On the Geometric Stiffness Matrices in Flexible Multibody Dynamics

A flexible branch body in a multibody chain undergoing large overall motions experiences geometric stiffening effects due to its own motions and interbody forces arising from bodies outboard of it. The self-motion effects are modelled through the use of 21 geometric stiffness matrices, in the literature, for an arbitrarily shaped flexible body. In this paper, the effect of interbody forces on the flexible body dynamics is modelled using up to 6 additional geometric stiffness matrices per outboard joint. Simulation results presented indicate that for a flexible body consisting of outboard bodies one may consider only the interbody force effects, without loss of accuracy, and thus significantly reduce the computational burden. This approach is especially suitable for multibody systems such as the Shuttle Remote Manipulator System, where the long boom masses are of similar magnitude, or when the payloads are several orders of magnitude larger than the link masses.