| 刘颖,马建敏,苏芳,张文.多体系统动力学方程的无违约数值计算方法[J].计算力学学报,2010,27(5):942~947 |
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| 多体系统动力学方程的无违约数值计算方法 |
| Precise numerical solution for multi-body system’s equations of motionbased on algorithm without constraint violation |
| 投稿时间：2008-12-01 |
| DOI：10.7511/jslx20105033 |
| 中文关键词: 多体系统 动力学分析 微分代数方程 约束违约 隐式龙格库塔法 |
| 英文关键词:multi-body system dynamics analysis differential algebraic equation constraint violation implicit Runge-Kutta method |
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| 摘要点击次数: 2587 |
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| 中文摘要: |
| 多体系统动力学方程为3阶微分代数方程,已有的约束违约稳定法存在位移违约问题,数值仿真准确性和稳定性不足。本文将求解高阶微分代数方程的降阶理论、ε嵌入处理方式与隐式龙格库塔法相结合,提出了直接满足位移约束条件的多体系统动力学方程的无违约算法,避免了约束违约问题。该方法先将多体动力学方程转化为2阶微分代数方程,并与位移约束方程联立;再应用ε嵌入隐式龙格库塔法进行数值求解。应用两种方法分别对单摆机构进行数值仿真,结果表明本文的方法不仅能适应较大步长,且准确性和稳定性均优于约束违约稳定法。 |
| 英文摘要: |
| The multi-body system’s equations of motion belong to differential algebraic equation (DAE) of index-3. For the constraint violation, the accuracy and stabilization of the constraint violation stabilization method (CVSM) is rather inadequate. In this paper, incorporating the theory of reducing-order for DAE of high index, ε embedding method and implicit Runge-Kutta method, a precise algorithm without constraint violation is presented. Applying the method, the constraint violation could be avoided. Firstly, the equations of motion are converted into DAE with index-2 and the displacement constraint equation remains. Secondly, implicit Runge-Kutta method embedded ε is applied to solve the equation directly. Using the two methods, respectively, a single-pendulum system is simulated. The results show that our method has better computational precision and stabilization than CVSM, even using large-steps. |
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