Multibody System Dynamics 6: 163–182, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands. 163 Complex Flexible Multibody Systems with Application to Vehicle Dynamics JORGE A.C. AMBRÓSIO and JOÃO P.C. GONÇALVES Instituto de Engenharia Mecânica (IDMEC), Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal; E-mail: jorge@dem.ist.utl.pt, web page: http://www.lemac.ist.utl.pt/IDMEC/I/index.html (Received: 22 November 1999; accepted in revised form: 10 April 2000) Abstract. A formulation to describe the linear elastodynamics of flexible multibody systems is presented in this paper. By using a lumped mass formulation the flexible body mass is represented by a collection of point masses with rotational inertia. Furthermore, the body deformations are described with respect to a body-fixed coordinate frame. The coupling between the flexible body deformation and its rigid body motion is completely preserved independently of the methods used to describe the body flexibility. In particular, if the finite element method is chosen for this purpose only the standard finite element parameters obtained from any commercial finite element code are used in the methodology. In this manner, not only the analyst can use any type of finite elements in the multibody model but the same finite element model can be used to evaluate the structural integrity of any system component also. To deal with complex-shaped structural models of flexible bodies it is necessary to reduce the number of generalized coordinates to a reasonable dimension. This is achieved with the component mode synthesis at the cost of specializing the formulation to flexible multibody models experiencing linear elastic deformations only. Structural damping is introduced to achieve better numerical performance without compromising the quality of the results. The motions of the rigid body and flexible body reference frames are described using Cartesian coordinates. The kinematic constraints between the different system components are evaluated in terms of this set of generalized coordinates. The equations of motion of the flexible multibody system are solved by using the augmented Lagrangean method and a sparse matrix solver. Finally, the methodology is applied to model a vehicle with a complex flexible chassis, simulated in typical handling scenarios. The results of the simulations are discussed in terms of their numerical precision and efficiency. Key words: multibody dynamics, flexible vehicle dynamics, lumped mass formulation, modal su- perposition. 1. Introduction The need for more accurate models to describe the complex behavior of flexible systems experiencing large motion while undergoing small elastic deformations motivated the development of many powerful analysis techniques. The most pop- ular formulations use time variant mass matrices to describe the inertia coupling between the rigid body gross motion and the system elastodynamics [1]. Some coefficients of these inertia coupling matrices are dependent on the type of finite elements used in the model. They do not appear in standard finite element develop-