The displacement vector of a linearly elastic shell can be computed by using the two-dimensional Koiter 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 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. In addition, in the case of shells with uniformly elliptic middle surface, taking into account the term depending on the rotation of the normal allows one to improve the asymptotic estimate between the three-dimensional displacement and Koiter's bidimensional displacement.
@article{hal-01478634,
author = {Lods, V\'eronique and Mardare, Cristinel},
title = {Asymptotic justification of the Kirchhoff-Love hypotheses for a linearly elastic clamped shell},
journal = {HAL},
volume = {1998},
number = {0},
year = {1998},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01478634}
}
Lods, Véronique; Mardare, Cristinel. Asymptotic justification of the Kirchhoff-Love hypotheses for a linearly elastic clamped shell. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-01478634/