EI、Scopus 收录
中文核心期刊

基于\pmb \theta_1方法的多体动力学数值算法研究

Numerical method of multibody dynamics based on \theta _1 method

  • 摘要: 将结构动力学领域的\theta_1方法拓展到数值求解多体系统运动方程------微分--代数方程(DAEs), 分别求解指标-3 DAEs形式的运动方程和指标-2超定DAEs(ODAEs)形式的运动方程. 通过数值算例验证了方法的有效性, 并得到\theta _1方法中参数\theta _1的选取与数值耗散量之间的关系. 数值算例还说明对于同一个多体系统, 采用指标-3的DAEs 描述时存在速度违约, 用指标-2的ODAEs描述时,从计算机精度上讲, 位置和速度约束方程同时满足, 并且\theta_1方法在求解非保守系统DAEs和ODAEs形式的运动方程时都具有2阶精度. 最后\theta_1 方法与其他直接积分法求解DAEs和ODAEs形式运动方程的CPU时间进行了比较.

     

    Abstract: In the numerical integration of ordinary differentialequations (ODEs) in structural dynamics community, \theta _1 method hascharacteristics of controlled numerical dissipation and second-orderaccuracy for systems with or without physical damping. Based on thesecharacteristics, \theta _1 method is extended to the numerical integrationof motion equations in multibody system dynamics. The solved motionequations are index-3 differential-algebraic equations (DAEs) andindex-2 over-determined DAEs (ODAEs). Numerical experiments validate the\theta_1 method, experiments also show the relationship of numericaldissipation with parameter \theta_1.As for theintegration of index-3 DAEs by \theta _1 method, it has violation ofvelocity constraint, while for index-2 ODAEs, there are no violation ofposition and velocity constraint in the view of computer precision. Inaddition, experiments illustrate that, for non-conservative system motionequations in the form of index-3 DAEs and index-2 ODAEs, \theta _1 methodhas second-order accuracy. In the end, \theta _1 methods for motionequations are compared with other direct-time integrations from the CPU timepoint of view.

     

/

返回文章
返回