基于绝对节点坐标法的弹性线方法研究

范纪华; 章定国; 谌宏

doi:10.6052/0459-1879-19-076

基于绝对节点坐标法的弹性线方法研究

范纪华^*†,,
章定国^**2),,
谌宏^†

* 江苏科技大学机电与动力工程学院, 江苏张家港 215600
? 江苏科技大学苏州理工学院, 江苏张家港 215600
** 南京理工大学理学院, 南京 210094

基金项目: 1) 国家自然科学基金项目(11502098);国家自然科学基金项目(11772158);江苏省高校自然科学研究面上项目(15KJB130003);江苏科技大学博士科研启动基金项目资助(120140003)

详细信息

通讯作者:
章定国

中图分类号: O313.7
计量
- 文章访问数: 1828
- HTML全文浏览量: 216
- PDF下载量: 238
出版历程
- 收稿日期: 2019-03-27
- 刊出日期: 2019-09-17

RESEARCH ON ELASTIC LINE METHOD BASED ON ABSOLUTE NODAL COORDINATE METHOD

Fan Jihua^*†,,
Zhang Dingguo^**2),,
Shen Hong^†

* School of Mechatronics and Power Engineering, Jiangsu University of Science and Technology, Zhangjiagang 215600, Jiangsu China
? Suzhou Institute of Technology, Jiangsu University of Science and Technology, Zhangjiagang 215600, Jiangsu China
** School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China

摘要

摘要: 相比于浮动坐标系法, 绝对节点坐标法(absolute nodal coordinateformulation, ANCF)在处理柔性体非线性大变形问题上具有显著优势,ANCF将单元节点坐标定义在全局坐标系下,采用斜率矢量代替节点转角坐标, 具有常数质量阵,不存在科氏离心力等优点, 然而弹性力阵为非线性项,其求解将比较耗时且占用资源. 据此, 在弹性力求解方法中,引入弹性线方法(elastic line method, ELM),该方法将格林--拉格朗日应变张量定义在中心线上,采用曲率公式来定义弯曲应变, 转角公式来定义扭转应变.同时采用有限元法对三维柔性梁位移场进行离散,求解梁单元常数质量阵、广义刚度阵、广义力阵,进而得到单元的动力学方程, 通过转换矩阵得到三维梁的动力学方程.接着从理论上指出连续介质力学方法(continuum mechanics method,CMM)和弹性线方法在求解弹性力上的不同点, 并编制动力学仿真软件.最后分别采用连续介质力学方法和弹性线方法对柔性单摆以及履带式车辆的动力学问题进行仿真分析,结果表明：弹性线方法能在保证精度的前提下有效提高计算效率.
- 绝对节点坐标法 /
- 连续介质力学方法 /
- 弹性线方法 /
- 动力学仿真 /
- 履带式车辆
Abstract: Compared with the floating frame of reference formulation, the absolute nodal coordinate formulation (ANCF) has significant advantages in dealing with the nonlinear large deformation problem of flexible bodies. ANCF defines the nodal co-ordinates in a global co-ordinate system, uses the global slopes instead of angles to define the orientation of the elements, has a constant mass matrix, and does not have the Coriolis centrifugal force. However,the elastic force matrix is a nonlinear term, and the solution will be time consuming and occupied resources. According to this,the elastic line method is introduced for solving the elastic force, the Green-Lagrangian strain tensor is defined on the centerline, the curvature formula is used to define the bending strain, and the torsion angle formula is used to define the torsional strain. At the same time, the finite element method is used to describe the displacement field of the three-dimensional flexible beam, and the constant mass matrix, the generalized stiffness matrix and the generalized force matrix of the beam element are solved, and then the dynamic equations of the element are obtained. The dynamic equations of the three-dimensional beam are obtained by the transformation matrix. Then the differences between the continuum mechanics method and the elastic line method are pointed out theoretically, and the dynamic simulation software is compiled. Finally, the dynamics behaviors of a flexible pendulum and a tracked vehicle are numerical investigated with the continuum mechanics method and the elastic line method. The results show that the elastic line method can effectively improve the calculation efficiency under the premise of ensuring accuracy.
- absolute nodal coordinate formulation /
- continuum mechanics method /
- elastic line method /
- dynamic simulation /
- tracked vehicle

