Component mode synthesis with constant mass and stiffness matrices applied to flexible multibody systems

• Published in: International journal for numerical methods in engineering 2008-03, Vol.73 (11), p.1518-1546
• Main Authors: Gerstmayr, J., Ambrósio, J. A. C.
• Format: Article
• Language: English
• Subjects: absolute coordinate formulation; component mode synthesis; Computational techniques; contact; Exact sciences and technology; finite elements; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; multibody systems; Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2133

In flexible multibody systems, component mode synthesis is used to reduce the size of system matrices of the single bodies from millions to a few hundred, while maintaining the full coupling between body deformation and overall rigid body motion. The combination of clamped eigenmodes and static deformation modes results in a dense and non‐diagonal structure of the system matrices which is computationally costly. In the present paper, the conventional concept of the floating frame of reference is transformed to a description based on absolute coordinates and a corotational linearization of the deformation. The constant mass matrix and the corotated stiffness matrix need to be factorized only once for the whole simulation. In a planar example, component mode synthesis is applied to this absolute coordinate formulation by using twice as many deformation modes as usual, while the solution of the overall system becomes less expensive due to efficient factorization. The size of the system matrices needs to be increased considerably for each axis of rotation. However, the computational complexity for the factorization reduces from cubic to quadratic. Numerical examples are presented in order to demonstrate the difference between standard procedures and the methodology now proposed. Copyright © 2007 John Wiley & Sons, Ltd.