As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed. Unfortunately, this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the associated computational cost is overwhelming. Consequently, beam models, which are one-dimensional approximations of three-dimensional elasticity, have become the workhorse of many flexible multibody dynamics codes. Numerous beam formulations have been proposed, such as the geometrically exact beam formulation or the absolute nodal coordinate formulation, to name just two. New solution strategies have been investigated as well, including the intrinsic beam formulation or the DAE approach. Finally, Lie group concepts are playing an increasing role in the field. Clearly, a systematic comparison of these various approaches is desirable and is the focus of this paper. The various beam formulations will be assessed by comparing their predictions for four benchmark problems. The first problem is the Princeton beam experiment, a study of the static large displacement and rotation behavior of a simple cantilevered beam under a gravity tip load. The second problem, the four-bar mechanism, focuses on a flexible mechanism involving beams and revolute joints. The third problem investigates the behavior of a beam bent in its plane of greatest flexural rigidity, resulting in lateral buckling when a critical value of the transverse load is reached. The last problem investigates the dynamic stability of a rotating shaft. The predictions of eight independent codes are compared for these four benchmark problems.
|Titolo:||Validation of Flexible Multibody Dynamics Beam Formulations Using Benchmark Problems|
|Autori interni:||MASARATI, PIERANGELO|
|Data di pubblicazione:||2014|
|Appare nelle tipologie:||04.1 Contributo in Atti di convegno|