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On the ellipticity of linear shell models. (English) Zbl 0765.73046

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 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)].

MSC:

74K15 Membranes
35Q72 Other PDE from mechanics (MSC2000)
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