On the Velocity-Based Description in Dynamic Analysis of Three-Dimensional Beams

In numerical formulations of three-dimensional beams, the choice of primary interpolated variables is highly important for the efficiency and accuracy of the method. Since the spatial and temporal derivatives of configuration variables directly describe the total mechanical energy of the system, they seem to be a natural choice for the primary unknowns but are surprisingly rarely chosen as such. The crucial idea exploited in our approach is thus to employ velocities in the fixed frame description and angular velocities in moving frame description to set the discrete computational model. We further employ the algebra of quaternions as a suitable tool to express the governing equations and relate rotations with their derivatives.