Multisymplectic Galerkin Lie group variational integrators for geometrically exact beam dynamics based on unit dual quaternion interpolation — no shear locking - Leitz, Thomas; Sato Martin de Almagro, Rodrigo; Leyendecker, Sigrid (Computer Methods in Applied Mechanics and Engineering, 2021)
We present a Galerkin multisymplectic Lie group variational integrator. It is suitable for dynamical systems defined on a two dimensional space–time and the integrator allows arbitrary convergence orders independently for both dimensions. As an example we use geometrically exact beam dynamics where a slender structure is modelled as a centre line with a cross section at every point. The Lie group in question is the special Euclidean group in three-dimensional space, SE(3)SE(3)" role="presentation" style="display: inline-block; line-height: normal; font-size: 16.200000762939453px; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border-width: 0px; position: relative;">, which we parametrize using unit dual quaternions. This allows a very simple and efficient interpolation method to be used, which additionally prevents shear locking present in more naive discretizations of geometrically exact beams.<br