this approximation is equal to the displacement vector of the two-dimensional Koiter's model. The term linear in x₃ depends on the rotation vector of the normal. After an appropriate scaling, we here estimate the difference between the three-dimensional displacement and the affine function in the case of shells clamped along their entire lateral face. Besides, in the case of shells with uniformly elliptic middle surface, taking into account the term depending of the rotation of the normal, allows to improve the asymptotic estimate between the three-dimensionnal displacement and Koiter's bidimensional displacement.