基于绝对节点坐标的多柔体系统动力学高效计算方法

绝对节点坐标法已经被广泛应用于柔性多体系统的动力学研究之中,但是其计算效率问题尚未得到很好的解决.基于绝对节点坐标方法计算弹性力及其对广义坐标的偏导数矩阵(Jacobi矩阵),通常是基于第二类Piola-Kirchhoff应力张量来完成,计算效率不高.根据虚功原理并采用第一类Piola-Kirchhoff应力张量的方法直接推导得到了弹性力及其Jacobi矩阵的解析表达式.基于不同方法所得的数值算例结果对比研究表明,该方法可使计算效率大大提高.

EFFICIENT COMPUTATIONAL METHOD FOR DYNAMICS OF FLEXIBLE MULTIBODY SYSTEMS BASED ON ABSOLUTE NODAL COORDINATE

The absolute nodal coordinate method has been widely used to study the dynamics of flexible multibody systems. The computational efficiency of this method, however, has much room to be improved. Generally, the second kind of Piola-Kirchhoff stress tensor is used to derive the elastic forces and corresponding Jacobians, namely, the partial derivative matrix of the elastic forces with respect to the generalized coordinates. Nevertheless, this method is inefficient enough. Based on the principle of virtual work, the analytical formulations for the elastic forces and their Jacobians are deducted directly by using the first kind of Piola-Kirchhoff stress tensor. Numerical example results based on different methods show that the proposed approach is able to enhance the computational efficiency significantly.