On the selection of p-version shape functions for plate vibration problems

This paper discusses the performance of the p-version shape function sets for plate vibration problems. First, the basic equations using the Reissner–Mindlin plate theory for vibration problems are introduced along with the shear locking phenomenon. Then, the two most common sets of shape functions for p version, the Lagrange set Q(p) and the serendipity set Q∗(p), are presented. The rest of the paper shows the behavior of both sets versus the shear locking problem and the efficiency of the sets to compute eigenvalues accurately. From the shear locking study, a new set is developed. This new set proves to be as stable as the Lagrange set and more efficient for the computation of accurate eigenvalues than the serendipity and Lagrange sets.