刚柔耦合约束多体系统的动力分析

DYNAMIC ANALYSIS OF CONSTRAINED MULTIBODY SYSTEM WITH COUPLED RIGID AND ELASTIC MOTIONS

本文提出了描述多体系统的牵连坐标轴系统。该坐标轴系统由惯性参考系、牵连坐标系、物体坐标系及单元坐标系组成，从而实现了对刚体平动、刚体转动及弹性运动的分解，较好地消除了由于刚体大角度转动而产生的刚弹耦合非线性特性，以有限元方法为基础，应用拉格朗日方程建立了在该坐标系下的刚弹耦合约束多体系统的动力方程。该方程具有形式简洁、易于推导和编程等优点，本文并对方程的数值解法进行了研究，提出求解的广义坐标分块法，最后给出了一个典型多体系统的数值算例。

A relative coordinate svstem is presented to describe the motion of multi-body systems.This coordinate system fully utilizes the property of translation matrix,sothat the nonlinear couplings between rigid motion and elastic motion are greatly reduced. The equations of planar and spatial deformable body are derived based on finite elemeiitmethod and Lagrange' s equation. Numerical methods for solving the equations are alsodiscussed and the generalized coordinate partitioning method is presented.According tothe above theory,the authors designed an analytical program of flexible multibody systems. An example is also given.