径向基点插值法在旋转柔性梁动力学中的应用

杜超凡; 章定国; 洪嘉振

doi:10.6052/0459-1879-14-334

径向基点插值法在旋转柔性梁动力学中的应用

doi: 10.6052/0459-1879-14-334

1.
南京理工大学理学院, 南京210094
2. 上海交通大学工程力学系, 上海200240

基金项目: 国家自然科学基金(11272155,11132007), 江苏省"333" 工程(BRA2011172) 和高校基本科研业务专项资金(30920130112009) 资助项目.

详细信息

通讯作者:
章定国,教授,主要研究方向:多体系统动力学与控制.E-mail:zhangdg419@mail.njust.edu.cn

中图分类号: O313.7
计量
- 文章访问数: 1078
- HTML全文浏览量: 108
- PDF下载量: 874
- 被引次数: 0
出版历程
- 收稿日期: 2014-10-24
- 修回日期: 2014-11-25
- 刊出日期: 2015-03-18

A MESHFREE METHOD BASED ON RADIAL POINT INTERPOLATION METHOD FOR THE DYNAMIC ANALYSIS OF ROTATING FLEXIBLE BEAMS

1.
School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China
2. Dept. of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200240, China

Funds: The project was supported by the National Natural Science Foundation of China (11272155,11132007), the 333 Project of Jiangsu Province, China (BRA2011172), and the Fundamental Research Funds for the Central Universities of China (30920130112009).

摘要

摘要: 将无网格径向基点插值法用于旋转柔性梁的动力学分析. 利用无网格方法对柔性梁的变形场进行离散,考虑梁的纵向拉伸变形和横向弯曲变形,并计入横向弯曲变形引起的纵向缩短,即非线性耦合项,运用第二类拉格朗日方程推导得到系统刚柔耦合动力学方程. 将无网格径向基点插值法的仿真结果有限元法和假设模态法进行比较分析,说明假设模态法的局限性,并表明其作为一种柔性体离散方法在刚柔耦合多体系统动力学的研究中具有可推广性,并讨论了径向基形状参数的影响. 同时运用3 种求解系统动力学方程的方法:纽马克方法、4阶龙格库塔法、亚当姆斯预报校正法,并比较各方法的计算效率, 结果表明纽马克方法最快.
- 柔性梁 /
- 径向基点插值法 /
- 无网格法 /
- 动力学 /
- 数值积分方法
Abstract: A meshfree method based on radial point interpolation method (RPIM) is proposed for dynamic analysis of a rotating flexible beam. The RPIM is used to describe the deformation of the flexible beam. The longitudinal and transverse deformations of the beam are both considered, and the coupling term of the deformation which is caused by the transverse deformation is included in the longitudinal deformation of the beam. The rigid-flexible coupling dynamic equations of the system are derived via employing Lagrange's equations of the second kind. Simulation results of the RPIM are compared with those obtained by using finite element method (FEM) and assumed modes method and show the limitations of assumed modes method. It is demonstrated that the meshfree method as a discrete method of the flexible body can be extended in the field of multibody system dynamics. Meanwhile, the influence of the radial basis shape parameters is discussed. What's more, three integration methods (Newmark method, fourth-order Runge—Kutta method and Adams prediction correction method) are used to solve the dynamic equations, and it shows that the Newmark method is the fastest with the computational effciency.
- flexible beam /
- radial point interpolation method /
- meshfree method /
- dynamics /
- integration methods

HTML全文

参考文献(22)

洪嘉振,尤超蓝. 刚柔耦合系统动力学研究进展. 动力学与控制学报,2004,2(2):1-6 (Hong Jiazhen, You Chaolan. Advances in dynamics of rigid-flexible coupling system. Journal of Dynamics and Control, 2004, 2(2):1-6 (in Chinese))

Dwivedy SK, Eberhard P. Dynamic analysis of flexible manipulators, a literature review. Mechanism and Machine Theory , 2006, 41(7): 749-777

