An Eulerian approach for large displacements of thin shells including geometrical non-linearities

This paper is devoted to the problem of large displacement of shells, the only non-linearity being geometrical. The geometry of the mid-surface of the shell is determined thanks to the knowledge of nodes and normal vectors, and is continuously updated. Stresses are also carried from one configuration to another, which enables us to linearize the equilibrium equations. It is then possible to build an Eulerian formulation. Moreover, some control strategies are proposed, in order to find limit points and unstable solutions. Finally, we check in some classical examples, the accuracy of this technique.