Complete geometric nonlinear formulation for rigid-flexible coupling dynamics

A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.