中文摘要：

本文对作大范围运动的中心刚体．柔性梁系统的耦合变形的影响进行研究。给出一种新的描述柔性梁耦合变形的有限元插值方法，该方法采用笛卡尔变形坐标对横向变形和纵向变形之间的耦合项进行描述，该耦合变形项只与本单元的节点变形坐标相关。分别讨论了耦合变形项对惯性力与弹性力的贡献，分析了它们对刚一柔耦合动力学行为的影响。通过研究指出当采用笛卡尔变形坐标描述时，如果在计算弹性力的时候考虑了耦合变形影响，无论在计算惯性力时是否考虑耦合变形影响，都可以得到稳定收敛的结果。反之，如果在计算弹性力时忽略了耦合变形影响，无论在计算惯性力时是否考虑耦合变形影响，当大范围运动的速度较高时，将会得到错误的发散的结果。因此，通过忽略耦合变形对质量分布的影响，只保留耦合变形对弹性力的影响，可实现对动力学方程的简化。

英文摘要：

The effect of coupling deformation was investigated for flexible hub-beam system undergoing large overall motion. A new finite element interpolation method was proposed for the description of coupling deformation of flexible beam, in which coupling deformation of longitudinal and transverse quantities of the beam was described with Cartesian coordinates. The contributions of coupling deformation term on inertia forces and elastic forces were discussed, and their effects on the dynamic behavior of rigid-flexible systems were investigated. Research results indicate that the 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, the 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.