PSRI elements for the Reissner–Mindlin free plate

The Reissner–Mindlin plate model in presence of free boundary conditions is considered. It is known that in this case the solution can suffer, for small thickness, from some boundary layer effects that reduce the regularity of the solution, in particular of the rotations and shear strains. This causes a loss of convergence order in the numerical approximation. For this reason a new model that modifies the free boundary conditions is considered. The approximation of this new model by means of an element of low degree of the partial selective reduced integration family has been analyzed both from the theoretical and the numerical point of view. Some numerical results have been presented showing the performance of this element when applied to free plates.