柔性多体系统动力学新型广义-α数值分析方法

New Generalized-α Algorithms for Multibody Dynamics

结合隐式数值积分解耦法,提出柔性多体系统动力学的新型广义-α数值分析方法。利用新型广义-α法乘以积分步长h或h2缩小因子的形式将积分步长引入至系统雅可比矩阵计算,获得离散的多体系统动力学方程和约束方程。基于隐式数值积分解耦法,获得系统变量的解耦方程组和系统雅可比矩阵。通过数值实例研究新型广义-α法的数值精度、收敛阶次、稳定性和计算效率。理论研究和数值分析表明,新型广义-α法极大减小了系统雅可比矩阵函数的估计数目和Newton-Raphson迭代次数,从而大大地减小了柔性多体系统动力学分析的求解规模,同时满足位移、速度及加速度约束。高效、高精度、可控数值阻尼的新型广义-α数值分析方法,对具有多柔体、接触冲击和摩擦等刚性性质的柔性多体系统动力学分析具有重要的理论参考意义和工程应用价值。

For analysis of multibody dynamics, a new generalized-α algorithm is proposed on the basis of implicit numerical integration decoupling algorithms. By applying the new generalized-α algorithm and introducing the scaling factor h or h2 of integration stepsize into the calculations of Jacobian matrix, discrete equations of multi-body dynamics and constraints equations are obtained. Decoupling equations for systems＇ variables and decoupling Jacobian matrix are obtained on the basis of implicit numerical integration decoupling algorithms, thereby improving the efficiency of calculation and avoiding poor Jacobian matrix. Accuracy, convergence, stability and efficiency analysis of the new generalized-α algorithm are carried out through numerical examples. Theoretical study and numerical analysis show that the new generalized-α algorithm reduces the number of evaluations of Jacobian matrix function, the iterations of Newton-Raphson and the calculations of dimensions of multi-flexible body dynamics greatly. The new generalized-α algorithm featuring efficiency, accuracy and controllable numerical damping has important theoretical reference meaning and practical application value to mechanical systems with multi flexible bodies, contact-impact and friction.