A novel finite element model incorporating rotary inertia in thin circular rods

In this article, we extend the finite element formulation proposed by Buckham et al.2 to include the effects of rotary inertia in isotropic circular rods (or cables). In developing our model, we first express the angular velocities in terms of the time derivatives of the Frenet frame and use this definition to determine the contributions of rotary inertia. A salient feature of this model is that only six variables representing the absolute position vectors are used as nodal coordinates. Galerkin’s weighted residual approach is used to complete the discretization.