Advanced modelling of flexible multibody systems using virtual bodies

Abstract

When new formulations for the description of flexible multibody systems are proposed, often they imply the use of new sets of generalized coordinates, even if the finite element method is used to describe the system flexibility. The adoption of such formulations implies that an additional effort must be made to describe the kinematic constraints that involve flexible bodies. The commercial multibody codes generally have good kinematic joint libraries for rigid bodies, but they are limited in the type of joints available in what flexible bodies are concerned. This work proposes and demonstrates that such limitations can be overcome by using virtual rigid bodies. The idea is to develop a single kinematic joint that restricts all relative degrees of freedom between one or more nodes of the flexible body and a rigid body. The designation of virtual body derives from assuming that it is a massless rigid body. In this form any of the kinematic joints between rigid bodies available in the multibody code libraries, can be used. In the process it is shown that the interaction of the user with the multibody code is much simpler. The numerical problems resulting from ill-conditioned mass matrix, due to the null inertias of the virtual bodies, are avoided by using a sparse matrix solver for the solution of the equations of motion. The proposed formulation is applied to a complex flexible multibody system, represented by the model of a road vehicle with flexible chassis, the results are presented and the discussion on the relative virtues and drawbacks of the current methodologies is made with emphasis on the models and algorithms used.