A two-loop sparse matrix numerical integration procedure for the solution of differential/algebraic equations: Application to multibody systems
A two-loop sparse matrix numerical integration procedure for the solution of differential/algebraic equations: Application to multibody systems
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DOI：
10.1016/j.jsv.2009.06.020
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发表时间：
2009-11
影响因子：
4.7
通讯作者：
A. Shabana;Bassam A. Hussein
中科院分区：
文献类型：
--
作者：
A. Shabana;Bassam A. Hussein
本文提出了一种用于求解约束刚性和柔性多体系统微分和代数方程的双循环隐式稀疏矩阵数值积分（TLISMNI）程序。所提出的方法确保在位置、速度和加速度水平上满足运动学约束方程。在该方法中，首先使用稀疏拉格朗日增广形式的运动方程来确保在加速度水平上满足约束，以求解所有加速度和拉格朗日乘子。然后使用 HTT 或 Newmark 公式识别并积分独立坐标和速度，在本文中仅以独立加速度表示。然后，在迭代牛顿-拉夫逊过程中使用位置级别的约束方程来确定相关坐标。相关速度通过求解线性代数方程组来确定。为了有效利用高效的稀疏矩阵技术并具有最小的存储要求，提出了一种两循环迭代方法。同样重要的是，所提出的方法避免了数值微分的使用，数值微分通常与多体系统算法中隐式积分方法的使用相关。给出数值示例是为了演示新积分过程的使用。
In this paper, a two-loop implicit sparse matrix numerical integration (TLISMNI) procedure for the solution of constrained rigid and flexible multibody system differential and algebraic equations is proposed. The proposed method ensures that the kinematic constraint equations are satisfied at the position, velocity and acceleration levels. In this method, a sparse Lagrangian augmented form of the equations of motion that ensures that the constraints are satisfied at the acceleration level is first used to solve for all the accelerations and Lagrange multipliers. The independent coordinates and velocities are then identified and integrated using HTT or Newmark formulas, expressed in this paper in terms of the independent accelerations only. The constraint equations at the position level are then used within an iterative Newton–Raphson procedure to determine the dependent coordinates. The dependent velocities are determined by solving a linear system of algebraic equations. In order to effectively exploit efficient sparse matrix techniques and have minimum storage requirements, a two-loop iterative method is proposed. Equally important, the proposed method avoids the use of numerical differentiation which is commonly associated with the use of implicit integration methods in multibody system algorithms. Numerical examples are presented in order to demonstrate the use of the new integration procedure.