基于Bathe积分算法的机械系统多体动力学方程求解方法

Solving Method for Dynamic Equations of Mechanical Multibody System by Using Bathe Integration Algorithm

准确与高效的求解算法一直是多体系统动力学领域的关键问题.重点研究了将Bathe积分算法应用于机械系统多体动力学方程的求解,将多体系统动力学方程整理为显含广义阻尼矩阵的一般形式.利用Bathe积分策略,推导了基于此形式动力学方程的求解流程,并将广义阻尼矩阵用于迭代计算时雅克比矩阵初值的选择,减少迭代计算次数.为了减小违约的影响,动力学方程中添加了Baumgarte违约稳定项.数值算例表明:利用Bathe积分算法求解多体系统动力学方程具有高准确性、良好的稳定性和较低的数值耗散,显含广义阻尼矩阵的动力学方程形式也使求解更加高效.

Accurate and efficient solving algorithms have always been the key issue in the field of multibody system dynamics.Solving dynamic equations of mechanical multibody system by using Bathe integration algorithm was investigated.The dynamic equations of multibody system were arranged into a general form containing the explicitly generalized damping matrix.Based on Bathe integration algorithm,the solution process according to the form of dynamic equations was derived,and the generalized damping matrix was used in obtaining the initial value of Jacobian matrix during iterative calculation which reduces the number of iterations.In order to reduce the influence of constraint violation,the Baumgarte constraint stabilization items were added to the dynamic equations.The numerical examples show that solving the dynamic equations of multibody system by utilizing the Bathe integration algorithm has a high accuracy,a good stability,and a low numerical dissipation,and the dynamic equation form with an explicity generalized damping matrix obviously makes the solution more efficient.