Akian, Jean-Luc; Sanchez-Palencia, Évariste Approximation of thin elastic shells by flat elements. Phenomena of membrane locking. (Approximation de coques élastiques minces par facettes planes. Phénomènes de blocage membranaire.) (French. Abridged English version) Zbl 0761.73068 C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 363-369 (1992). Summary: We consider elastic shells in the so called “non-inhibited” case, when the mean surface \(S\) with the kinematic boundary conditions admits inextensional displacements, which form a space \(G\neq\{0\}\). The asymptotic behaviour of the shell when its thickness tends to zero is described in terms of \(G\). Approximating the surface \(S\) by polyhedral surfaces \(S_ h\) the edges enjoy stiffness properties implying that \(G_ h\) is in general very different from \(G\). The approximation by flat elements is then unfitted for thin shells (membrane locking). We exhibit precise counter-examples to the approximation. We also consider an example of a finite element approximation. Cited in 3 Documents MSC: 74K15 Membranes 74S05 Finite element methods applied to problems in solid mechanics Keywords:inextensional displacements; asymptotic behaviour; polyhedral surfaces PDF BibTeX XML Cite \textit{J.-L. Akian} and \textit{É. Sanchez-Palencia}, C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 363--369 (1992; Zbl 0761.73068)