一种含闭环约束多体系统高精度求解方法

赵天骄; 齐朝晖; 王天堉; 徐金帅

doi:10.21656/1000-0887.450230

一种含闭环约束多体系统高精度求解方法

doi: 10.21656/1000-0887.450230

1. 中国科学院大连化学物理研究所，辽宁大连 116024;
2. 大连理工大学，辽宁大连 116024

基金项目:

国家自然科学基金（11872137）

详细信息

作者简介:
赵天骄（1991—），男，博士(通信作者. E-mail: 1657268906@qq.com);齐朝晖（1964—），男，教授，博士，博士生导师(E-mail: zhaohuiq@dlut.edu.cn).

通讯作者:
赵天骄（1991—），男，博士(通信作者. E-mail: 1657268906@qq.com)

中图分类号: O313.7
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- 文章访问数: 19
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- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2024-08-14
- 修回日期: 2025-02-11
- 网络出版日期: 2026-07-30
- 刊出日期: 2026-08-01

High Precision Methods for Solving Multi-Body Systems With Close Loop Constraints

1. Dalian Institute of Chemical Physics, Chinese Academy of Sciences,Dalian, Liaoning 116024, P.R. China;

Funds:

The National Science Foundation of China(11872137)

摘要

摘要: 含闭环约束多体系统的动力学方程是一组微分代数混合方程，它在数值求解过程中的主要难点有： ① 难以同时较高精度满足位移、速度、加速度约束方程，会随着误差的积累引起较大的违约； ② 经常存在冗余约束以及奇异构型问题，严重影响求解过程的数值性态和结果的准确性.本文提出了一种可处理奇异构型闭环多体系统的数值求解方法，该方法摒弃了传统的约束独立性假设，在形成运动方程之前，对位置和速度进行修正，使其满足约束方程，而不是在每个积分步骤结束时纠正约束违约.并且根据约束的几何特性可知，速度和加速度在超曲面约束法空间中的分量全部由约束决定.通过列置换的QR分解得到约束法切空间的正交基向量，建立起系统广义速度与独立广义速度之间的关系，进而将微分代数混合方程转换为满足速度与加速度约束的纯微分方程（方程个数等于系统的广义坐标数），这种方法可以与任何标准ODE求解器协作.然后，将正交投影违约修正的方法应用到系统中，通过几次迭代有效地抑制系统位置和速度的违约量.同时，依据虚功率等效原理，进一步揭示了Lagrange乘子在求解切断铰约束反力和约束反力矩中的重要物理意义.本文所提方法可以动态识别独立约束，处理冗余约束和奇异构型问题，可高精度求解含闭环约束多体系统.最后，通过几个数值算例验证了方法的有效性.
- 闭环约束 /
- 多体系统 /
- 微分代数混合方程 /
- 铰约束反力 /
- 违约修正
Abstract: The dynamics equations for multi-body systems with closed-loop constraints are a set of differential algebraic mixed equations. The main difficulties in their numerical solution are as follow: it is difficult to satisfy the displacement, velocity and acceleration constraint equations with high precision at the same time, which will cause large defaults with the accumulation of errors; there are often redundant constraints and singular configuration problems, which seriously affect the numerical behavior of the solution process and the accuracy of the results. Herein, a numerical method for solving singular configuration closed-loop multibody systems was presented, without the traditional constraint independence assumption. The correction of position and velocity were done to satisfy the constraint equations before the motion equation formulation, rather than the correction of the constraint default at the end of each integration step. This method works with any standard ODE solver. According to the geometric characteristics of constraints, the components of velocity and acceleration in the hypersurface constraint space were all determined by constraints. The orthogonal basis vectors of the constrained tangent space were obtained through QR decomposition of the column permutation. The relationship between the generalized velocity of the system and the independent generalized velocity was established, and the default values of the generalized velocity and the generalized acceleration were filtered out in the dynamic calculation process, and the differential algebraic mixed equation was transformed into a pure differential equation satisfying the velocity and acceleration constraints ( with the number of equations equal to the generalized coordinate number of the system). Then, the orthogonal projection default correction method was applied to the system, and the default magnitude of the system position and speed was effectively suppressed by several iterations. At the same time, according to the principle of virtual power equivalence, the physical significance of the Laplace multiplier in solving the constraint reaction torque of the cut hinge was further revealed. Numerical examples show that, the precision of displacement, velocity and acceleration constraints of the proposed method is higher than that of the traditional augmented method and the penalty function method. The proposed method can deal with redundant constraints and singular configuration problems, and can be programmed to solve multi-body systems with closed-loop constraints with high precision. The proposed method can identify the independent constraints dynamically and modify the motion equation accordingly. Numerical examples demonstrate the effectiveness of the proposed method.
- closed-loop constraint /
- multi-body system /
- mixed differential algebraic equation /
- joint constraint force /
- correction of default

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参考文献(35)

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一种含闭环约束多体系统高精度求解方法

doi: 10.21656/1000-0887.450230

作者简介:
赵天骄（1991—），男，博士(通信作者. E-mail: 1657268906@qq.com);齐朝晖（1964—），男，教授，博士，博士生导师(E-mail: zhaohuiq@dlut.edu.cn).

通讯作者:
赵天骄（1991—），男，博士(通信作者. E-mail: 1657268906@qq.com)

计量

High Precision Methods for Solving Multi-Body Systems With Close Loop Constraints

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目录

留言板

一种含闭环约束多体系统高精度求解方法

doi: 10.21656/1000-0887.450230

作者简介: 赵天骄（1991—），男，博士(通信作者. E-mail: 1657268906@qq.com);齐朝晖（1964—），男，教授，博士，博士生导师(E-mail: zhaohuiq@dlut.edu.cn).

通讯作者: 赵天骄（1991—），男，博士(通信作者. E-mail: 1657268906@qq.com)

计量

出版历程

High Precision Methods for Solving Multi-Body Systems With Close Loop Constraints

计量

出版历程

目录

作者简介:
赵天骄（1991—），男，博士(通信作者. E-mail: 1657268906@qq.com);齐朝晖（1964—），男，教授，博士，博士生导师(E-mail: zhaohuiq@dlut.edu.cn).

通讯作者:
赵天骄（1991—），男，博士(通信作者. E-mail: 1657268906@qq.com)