Keywords: multi-body systems, modal-space solution, geometric nonlinearity.

Multi-body system (MBS) software packages have been originally developed with the primary objective to enable efficient simulation of rigid body system dynamics. However, many physical systems require consideration of the behaviour of flexible bodies in a MBS in order to meet the requirement for improved simulation accuracy. Any improvement in the accuracy is closely related to a higher complexity of formalisms used for computations and, therefore, leads to higher numerical effort. Regarding MBS software packages, this increase in numerical effort needs to be kept within acceptable limits. The finite element (FE) method has become essential in the field of structural analysis. Direct inclusion of full FE models into the MBS is prohibitively expensive, because FE models are characterized by a rather large number of degrees of freedom. An alternative could be a co-simulation, which implies separate MBS and FE computations and data transfer between the two. But such an approach also results in a great numerical effort and is, therefore, rather time-consuming. Hence, in order to retain the numerical efficiency of MBS computations, flexible body behaviour is accounted for by a significant FE model reduction. This is typically done by modal-space based approaches, where modes become the degrees of freedom in terms of which the elastic behaviour is determined and the solution is obtained by modal superposition. Again for the sake of numerical efficiency, it is operated with orthogonal modes, thus decoupling the part of the system of equations related to the flexible body behaviour. The choice of the modes is of crucial importance for the accuracy of the solution obtained. In MBS programs the component mode synthesis (CMS) technique is used, particularly the Craig-Bampton method. The method implies that fixed-boundary normal modes and constraint modes are first computed and the so-obtained set of modes is orthonormalized prior to use within MBS.

Numerically efficient as it is, this approach suffers, however, a severe limitation. Namely, modal-space based solutions allow intrinsically only consideration of deformations in the linear domain within the local coordinate system of the flexible body. In many cases, the amount of induced deformation may require consideration of geometric nonlinearities in elastic behaviour of flexible bodies. The focus of the paper is on this aspect. Hence, approaches to include geometric nonlinearities in the modal-space based solutions with the aim of improving the accuracy of the results for moderately large deformations are discussed. Stress stiffening effects are briefly addressed. Changes in the structural configuration during the course of the deformation, as a source of nonlinearity in structural response, are given greater attention. A method to address this aspect is proposed and discussed. It is described on a rather simple example and an extension for more complex structures is offered. An example from the car industry is given to illustrate the method.

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