Investigation on the choice of boundary conditions and shape functions for flexible multi-body system

The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference (FFR) formulation. The deformations obtained by the absolute nodal coordinate (ANC) formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Numerical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free-free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time. The project was supported by the National Natural Science Foundation of China (10872126) and the Research Fund of the Doctoral Program of Higher Education of China (20100073110007).

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