多体系统动力学方程的基于离散零空间理论的Newmark积分算法

Discrete Null Space Method for the Newmark Integration of Multibody Dynamic Systems

考虑到多体系统动力学方程的数值计算方法是系统动力学分析的基础,提出一种基于离散零空间理论的Newmark积分算法。应用Newmark积分框架对多体系统动力学方程在时域上进行离散,通过离散零空间矩阵消去动力学方程中的拉格朗日乘子项,建立离散的达朗贝尔动力学方程,采用局部结点参数化进一步获得降维的达朗贝尔动力学方程。以空间双摆为算例,数值结果表明:该算法能够在实现系统降维、提高计算效率的同时,进行有效的数值分析,约束违约很小。

Considering that the algorithm of the equations of motion of multibody systems is the base for the analysis of dynamics,the discrete null space method for the Newmark integration is proposed.The procedure is essentially based upon the following steps.The equations of motion of constrained multibody systems are directly discretized by the Newmark time stepping scheme.The discrete Lagrange multipliers are eliminated by using a discrete null space matrix and the discrete d＇Alembert-type formulation is obtained.The number of unknowns is reduced further by employing specific local reparametrizations.It is shown that the developed method can not only reduce the dimension of the equations of motion,thus improving the computational efficiency,but also obtain the good results with less constraint violation.