Locking-Free Optimal Discontinuous Galerkin Methods for Timoshenko Beams

In this paper, we consider the so-called hp-version of discontinuous Galerkin methods for Timoshenko beams. We prove that, when the numerical traces are properly chosen, the methods display optimal convergence uniformly with respect to the thickness of the beam. These methods are thus free from shear locking. We also prove that, when polynomials of degree p are used, all the numerical traces superconverge with a rate of order ${\rm{h}}^{{\rm{2p + 1}}} {\rm{/p}}^{{\rm{2p + 1}}} {\rm{.}}$ Numerical experiments verifying the above-mentioned theoretical results are shown.