吴胜宝,章定国,康新. 刚体-微梁系统的动力学特性. 机械工程学报, 2010,46(3): 76-82 (Wu Shengbao, Zhang Dingguo, Kang Xin. Dynamic properties of hub-microbeam system. Journal of Mechanical Engineering , 2010, 46(3):76-82 (in Chinese))

张雄,刘岩,马上. 无网格法的理论及应用. 力学进展,2009, 39(1): 1-36 (Zhang Xiong, Liu Yan, Ma Shang. Meshfree methods and their applications. Advanes in Mechanics, 2009: 39(1): 1-36 (in Chinese))

刘桂荣,顾元通.无网格法理论及程序设计. 王建明,周学军译. 济南:山东大学出版社,2007:45-133 (Liu Guirong, Gu Yuantong. An Introduction to Meshfree Methods and Their Programming. Shandong: Shandong University Press, 2007: 45-133 (in Chinese))

Sanborn GG, Shanana AA. On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation. Multibody Syst Dyn , 2009, 22: 181-197

Sanborn GG, Shanana AA. A rational finite element method based on the absolute nodal coordinate formulation. Nonlinear Dyn , 2009, 58: 565-572

范纪华,章定国. 旋转悬臂梁动力学的B样条差值方法. 机械工程学报,2012, 48(23): 59-64 (Fan Jihua, Zhang Dingguo. B-spline interpolation method for the dynamics of rotating cantilever beam. Journal of Mechanical Engineering , 2012, 48(23): 59-64 (in Chinese))

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 (Fan Jihua, Zhang Dingguo. Bezier interpolation method for the dynamics of rotating flexible cantilever beam. Acta Phys Sin , 2014, 63(15): 154501 (in Chinese))

Belytschko T, Krongauz Y, Organ D, et al. Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng, 1996, 139: 3-47

Liu GR, Gu Y, A point interpolation method for two-dimensional solids. Int J Muner Meth Engng, 2001, 50: 937-951

Liu GR, Dai KY, Lim KM, et al. A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures. Computational Mechanics, 2002, 29(6): 510-519

Wang JG, Liu GR. A point interpolation meshless method based on radial basis functions. Int J Numer Meth Eng, 2002, 54(11): 1623-1648

Belytschko T, Lu YY, Gu L. Element free Galerkin methods. International Journal for Numerical Methods in Engineering , 1994, 37(2): 229-256

Cheng RJ, Cheng YM, Ge HX. Element-free Galerkin (EFG) method for a kind of two-dimensional linear hyperbolic equation. Chin Phys B, 2009, 18(10): 4059-4064

Atluri SN, Zhu T. A new meshless local Petrov-!-Galerkin (MLPG) approach in computational mechanics. Computational Mehcanics, 1998, 22(2): 117-127

Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. Int J Numer Meth Fluids , 1995, 20: 1081-1106

夏茂辉,贾延,刘广君. 弹性力学问题的径向点插值法. 青岛科技大学学报, 2006, 27(2): 155-158 (Xia Maohui, Jia Yan, Liu Guangjun. A radial point interpolation method for the elasticity problem. Journal of Qing dao University of Science and Technology, 2006, 27(2): 155-158 (in Chinese))

Chung J, Yoo HH. Dynamic analysis of a rotating cantilever beam by using the finite element method. Journal of Sound and Vibration, 2002, 249(1): 147-164

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 (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(2): 251-256 (in Chinese))

章定国,余纪邦. 作大范围运动的柔性梁的动力学分析. 振动工程学报, 2006,19(4): 475-479 (Zhang Dingguo, Yu Jibang. Dynamical analysis of a flexible cantilever beam with large overall motions. Journal of Vibration Engineering, 2006,19(4): 475-479 (in Chinese))

马振华. 现代应用数学手册. 北京:清华大学出版社,2005. 567-611 (Ma Zhenhua. The Application of Modern Mathematics Handbook. Beijing: Tsinghua University Press, 2005. 567-611 (in Chinese))

施引文献

资源附件(0)

访问统计