Study On Modeling Theory And Simulation Technique For Rigid-Flexible Coupling Systems Dynamics

In this dissertation, the modeling theory and simulation technique of rigid-flexible coupling systems dynamics are investigated.The traditional hybrid-coordinate method of flexible multi-body systems is essentially a coupling modeling method of zero order approximation(MZOA), in which small elastic deformation assumption in structure dynamics is adopted and the high-order coupling terms of flexible body deformation are ignored. In 1987, Kane et al studied the dynamic performance of a flexible beam with rotation motion and the results indicate that the MZOA fails to describe dynamics of the system when the system is in high rotating velocity. Recently, a modeling method of rigid-flexible dynamics based on axial integral (MBAI) was developed by the group of professor Hong Jia-zhen based on the theory of continuum medium mechanics and the theory of analysis dynamics, which was a first-order approximation coupling model method, and second-order coupling term of deformation of flexible body were taken into count. The validity of the MBAI was verified by physical experiments. However, for the coupling deformation term of an arbitrary point in flexible beam is in integral from the bottom point when using the MBAI, which is a limitation for MBAI to investigate the rigid-flexible coupling dynamics of general flexible bodies. Later, the group proposed a modeling method base on Co-rotational coordinates (MBCR) to describe the non-linear deformation field of flexible bodied, which could break the limitation of MBAI. However, the computational efficiency of MBCR is poor.The first standard to evaluate a dynamical model is whether it could satisfy the request of reliability to reflect the essence the rigid-flexible coupling dynamics exactly. Moreover, it should have good numerical character and computational efficiency, which makes it easy to realize numerical simulation in computer. Therefore, it become the object of this dissertation to established a more general and efficient dynamic model of rigid-flexible coupling systems for the requirement of the engineering.In this dissertation, the dynamic modeling method of rigid-flexible coupling system based on element coupling deformation (MBECD) is proposed, in which three reference frames (global frame, floating frame, and element translate frame) are used to describe the configuration of arbitrary point in the flexible body. The floating frame is used to realizes the separation of the rigid motion and elastic deformation, and element translate frame is used to describe nonlinear coupling deformation. Firstly, the relationship of Cartesian deformation coordinate and non-Cartesian deformation coordinate is derived based on principle of continuum mechanics; the deformation of a arbitrary point in the element can be interpolated with non-Cartesian nodal deformation coordinates through element shape functions; non-Cartesian nodal deformation coordinates are transferred into Cartesian nodal deformation coordinates and allocated in floating frame, then the nonlinear coupling deformation field is obtained. In MBAI method, the coupling deformation terms of an arbitrary point are related with all the elements between the local element and the bottom. However, in MBECD prospected in this dissertation, the coupling deformation terms only relate with the located element nodal coordinates, which makes it possible for MBECD to investigate general shape flexible bodies.The rigid-flexible coupling dynamics of flexible bodies are studied by using MBECD prospected in this dissertation. The dynamic equations of flexible beam and thin plate undergoing overall large motions are derived based on Hamiltion principle and Jourdan velocity variation principle respectively. The simulation examples of flexible beam and thin plate undergoing prescribed motions and free motions are investigated to verify the validity of the MBECD to be applied in rigid-flexible coupling dynamic analysis of flexible bodies, which will not suffer the numerical divergence as ZOAC does. Simulation results also show the MBECD has good element convergence and relative high computational efficiency. Moreover, the simulation examples of curve beam and irregular plate are given to verify that the MBECD can be used to study the rigid-flexible coupling dynamics of complex shape flexible bodies.To improve the computational efficiency, and be applied in engineering conveniently, the simplification of rigid-flexible coupling dynamic equations of flexible bodies undergoing overall large motions are studied. The effects of coupling deformation term on the dynamic behavior of rigid-flexible systems are investigated. Research results indicate that stable solution can be obtained with Cartesian deformation coordinates when the effect of coupling deformation on calculating elastic forces is considered, regardless of the effect of coupling deformation on calculating inertia forces is ignored or not. On other hand, unstable solution can be obtained with high speed motion when the effect of coupling deformation on calculating elastic forces is ignored, regardless of the effect of coupling deformation on calculating inertia forces is ignored or not. It is possible to reduce the dynamic model of rigid-flexible systems through ignoring the effects of coupling deformation on calculating inertia forces and considering the effects of coupling deformation on calculating elastic forces when the Cartesian deformation coordinates are used.