Reduction Methods for large scale multibody systems

The floating frame of reference formulation (FFRF) has become a standard for the modeling of deformable moving bodies. In the FFRF, the component mode synthesis method is utilized in order to reduce the number of unknowns in a complex model. Some of the drawbacks of this methodology are the large number of static modes in the case of complex coupling of bodies, e.g. in contact problems or in advanced joint models, and the large number of dynamic modes for the case of high frequency analysis, e.g. for the analysis of the acoustic behavior of a car body. Standard nonlinear finite element methods are known to be computationally very expensive compared to modally reduced methods. An efficient formulation based on absolute coordinates with a reduced co-rotated strain tensor has been derived recently and the analogy to the floating frame of reference formulation has been shown. The efficiency of this formulation is based on a co-rotated constant mass and stiffness matrix that is factorized only once for the whole simulation. It turned out that this formulation has advantages in the case of problems with nonlinear materials or contact of flexible bodies. Furthermore, a modal reduction is possible for this formulation in the planar and linear elastic case, which can reduce the computational costs again. As a common problem in the multibody formulations, the number of constraints significantly influences the performance. It is therefore shown in the present paper how to reduce the number of constraint conditions for finite element meshes, while the overall results stay the same. The constraint reduction is based on the equilibrium of forces, moments and possibly higher order moments. Numerical examples are presented for several models of a flexible slider-crank mechanism, where the computational time could be reduced by some factors compared to conventional methods. The solution and the CPU times of the proposed methods, implemented in the computer code HOTINT, are compared with the commercial code MSC.ADAMS.