On conservation of energy and kinematic compatibility in dynamics of nonlinear velocity-based three-dimensional beams
Zupan, Eva ; Zupan, Dejan, mehanik
In this paper, we present an original energypreserving numerical formulation for velocity-based geometrically exact three-dimensional beams. We employ the algebra of quaternions as a suitable tool to ...express the governing equations and relate rotations with their derivatives,while the finite-element discretization is based on interpolation of velocities in a fixed frame and angular velocities in a moving frame description. The proposed time discretization of governing equations directly relates the energy conservation constraint with the time-discrete kinematic compatibility equations. We show that a suitable choice of primary unknowns together with a convenient choice of the frame of reference for quantities and equations is beneficial for the conservation of energy and enables admissible approximations in a simple manner and without any additional effort. The result of this study is simple and efficient, yet accurate and robust numerical model.
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