Hierarchic finite elements for thin naghdi shell model

Two approaches have traditionally been used when general shell structures have been analysed. The first approach has been devised by Kirchhoff and Love and later the model has been improved by Koiter. A second class of models is based on the notion of surface introduced by Cosserat. Naghdi has developed this model, where the Reissner-Mindlin-type assumptions are taken into account. In this paper we consider the shell model arising from the Naghdi formulation. It is known that finite element schemes for this model suffer from both shear and membrane locking. Several solutions to avoid the numerical locking have been proposed. Here a displacement finite element scheme is developed using C" finite elements of hierarchic type with degrees ranging from one to four. Two severe test problems are solved. The results show that good performances are achieved by using high-order finite elements to solve the shell problem in its displacement formulation. The numerical results indicate that high-order elements perform very well in both test problems and match all the available benchmark results.