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Compatibility of boundary angular velocities in the velocity-based 3D beam formulation
Zupan, Eva ; Zupan, Dejan, mehanik
In this paper, a new velocity-based finite element approach for non-linear dynamics of beam-like structures is introduced. In contrast to standard approaches we here base the formulation on ...velocities and angular velocities expressed in the most suitable basis regarding standard approximation and interpolation techniques. The additivity of angular velocities in local frame description brings several benefits, such as trivial discretization and update procedure for the primary unknowns and improved stability properties of the time integrator. On the other hand, different initial orientations of elements connected together lead to nodal angular velocities that are expressed in different frames and cannot be directly equalized. The compatibility of angular velocities over the finite element boundaries thus needs to be solved. We avoid introducing constraint equations and additional degrees of freedom and introduce a computationally cheap solution instead.
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