滑轮绳索系统中动态节点绳索单元

齐朝晖; 国树东; 卓英鹏

doi:10.6052/0459-1879-19-168

滑轮绳索系统中动态节点绳索单元

doi: 10.6052/0459-1879-19-168

大连理工大学工程力学系, 大连 116024

基金项目: 1) 国家自然科学基金资助项目(11872137);1) 国家自然科学基金资助项目(91748203)

详细信息

通讯作者:
齐朝晖

中图分类号: O313.7
计量
- 文章访问数: 1257
- HTML全文浏览量: 284
- PDF下载量: 152
- 被引次数: 0
出版历程
- 收稿日期: 2019-06-29
- 刊出日期: 2019-11-18

ROPE ELEMENTS WITH MOVING NODES IN ROPE-PULLEY SYSTEMS

Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 解除了传统有限元方法中单元节点与物质点固结的假设, 建立了空间点的速度和加速度与相应物质点的速度和加速度之间的数学关系, 强调了虚功率原理中出现的速度和加速度皆为物质速度和物质加速度. 在此基础上构造了单元节点既不与空间坐标固定也不与物质坐标固定的动态节点绳索单元. 根据滑轮绳索系统的特点, 选取绳索出入绳点的弧长坐标、出入绳角、面外摆角以及拉伸应变等空间参数描述了滑轮绳索系统的运动. 将绳索与滑轮以及绳索与卷筒之间的相互作用合理简化为物质速度间的约束条件, 避免了传统方法中接触力计算不收敛、效率低等缺点. 所提方法可精细求解绳索与滑轮间接触边界点位置和卷筒入绳点在卷筒上的运动、滑轮的中心和其连体基的运动、绳索出入滑轮和卷筒时空间方位的变化以及绳索上任意点的拉力变化等细节. 可为含绳索机械系统的力学分析提供新的理论基础. 所用的解除单元节点与物质点绑定的理论具有一定的普适性, 可为有限元方法的理论和应用提供参考.
- 多柔体系统动力学 /
- 有限元方法 /
- 滑轮绳索系统 /
- 动态节点 /
- 空间描述
Abstract: In traditional finite element methods, a common hypothesis is the nodes of an element being fixed with material points, which place restrictions on the description of a system. In this paper, this hypothesis is released and a new kind of rope element with nodes being no longer fixed with either spatial coordinates or material coordinates is presented. The theory of obtaining material velocity and acceleration of a point from the corresponding spatial velocity and acceleration of the point is established. The velocities and accelerations in the principle of virtual power should being material velocities and accelerations respectively is emphasized and applied. According to the feature of a rope-pulley system, its movement can be described by a new group of variables, such as arc-lengths, azimuthal angles and strains of ropes at entrance and exit contacting points. Instead of traditional methods, conditions of contact between rope and pulley are modeled as the material velocity of a point on the contacting rope being equal to the corresponding point on the pulley. By means of the presented methods, some obstacles, such as frequently divergence and high time consuming that resulting from traditional finite element methods can be removed. Motion equation of the rope-pulley system is derived by the principle of virtual power. Arc-length coordinates, positions of contact boundary points, the movement of pulley centers and their body-fixed reference coordinate systems, shape and positions changing of ropes as well as the tension forces in every point of a rope, can be obtained high precisely. The presented method can provide a new theoretical basis for analysis of mechanical systems with ropes and pulleys. The presented theory of using spatial points as describing variables to replace traditional material points is of applicable widely. It can be a reference for theory and application of finite element methods.
- dynamics of multi-flexible bodies /
- finite element methods /
- rope-pulley system /
- moving node /
- spatial description

HTML全文

参考文献(1)

