Complex Flexible Multibody Systems with Application to Vehicle Dynamics

Abstract

A formulation to describe the linear elastodynamics offlexible multibody systems is presented in this paper. By using a lumpedmass formulation the flexible body mass is represented by a collectionof point masses with rotational inertia. Furthermore, the bodydeformations are described with respect to a body-fixed coordinateframe. The coupling between the flexible body deformation and its rigidbody motion is completely preserved independently of the methods used todescribe the body flexibility. In particular, if the finite elementmethod is chosen for this purpose only the standard finite elementparameters obtained from any commercial finite element code are used inthe methodology. In this manner, not only the analyst can use any typeof finite elements in the multibody model but the same finite elementmodel can be used to evaluate the structural integrity of any systemcomponent also. To deal with complex-shaped structural models offlexible bodies it is necessary to reduce the number of generalizedcoordinates to a reasonable dimension. This is achieved with thecomponent mode synthesis at the cost of specializing the formulation toflexible multibody models experiencing linear elastic deformations only.Structural damping is introduced to achieve better numerical performancewithout compromising the quality of the results. The motions of therigid body and flexible body reference frames are described usingCartesian coordinates. The kinematic constraints between the differentsystem components are evaluated in terms of this set of generalizedcoordinates. The equations of motion of the flexible multibody systemare solved by using the augmented Lagrangean method and a sparse matrixsolver. Finally, the methodology is applied to model a vehicle with acomplex flexible chassis, simulated in typical handling scenarios. Theresults of the simulations are discussed in terms of their numericalprecision and efficiency.