On the ellipticity of linear shell models (Q1194090)

The refined shell theory approximating the exact three-dimensional stress state of thin shells introduced by W. T. Koiter is analyzed. A new proof of the ellipticity of the Koiter's two-dimensional strain energy is given. The proof is based on the lemma of J. L. Lions (used originally for the establishing of the generalized Korn's inequality) and on the ``rigid displacement lemma'' due to \textit{M. Bernadou} and the first author [Lect. Notes Econ. Math. Syst. 134, 89-136 (1976; Zbl 0356.73066), C. R. Acad. Sci., Paris, Ser. A 282, 793-795 (1976; Zbl 0331.73091)].