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.