Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams

In this paper, we introduce a new class of discontinuous Galerkin methods for Timoshenko beams. The main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to approximations to the displacement and bending moment at the element boundaries. After displaying the methods, we obtain conditions under which they are well defined. We then compare these new methods with the already existing discontinuous Galerkin methods for Timoshenko beams. Finally, we display extensive numerical results to ascertain the influence of the stabilization parameters on the accuracy of the approximation. In particular, we find specific choices for which all the variables, namely, the displacement, the rotation, the bending moment and the shear force converge with the optimal order of k+1 when each of their approximations are taken to be piecewise polynomial of degree k ≥ 0.