约束机械系统动力学的一类完全解耦方法

A Complete Decoupling Method for Dynamics of Constrained Mechanical Systems

针对约束机械系统动力学分析所要处理的微分 代数方程组 ,先将其转化为基于隐式线性多步法的超定微分 代数方程组形式 ,然后采用一种微分流形的“投影”技术消除超定性 ,再对变化后的微分 代数方程组按照位置、速度、加速度的顺序进行解耦 ,化为线性方程组的求解序列 ,从而得到一类完全解耦算法 .算法可用于处理刚性问题 ,无需预估式 ,具有较高的效率 .算例证明了该算法的有效性 .

Aiming at the differential algebraic equations(DAEs) in dynamics of constrained mechanical system, this paper presents an algorithm which first converts the DAEs into overdetermined differential algebraic equations based on the implicit linear multistep method, then eliminates its overdetermination with certain 'projection' technology of differential manifold, finally decouples the equations and transforms them into linear equations sequences to solve the position, velocity and acceleration. The complete decoupling algorithm that can be used to solve the stiff problem without prediction is obtained. The validity of algorithm has been proved in the numerical experiment.