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

*(English)*Zbl 1162.74019Summary: In flexible multibody systems, component mode synthesis is used to reduce the size of system matrices of 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 non-diagonal structure of 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.

##### MSC:

74H45 | Vibrations in dynamical problems in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |

##### Software:

BEAM189
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\textit{J. Gerstmayr} and \textit{J. A. C. Ambrósio}, Int. J. Numer. Methods Eng. 73, No. 11, 1518--1546 (2008; Zbl 1162.74019)

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