HTML全文

参考文献(1)

[1]	Rafiee M, Nitzsche F, Labrosse M . Dynamics, vibration and control of rotating composite beams and blades: A critical review. Thin-Walled Structures, 2017,119:795-819
[2]	曹登庆, 白坤朝, 丁虎等. 大型柔性航天器动力学与振动控制研究进展. 力学学报, 2019,51(1):1-13
[2]	( Cao Dengqing, Bai Kunchao, Ding Hu , et al. Advances in dynamics and vibration control of large-scale flexible spacecraft. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):1-13 (in Chinese))
[3]	Liu JY, Hong JZ . Geometric stiffening effect on rigid-flexible coupling dynamics of an elastic beam. Journal of Sound and Vibration, 2004,278(4-5):1147-1162
[4]	高晨彤, 黎亮, 章定国等. 考虑剪切效应的旋转 FGM 楔形梁刚柔耦合动力学建模与仿真. 力学学报, 2018,50(3):654-666
[4]	( Gao Chentong, Li Liang, Zhang Dingguo , et al. Dynamic modeling and simulation of rotating FGM tapered beams with shear effect. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(3):654-666 (in Chinese))
[5]	Cai GP, Hong JZ, Yang SX . Dynamic analysis of a flexible hub-beam system with tip mass. Mechanics Research Communications, 2005,32(2):173-190
[6]	和兴锁, 李雪华, 邓峰岩 . 平面柔性梁的刚--柔耦合动力学特性分析与仿真. 物理学报, 2011,60(2):024502
[6]	( He Xingsuo, Li Xuehua, Deng Fengyan . Analysis and imitation of dynamic properties for rigid-flexible coupling systems of a planar flexible beam. Acta Physica Sinica, 2011,60(2):024502 (in Chinese))
[7]	陈思佳, 章定国, 洪嘉振 . 大变形旋转柔性梁的一种高次刚柔耦合动力学模型. 力学学报, 2013,45(2):251-256
[7]	( Chen Sijia, Zhang Dingguo, Hong Jiazhen . A high-order rigid-flexible coupling model of a rotating flexible beam under large deformation. Chinese Journal of Theoretical and Applied Mechanics, 2013,45(3):251-256 (in Chinese))
[8]	范纪华, 章定国 . 旋转柔性悬臂梁动力学的Bezier 插值离散方法研究. 物理学报, 2014,63(15):154501
[8]	( Fan Jihua, Zhang Dingguo . Bezier interpolation method for the dynamics of rotating flexible cantilever beam. Acta Physica Sinica, 2014,63(15):154501 (in Chinese))
[9]	杜超凡, 章定国, 洪嘉振 . 径向基点插值法在旋转柔性梁动力学中的应用. 力学学报, 2015,47(2):279-288
[9]	( Du Chaofan, Zhang Dingguo, Hong Jiazhen . A meshfree method based on radial point interpolation method for the dynamic analysis of rotating flexible beams. Chinese Journal of Theoretical and Applied Mechanics, 2015,47(2):279-288 (in Chinese))
[10]	范纪华, 章定国 . 基于变形场不同离散方法的柔性机器人动力学建模与仿真. 力学学报, 2016,48(4):843-856
[10]	( Fan Jihua, Zhang Dingguo . Dynamic modeling and simulation of flexible robots based on different discretization methods. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(4):843-856 (in Chinese))
[11]	章孝顺, 章定国, 洪嘉振 . 考虑曲率纵向变形效应的大变形柔性梁刚柔耦合动力学建模与仿真. 力学学报, 2016,48(3):692-701
[11]	( Zhang Xiaoshun, Zhang Dingguo, Hong Jiazhen . Rigid-flexible coupling dynamic modeling and simulation with the longitudinal deformation induced curvature effect for a rotating flexible beam under large deformation. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(3):692-701 (in Chinese))
[12]	Zhao G, Wu Z . Coupling vibration analysis of rotating three-dimensional cantilever beam. Computers & Structures, 2017,179:64-74
[13]	Sujash B, Debabrata D . Free vibration analysis of bidirectional-functionally graded and doubletapered rotating micro-beam in thermal environment using modified couple stress theory. Composite Structures, 2019,215:471-492
[14]	Tian JJ, Zhang ZG, Hua HX . Free vibration analysis of rotating functionally graded double-tapered beam including porosities. International Journal of Mechanical Sciences, 2019,150:526-538
[15]	Fang JS, Wang HW, Zhang XP . On size-dependent dynamic behavior of rotating functionally graded Kirchhoff microplates. International Journal of Mechanical Sciences, 2019,152:34-50
[16]	Shabana AA. Computational Continuum Mechanics, New York: Cambridge University Press, 2008
[17]	Bonet J, Wood RD. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge: Cambridge University Press, 1997
[18]	Simo JC, Vu-Quoc L . On the dynamics in space of rods undergoing large motions the planar case: Part I-II. ASME Transactions, Journal of Applied Mechanics, 1986,53:849-863
[19]	Berzeri M, Shabana AA . Development of simple models for the elastic forces in the absolute nodal coordinate formulation. Journal of Sound and Vibration, 2000,235(4):539-565
