A review on plate and shell theories for laminated and sandwich structures highlighting the Finite Element Method

In engineering, the amount of complex geometrical problems, which needs to be solved by using plates and shells theories, is remarkable. This is the reason why there are so many theories, which attempt to simplify three-dimensional problems into simpler ones. Additionally, the current increasing use of laminated and sandwich structures demands a minimum of accuracy from two-dimensional formulations. In the literature, one can find a variety of bi-dimensional theories and solution methods to solve these problems. Laminated and sandwich structure formulations are mainly classified according to the treatment of the variables in the normal direction of the plate/shell surface: equivalent single layer, Zig-Zag and layer-wise theories. The contribution of this paper is to set the stage for new theories and solution methods for laminated and sandwich structures by reviewing over 100 papers. To show the importance of the coupling between plate/shell theories and the respective solution method, a detailed review on theories and the respective solution methods is firstly given to update the current state of art. After that, solution methods based on the Finite Element Method are explained to exhibit how particular and/or complex an approach can get. In fact, this review gives a clearer picture on plate/shell theories.