## 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

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