Velocity-based approach in non-linear dynamics of three-dimensional beams with enforced kinematic compatibility

•We present velocity-based approach for dynamic analysis of three-dimensional beams.•Spatial and temporal discretization are based on additive quantities.•Rotational degrees of freedom are handled using quaternion algebra.•A special care is taken in deriving discrete kinematic compatibility equations.

In the paper we present a new finite-element formulation for the dynamic analysis of geometrically exact three-dimensional beams. We limit our studies to implicit time-integration schemes and possible approaches for increasing their robustness and numerical stability. In contrast to standard displacement-rotation based approach we present here a spatial and temporal discretization based on velocities and angular velocities. To describe the rotational degrees of freedom quaternions are used. The time-integration scheme and the governing equations of the three-dimensional beam are modified accordingly. In the numerical implementation the Galerkin-type discretization is employed to obtain the finite-element formulation of the problem. The result of our studies is simple, but accurate, efficient and robust numerical model.