1	Zienkiewicz OC, Taylor RL, Zhu JZ . The Finite Element Method: Its Basis and Fundamentals. Elsevier Science, 2013
2	Zienkiewicz OC, Taylor RL . The Finite Element Method for Solid and Structural Mechanics. Elsevier Science, 2013
3	Zienkiewicz OC, Taylor RL, Nithiarasu P . The Finite Element Method for Fluid Dynamics. Elsevier Science, 2013
4	钱伟长 . 广义变分原理. 上海: 知识出版社, 1985
4	( Qian Weichang. Generalized Variational Principle. Shanghai: Knowledge Publishing House, 1985 (in Chinese))
5	龙驭球, 龙志飞, 岑松 . 新型有限元论. 北京: 清华大学出版社, 2003
5	( Long Yuqiu, Long Zhifei, Cen Song. New Finite Element Theory. Beijing: Tsinghua University Press, 2003 (in Chinese))
6	Saritas A, Soydas O. Variational base and solution strategies for non-linear force-based beam finite elements. International Journal of Non-Linear Mechanics, 2012,47(3):54-64
7	Lee CK, Angela ML, Hale JS, et al. Strain smoothing for compressible and nearly-incompressible finite elasticity. Computers & Structures, 2017,182(1):540-555
8	Antonietti P, Verani M, Vergara C, et al. Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids. Finite Elements in Analysis & Design, 2019,159(1):1-14
9	Sun YP, Chen SC, Yang YQ. The families of nonconforming mixed finite elements for linear elasticity on simplex grids. Applied Mathematics and Computation, 2019,358(1):348-362
10	Li YH, Niu RP, Liu GR. Highly accurate smoothed finite element methods based on simplified eight-noded hexahedron elements. Engineering Analysis with Boundary Elements, 2019,105(1):165-177
11	Durand R, Pantoja-Rosero BG, Oliveira V. A general mesh smoothing method for finite elements. Finite Elements in Analysis & Design, 2019,158(1):17-30
12	何涛 . 基于ALE有限元法的流固耦合强耦合数值模拟. 力学学报, 2018,50(2):395-404
12	( He Tao, A partitioned strong coupling algorithm for fluid-structure interaction using arbitrary lagrangian-eulerian finite element formulation. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(2):395-404 (in Chinese))
13	江守燕, 李云, 杜成斌 . 改进型扩展比例边界有限元法. 力学学报, 2019,51(1):278-288
13	( Jiang Shouyan, Li Yun, Du Chengbin, Improved extended scaled boundary finite element methods. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):278-288 (in Chinese))
14	Murdoch AI. Physical Foundations of Continuum Mechanics. Cambridge: Cambridge University Press, 2012
15	金栋平, 文浩, 胡海岩 . 绳索系统的建模、动力学和控制. 力学进展, 2004,34(3):304-313
15	( Jin Dongping, Wen Hao, Hu Haiyan, Modeling,dynamics and control of cable systems. Advances in Mechanics, 2004,34(3):304-313 (in Chinese))
16	胡海岩, 田强, 张伟等. 大型网架式可展开空间结构的非线性动力学与控制. 力学进展, 2013,43(4):390-414
16	( Hu Haiyan, Tian Qiang, Zhang Wei, et al. Nonlinear dynamics and control of large deployable space structures composed of trusses and meshes. Advances in Mechanics, 2013,43(4):390-414 (in Chinese))
17	浦汉军, 谢小鹏, 牛高产等. 钢丝绳吊重提升系统的动载分析. 中国机械工程, 2012,23(24):2926-2929
17	( Pu Hanjun, Xie Xiaopeng, Niu Gaochan, et al. Study on dynamic load in load-lifting system of wire rope. China Mechanical Engineering, 2012,23(24):2926-2929 (in Chinese))
18	沈文厚, 赵治华, 任革学等. 拦阻索冲击的多体动力学仿真研究. 振动与冲击, 2015,34(5):73-77
18	( Shen Wenhou, Zhao Zhihua, Ren Gexue, et al. Multi-body dynamic simulation of impact on cross deck pendant. Journal of Vibration and Shock, 2015,34(5):73-77 (in Chinese))
19	Wang JJ, Cao GH, Wang YD, et al. A novel driving strategy for dynamic simulation of hoisting rope with timeivarying length. International Journal of Modeling Simulation & Scientific Computing, 2013,4(3):135009-1350025
