A p-version MITC finite element method for Reissner–Mindlin plates with curved boundaries

摘要

We consider the approximation of Reissner–Mindlin plates with curved boundaries, using a p-version MITC finite element method. We describe in detail the formulation and implementation of the method, and emphasize the need for a Piola-type map in order to handle the curved geometry of the elements. The results of our numerical computations demonstrate the robustness of the method and suggest that it gives near exponential convergence when the error is measured in the energy norm. For the robust computation of quantities of engineering interest, such as the shear force, the proposed method yields very satisfactory results without the need for any additional post-processing. Comparisons are made with the standard finite element formulation, with and without post-processing.