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

Akian, Jean-Luc; Sanchez-Palencia, Évariste

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.

MSC:

74K15	Membranes
74S05	Finite element methods applied to problems in solid mechanics

Keywords:

inextensional displacements; asymptotic behaviour; polyhedral surfaces