Abstract
The paper develops a new type of geometrically exact beam element featuring large displacements and rotations together with small warping. The dimension reduction approach based on variational asymptotic method has been explored, and a linear two-dimensional finite element procedure has been implemented to predict the cross-sectional stiffness and recover the cross-sectional strain fields of the beam. The total and incremental variables mixed formula of governing equations of motion is presented, in which the Wiener–Milenković parameters are selected to vectorize the finite rotation. The dynamic problem of geometrically exact beam has been solved by the implicit Radau IIA algorithms, the time histories of large translations and rotations with small three-dimensional warping have been integrated. Numerical simulations have been performed and the results have been compared to those of commercial software LS-DYNA. It can be concluded that the current modeling approach features high accuracy and that the new geometrically exact beam with warping is robust enough to predict large deformations with small strain.
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The paper was written under the supports of both “2011 China overseas personnel science and technology activities supporting project” and “2011 Beijing overseas personnel science and technology activities supporting project”.
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Wang, J. Implementation of geometrically exact beam element for nonlinear dynamics modeling. Multibody Syst Dyn 35, 377–392 (2015). https://doi.org/10.1007/s11044-015-9457-8
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DOI: https://doi.org/10.1007/s11044-015-9457-8