Isogeometric collocation methods for the dynamics of three-dimensional geometrically exact beams

In this paper we review some of the most recent computational techniques based on the isogeometric analysis for the solution of the dynamic problem of geometrically exact beams. The kinematics of a spatial Timoshenko beam undergoing finite displacements and rotations involves the Lie group SO(3). Most of the computational complexities originate from the presence of such a non-additive and non-commutative rotation group. By employing the incremental rotation vector to describe the evolution of finite rotations, we discuss how the isogeometric collocation (IGA-C) method can be efficiently used in both explicit and implicit Newmark-based schemes.