20	陈伟海, 陈泉柱, 刘荣强等. 绳驱动拟人臂机器人回零算法分析. 浙江大学学报(工学版), 2013,47(2):345-352
20	( Chen Weihai, Chen Quanzhu, Liu Rongqiang, et al. Homing algorithm analysis of a cable-driven humanoid-arm manipulator. Journal of Zhejiang University (Engineering Science), 2013,47(2):345-352 (in Chinese))
21	谭春林, 魏承 . 绳索动力学基础研究. 北京: 科学出版社, 2018
21	( Tan Chunlin, Wei Cheng. Basic Research of Rope Dynamics. Beijing: Science Press, 2018 (in Chinese))
22	王郡, 朱永宁, 徐鉴 . 自主泳动弹性绳的轨迹模拟. 力学学报, 2019,51(1):198-208
22	( Wang Jun, Zhu Yongning, Xu Jian, Trajectory simulation of self-propelled elastic rods in fluid. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):198-208 (in Chinese))
23	齐朝晖, 宋慧涛, 张志刚 . 核环吊平衡路径与吊重轨迹偏差. 工程力学, 2014,31(1):209-217
23	( Qi Zhaohui, Song Huitao, Zhang Zhigang, Equilibrium paths and load trajectory deflections of nuclear ring cranes. Engineering Mechanics, 2014,31(1):209-217 (in Chinese))
24	Fritzkowski P, Kaminski H. Dynamics of a rope modeled as a multi-body system with elastic joints. Computational Mechanics, 2010,46(6):901-909
25	Kamman JW, Huston RL. Multibody dynamics modeling of variable length cable systems. Multibody Syst Dyn, 2001,5(3):211-221
26	Danilin AN, Grishanina TV, Shklyarchuk FN, et al. Dynamics of a space vehicle with elastic deploying tether. Computers & Structures, 1999,72(1-3):141-147
27	Russell JJ, Anderson WJ. Equilibrium and stability of a whirling rod-mass system. International Journal of Non-Linear Mechanics, 1977,12(2):91-101
28	Kamman JW, Huston RL. Dynamics of constrained multibody systems. Journal of Applied Mechanics, 1984,51(4):899-903
29	谭益松, 刘伊威, 刘宏等. 空间大型末端执行器柔性钢丝绳的建模与捕获动力学. 机器人, 2011,33(2):156-160
29	( Tan Yisong, Liu Yiwei, Liu Hong, et al. Modeling and capture dynamics of flexible cables used in large-scale space end-effector. Robot, 2011,33(2):156-160 (in Chinese))
30	Wittbrodt E, Adamiec-Wójcik I, Wojciech S . Dynamics of Flexible Multibody Systems: Rigid Finite Element Method. Berlin: Springer, 2006
31	Ju F, Choo YS. Super element approach to cable passing through multiple pulleys. International Journal of Solids & Structures, 2005,42(11-12):3533-3547
32	Hong D, Ren G. A modeling of sliding joint on one dimensional flexible medium. Multibody Syst Dyn, 2011,26:91-106.
33	Escalona JoséL. An arbitrary Lagrangian--Eulerian discretization method for modeling and simulation of reeving systems in multibody dynamics. Mechanism and Machine Theory, 2017,112:1-21
34	Sun J, Tian Q, Hu H, et al. Axially variable-length solid element of absolute nodal coordinate formulation. Acta Mechanica Sinica, 2019,35(3):653-663
35	Du JL, Bao H, Cui CZ, et al. Dynamic analysis of cable-driven parallel manipulators with time-varying cable lengths. Finite Elements in Analysis and Design, 2012,48(1):1392-1399
36	Banfi C, Marzocchi A, Musesti A. On the principle of virtual powers in continuum mechanics. Ricerche Di Matematica, 2006,55(2):139-150
37	Maugin GA. The principle of virtual power: from eliminating metaphysical forces to providing an efficient modelling tool. Continuum Mechanics & Thermodynamics, 2013,25(2-4):127-146
38	齐朝晖, 曹艳, 王刚 . 多柔体系统数值分析的模型降噪方法. 力学学报, 2018,50(4):863-870
38	( Qi Zhaohui, Cao Yan, Wang Gang, Model smoothing methods in numerical analysis of flexible multibody systems. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(4):863-870 (in Chinese))