On the accuracy of p-version elements for the Reissner-Mindlin plate problem

This paper addresses the question of accuracy of p-version finite element formulations for Reissner-Mindlin plate problems. Three model problems, a circular arc, a rhombic plate and a geometrically complex structure are investigated. Whereas displacements and bending moments turn out to be very accurate without any post-processing even for very coarse meshes, the quality of shear forces computed from constitutive equations is poor. It is shown that significantly improved results can be obtained, if shear forces are computed from equilibrium equations instead. A consistent computation of second derivatives of the shape functions is derived.