A brief overview of plate finite element methods

In this chapter we present a brief account of possible finite element methods (FEMs) for the plate bending problem, when described by means of the Reissner–Mindlin model. We point out that the following overview is far from being exhaustive: we are perfectly aware that many important approaches are not even mentioned. Accordingly, also the references are very limited and lack completeness. The choice of schemes that are going to be described is strongly biased by the author’s experience, and it does not correspond to any efficiency or robustness criterion. We also remark that we are not going to detail any rigorous convergence and stability proof. Rather, we will try to heuristically explain 1. the main troubles arising from the FEM discretization of plate problems (Section 25.2); 2. why the methods under consideration succeed in the solution approximation (Section 25.3).