Some new results and current challenges in the finite element analysis of shells

Finite element procedures are widely used in engineering practice to analyse the behaviour of shell structures. However, the concept of “shell finite element” is still somewhat fuzzy, as it may correspond to very different ideas and techniques in various actual implementations. In particular, a significant distinction can be made between shell elements that are obtained via the discretization of shell models, and shell elements-such as the general shell elements-derived from 3D formulations using some kinematical assumptions, without the use of any shell theory. Our first objective in this paper is to give a unified perspective of these two families of shell elements. This is expected to be very useful as it paves the way for further thorough mathematical analyses of shell elements. A particularly important motivation for this is the understanding and the treatment of the deficiencies associated with the analysis of thin shells (among which the locking phenomenon). We then survey these deficiencies, in the framework of the asymptotic behawiours of shell models. We conclude the article by giving some detailed guidelines to numerically assess the performance of shell finite elements as regards these pathological phenomena, which is essential to design improved procedures.