Asymptotic analysis of linearly elastic shells: `Generalized membrane shells' (Q1357206)

The aim of this paper is to complete and conclude the asymptotic analysis of linearly elastic shells undertaken by Ciarlet, Lods and Miara in 1996 (see, e.g. the authors [Arch. Ration. Mech. Anal. 136, No. 2, 119-161 (1996); ibid., 191-200 (1996)]; the authors and \textit{B. Miara} [ibid., 163-190 (1996)]; the authors [J. Math. Pures Appl., IX. Sér. 75, No. 2, 107-124 (1996; Zbl 0870.73037)]). Based on certain geometric and kinematic assumptions, the corresponding limiting problems are derived and discussed, and a kind of generalized membrane shell theory is formulated.