On general shell finite elements and mathematical shell models

Abstract: We show that, although no actual mathematical shell model is explicitly used in ``general shell element'' formulations, we can identify an implicit shell model underlying these finite element procedures. This ``underlying model'' compares well with classical shell models since it displays the same asymptotic behaviours-when the thickness of the shell becomes very small-as, for example, the Naghdi model. Moreover, we substantiate the connection between general shell element procedures and this underlying model by mathematically proving a convergence result from the finite element solution to the solution of the model.