Recursive algorithm with efficient variables for flexible multibody dynamics with multiloop constraints

An algorithm is given to reduce computer time for simulation of motion of hinge-connected flexible multibody systems with multiple structural loops. The algorithm is based on using efficient motion variables for elastic motion and hinge rotation in a recursive formulation for an articulated system of bodies in a tree configuration. This formulation is then used for multiloop systems by cutting the loops at joints and exposing unknown constraint forces. A new development is given of the intertwining of the effects of the constraint forces on the accelerations of the bodies, with constraint force contributions requiring a two-stage update. Explicit expression of the accelerations in terms of the constraint forces leads to a particularly simple form for the evaluation of the latter. Numerical efficiency of the algorithm is shown by examples comparing to a standard, nonrecursive formulation using customary motion variables. Examples include large-angle slewing of a flexible solar sail, flexible multiantenna spacecraft with prescribed motion for internal loads calculation, a whirling chain of flexible bodies with two ends pinned, and a multiloop, flexible multibody mechanism. All the examples demonstrate the relative computational efficiency of the new formulation, with efficiency increasing with increased number of modes per flexible body.