State-of-the-art flexible multibody system simulation tools rely on geometrically exact formulations for the flexible structural components and exact enforcement of the kinematic constraints. In these formulations, the displacement and rotation fields are treated independently. In the motion formalism, the displacement and rotation fields are treated as a single entity and the resulting equations of motion for flexible multibody systems are intrinsic, i.e., only depend on quantities that are invariant, with respect to rigid-body transformations. This leads to low-order nonlinearities and significant opportunities to reduce the computation cost of dynamic simulations.
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