Isogeometric collocation method for geometrically exact timoshenko beams

This paper reports and discusses the main theoretical and computational aspects of a displacement-based and a mixed isogeometric collocation formulations for three-dimensional geometrically exact shear-deformable beams recently proposed by the author. The attention is focused on the geometric structure of the underlying configuration manifold of the Timoshenko beam model. High efficiency and accuracy are achieved by exploiting the computational features of the isogeometric collocation method in combination with a geometrically consistent kinematic model for the description of finite rotations which does not require collocation of extra equations.