The interpolation of rotations and its application to finite element models of geometrically exact rods

Abstract

The finite element formulation of geometrically exact rod models depends crucially on the interpolation of the rotation field from the nodes to the integration points where the internal forces and tangent stiffness are evaluated. Since the rotational group is a nonlinear space, standard (isoparametric) interpolation of these degrees of freedom does not guarantee the orthogonality of the interpolated field hence, more sophisticated interpolation strategies have to be devised. We review and classify the rotation interpolation techniques most commonly used in the context of nonlinear rod models and suggest new ones. All of them are compared and their advantages and disadvantages discussed. In particular, their effect on the frame invariance of the resulting discrete models is analyzed.