Rigid-flexible multibody equations of motion suitable for vehicle dynamics and crash analysis

In this paper several formulations for automatic generation of the equations of motion for rigid and flexible multibody systems are reviewed. These formulations are of special interest for vehicle dynamics and crash analysis. We first discuss a so-called body-coordinate formulation to construct the Newton-Euler equations of motion for constrained rigid multibody systems. Then we review a nonconventional point-coordinate formulation. An easy-to-use method for deriving the equations of motion for flexible bodies in a multibody environment is also presented. Several ideas on how a body-fixed frame can be attached to a flexible body are discussed. It is shown how these formulations for rigid and flexible bodies could be mixed in order to construct the complete set of equations of motion. The constructed equations are normally a large set of mixed differential-algebraic equations. The method of joint-coordinates for transforming these equations to a smaller set is briefly discussed. Two application examples for ride/handling and crash analyses are also presented.