[20]	Omar MA, Shabana AA . A two-dimensional shear deformable beam for large rotation and deformation problems. Journal of Sound and Vibration, 2001,243(3):565-576
[21]	Dufva KE, Sopanen JT, Mikkola AM . A two-dimensional shear deformation beam element based on the absolute nodal coordinate formulation. Journal of Sound and Vibration, 2005,280:719-738
[22]	Shabana AA, Yakoub RY . Three dimensional absolute nodal coordinate formulation for beam elements: Theory. Journal of Mechanical Design, 2001,123(4):606-613
[23]	Yakoub RY, Shabana AA . Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications. Journal of Mechanical Design, 2001,123(4):614-621
[24]	Tian Q, Zhang Y, Chen L , et al. Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dynamics, 2010,60(4):489-511
[25]	Liu C, Tian Q, Hu H . New spatial curved beam and cylindrical shell elements of gradient-deficient absolute nodal coordinate formulation. Nonlinear Dynamics, 2012,70(3):1903-1918
[26]	过佳雯, 魏承, 谭春林等. 含芯拧绞绳非线性弯曲动力学特性分析与研究. 力学学报, 2018,50(2):373-384
[26]	( Guo Jiawen, Wei Cheng, Tan Chunlin , et al. Analysis of the cored stranded wire rope on the nonlinear bending dynamic characteristics. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(2):373-384 (in Chinese))
[27]	兰朋, 崔雅琦, 於祖庆 . 完备化ANCF 薄板单元及在钢板弹簧动力学建模中的应用. 力学学报, 2018,50(5):1156-1167
[27]	( Lan Peng, Cui Yaqi, Yu Zuqing . The completed form of elastic model for ANCF thin plate element and its application on dynamic modeling of the leaf spring. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(5):1156-1167 (in Chinese))
[28]	郑彤, 章定国, 洪嘉振 . 三维大变形梁系统的动力学建模与仿真. 机械工程学报, 2016,52(19):81-87
[28]	( Zheng Tong, Zhang Dingguo, Hong Jiazhen . Dynamic modeling and simulation for three dimensional flexible beam systems with large deformations. Journal of Mechanical Engineering, 2016,52(19):81-87 (in Chinese))
[29]	赵春璋, 余海东, 王皓等. 基于绝对节点坐标法的变截面梁动力学建模与运动变形分析. 机械工程学报, 2014,50(17):38-45
[29]	( Zhao Chunzhang, Yu Haidong, Wang Hao , et al. Dynamic modeling and kinematic behavior of variable cross-section beam based on the absolute nodal coordinate formulation. Journal of Mechanical Engineering, 2014,50(17):38-45 (in Chinese))
[30]	Cui YQ, Yu ZQ, Lan P . A novel method of thermo-mechanical coupled analysis based on the unified description. Mechanism and Machine Theory, 2019,134:376-392
[31]	Liu J, Pan K . Rigid-flexible-thermal coupling dynamic formulation for satellite and plate multibody system. Aerospace Science and Technology, 2016,52:102-114
[32]	Shen Z, Li H, Liu X , et al. Thermal shock induced dynamics of a spacecraft with a flexible deploying boom. Acta Astronautica, 2017,141:123-131
[33]	García-Vallejo D, Mayo J, Escalona JL , et al. Efficient evaluation of the elastic forces and the Jacobian in the absolute nodal coordinate formulation. Nonlinear Dynamics, 2004,35(4):313-329
[34]	章孝顺, 章定国, 陈思佳等. 基于绝对节点坐标法的大变形柔性梁几种动力学模型研究. 物理学报, 2016,65(9):094501
[34]	( Zhang Xiaoshun, Zhang Dingguo, Chen Sijia , et al. Several dynamic models of a large deformation flexible beam based on the absolute nodal coordinate formulation. Acta Physica Sinica, 2016,65(9):094501 (in Chinese))
[35]	陈渊钊, 章定国, 黎亮 . 平面细长梁基于无网格径向基点插值的绝对节点坐标法. 振动工程学报, 2018,31(2):245-254
[35]	( Chen Yuanzhao, Zhang Dingguo, Li Liang . An absolute nodal coordinate formation based on radial point interpolation method for planar slender beams. Journal of Vibration Engineering, 2018,31(3):245-254 (in Chinese))
[36]	Chen Y, Zhang D, Li L . Dynamic analysis of rotating curved beams by using absolute nodal coordinate formulation based on radial point interpolation method. Journal of Sound and Vibration, 2019,441:63-83
[37]	Zemljari$\check{\rm o}$B, A$\check{\rm z}$be V . Analytically derived matrix end-form elastic-forces equations for a low-order cable element using the absolute nodal coordinate formulation. Journal of Sound and Vibration, 2019,446:263-272
[38]	Luo K, Hu H, Liu C , et al. Model order reduction for dynamic simulation of a flexible multibody system via absolute nodal coordinate formulation. Computer Methods in Applied Mechanics and Engineering, 2017,324:573-594

