使用路径跟踪法寻找用还原传递矩阵法建模的多体系统的静态平衡点

IF 2.6 2区 工程技术 Q2 MECHANICS Multibody System Dynamics Pub Date : 2024-06-05 DOI:10.1007/s11044-024-09996-y
Xizhe Zhang, Xiaoting Rui, Jianshu Zhang, Lina Zhang, Junjie Gu
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引用次数: 0

摘要

寻找多体系统的稳定静态平衡位置是一个众所周知的问题。工程中经常使用动态松弛法,但这种方法往往需要大量时间。另外,大多数商业软件都采用牛顿-拉斐森迭代法来求解一组非线性方程,直接找到平衡位置,其中任何量的时间导数都设为零。然而,这种方法高度依赖于初始条件,无论系统有多少自由度,对于特定的初始条件只能找到一个平衡位置。本文采用路径跟踪法来寻找多体系统的平衡位置,利用还原多体系统传递矩阵法来评估加速度函数及其雅各布矩阵,其中应用了直接微分的概念。然后使用弧长法跟踪广义加速度变化的求解曲线,如果它们消失,则获得候选平衡状态,并确定稳定的静态平衡位置。为了证明所提方法的有效性,我们给出了数值示例,详细介绍了完整的计算流程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Use of a path-following method for finding static equilibria of multibody systems modeled by the reduced transfer matrix method

Finding the stable static equilibrium position of multibody systems is a well-known problem. Dynamic relaxation methods are frequently utilized in engineering, however, they often require a significant amount of time. Alternatively, most commercial software employs the Newton–Raphson iterative method to solve a set of nonlinear equations to find the equilibrium position directly, in which the time derivatives of any quantity are set to zero. Nevertheless, this approach is highly dependent on initial conditions and can only find one equilibrium position for a specific initial condition, no matter how many degrees of freedom a system has. A path-following method is implemented in this paper to find the equilibrium position of the multibody system by using the reduced multibody system transfer matrix method to evaluate the acceleration functions and its Jacobian matrix, where the notion of direct differentiation is applied. The solution curves for changing generalized accelerations are then tracked using the arc-length method to obtain candidate equilibrium states if they vanish and identify the stable static equilibrium position. To demonstrate the effectiveness of the proposed method, numerical examples are presented, which provide a detailed overview of the complete computational flow.

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来源期刊
CiteScore
6.00
自引率
17.60%
发文量
46
审稿时长
12 months
期刊介绍: The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations. The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
期刊最新文献
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