施引文献(16)

期刊类型引用(13)

1.	张国策，聂磊，陈云. 简谐振动初相位之唯一性浅谈. 动力学与控制学报. 2024(03): 88-92 . 百度学术
2.	孙禹晗，王泽峰，宋智广. 基于模态参数及小波变换的旋转梁结构损伤识别. 动力学与控制学报. 2023(01): 51-59 . 百度学术
3.	隋鹏，申永军，王晓娜. 复变量平均法与其他近似方法的异同. 振动与冲击. 2023(10): 289-296 . 百度学术
4.	于香杰，游斌弟，魏承，赵阳，夏斌，刘朝旭. 中性线修正型变截面梁类构件压电控制. 力学学报. 2022(01): 209-219 . 本站查看
5.	钱韦吉，雍胜杰. 基于钢轨吸振器的多模态复合式俘能器性能研究. 中国机械工程. 2022(06): 672-682 . 百度学术
6.	王娜. 基于大数据模糊PID控制的切削机械加工稳定性分析. 机械与电子. 2022(07): 17-21 . 百度学术
7.	吕书锋，李宏洁，张伟，宋晓娟. 金属/陶瓷功能梯度悬臂板的振动抑制研究. 振动与冲击. 2022(20): 185-194 . 百度学术
8.	张博，丁虎，陈立群. 基于压电纤维复合材料的旋转叶片主动控制. 力学学报. 2021(04): 1093-1102 . 本站查看
9.	何琦，赵振刚，许晓平，罗川，李川. 光纤Bragg光栅等强度悬臂梁型称重传感器的标定与不确定度分析. 光电子·激光. 2021(10): 1092-1098 . 百度学术
10.	刘轩，吴义鹏，裘进浩，季宏丽. 基于反激变压器的压电振动能量双向操控技术. 力学学报. 2021(11): 3045-3055 . 本站查看
11.	解娜娜，葛根. 白噪声激励下含惯性非线性梁的振动响应. 应用力学学报. 2021(06): 2236-2242 . 百度学术
12.	邱志平，姜南. 随机和区间非齐次线性哈密顿系统的比较研究及其应用. 力学学报. 2020(01): 60-72 . 本站查看
13.	戴宁，彭来湖，胡旭东，崔英，钟垚森，王越峰. 纬编针织机织针自由状态下固有频率测试方法. 纺织学报. 2020(11): 150-155 . 百度学术