基于流动坐标系的3维空间动力非线性有限元方法

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (16) : 14-23.

论文

王涛，刘德贵，胡安杰

作者信息 +

A nonlinear dynamic finite element method in 3D space based on the Co-rotational formulation

WANG Tao,LIU Degui,HU Anjie

Author information +

文章历史 +

摘要

为了考虑3维空间中柔性结构大幅振动的几何非线性振动效应，建立了基于流动坐标系（CR列式）的Newmark-β非线性有限元动力时程计算方法。在动力时程计算的每一个时间步中，考虑结构的几何非线性，考虑初始应力和重力的时变效应，通过平衡迭代计算，得到有限元模型各个节点的位移、速度、加速度。开发了使用杆、梁单元的有限元计算程序，并提供了详细的计算方法与计算流程。设计了多个算例，计算得到了柔性结构在3维空间的非线性振动现象，依据非线性振动理论解释了现象的原理。通过算例与ANSYS的进行了对比，结果表明：算法与程序编制正确可靠，计算效率高，适用于柔性结构在3维空间中大幅度非线性振动的计算与研究。

Abstract

Considering the geometric nonlinear effect of large amplitude vibration of flexible structures in 3 Dimension (3D) space, a nonlinear dynamic FEM time-history Newmark-β method was built based on the Co-rotational formulation theory.In each step of time-history calculation, geometric nonlinearity, time variant effect of stress and gravity in the structure were considered.The equilibrium iteration calculation was used to get the displacement, velocity, acceleration of the nodes in the FE model.An FEM program which used link and beam elements was developed.The methods and calculation flow were discussed.Three numerical examples were designed.The calculation results reflect the nonlinear vibration of the flexible structures in 3D space.And these phenomena were explained by the nonlinear vibration theory.The computational results of the samples were compared with ANSYS.The results indicate that the algorithm and program are reliable and efficient, which can be applied for large amplitude vibration calculation and investigation on flexible construction in 3D space.

导出引用

王涛，刘德贵，胡安杰. 基于流动坐标系的3维空间动力非线性有限元方法[J]. 振动与冲击, 2018, 37(16): 14-23

WANG Tao,LIU Degui,HU Anjie. A nonlinear dynamic finite element method in 3D space based on the Co-rotational formulation[J]. Journal of Vibration and Shock, 2018, 37(16): 14-23

参考文献

[1] Bathe K J, Bolourchis. Large displacement analysis of three-dimensional beam structures[J]. International Journal of Numerical Methods and Engineering, 1979, 14(7): 961-986.
[2] 陈政清,曾庆元,颜全胜. 空间杆系结构大挠度问题内力分析的UL列式法[J]. 土木工程学报, 1992, 25(5):34-44. (Chen Zhengqing, Zeng Qingyuan, Yan Quansheng. A U.L. formulation for internal force analysis of spatial frame structures with large displacement[J]. China Civil Engineering Journal. 1992, 25(5): 34-44 (in Chinese))
[3] Wempner G A. Finite elements, finite rotations and small strains of flexible shells[J]. International Journal of Solids and Structures, 1969, 5(7): 117-153.
[4]   Crisfieldm A, Moita G F. A unified co-rotational framework for solids, shells and beams[J]. International Journal of Solids and Structures, 1996, 33(24): 2969-2992.
[5]   Felippa C A, Haugen B. A unified formulation of small-strain co-rotational finite elements[J]. Theory Computer Methods in Applied Mechanics and Engineering, 2005, 194(19): 2285-2 335.
[6] Zhang L, Gao Q, Zhang H W. An efficient algorithm for mechanical analysis of bimodular truss and tensegrity structures[J]. International Journal of Mechanical Sciences, 2013, 70(5):57-68.
[7] Liang K, Ruess M, Abdalla M. Co-rotational finite element formulation used in the Koiter-Newton method for nonlinear buckling analyses[J]. Finite Elements in Analysis & Design, 2016, 116:38-54.
[8] 邓继华, 邵旭东, 谭平. 几何非线性与徐变共同作用下三维杆系结构有限元分析[J]. 工程力学, 2015(6):117-123.
       DENG Jihua, Shao Xudong, Tan Ping. finite element analysis for 3-d frame structures under combined actions of geometric nonlinearity and creep [J]. Engineering Mechanics, 2015(6):117-123.
[9]   潘永仁. 悬索桥结构非线性分析理论与方法[M]. 北京：人民交通出版社,2001.
Pan Yongren. Non-linear analysis theory method for suspension bridge structure[M]. Beijing: China communication Press, 2001.
[10] 康厚军，郭铁丁，赵跃宇. 大跨度斜拉桥非线性振动模型与理论研究进展[J]. 力学学报， 2016, 48(3): 519-535.
Kang Houjun, Guo Tieding, Zhao Yueyu. Review on nonlinear vibration and modeling of large span cable-stayed bridge[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 519-535.
[11] 吴庆雄, 王文平, 陈宝春. 索梁结构非线性振动有限元分析. 工程力学[J]. 2013.30(3):347-382.
Wu Qingxiong, Wang Wenping, Chen Baochun. Finite Element Analysis for Nonlinear Vibration of Cable-Beam Structure[J]. Engineering Mechanics. 2013.30(3):347-382.
[12]曹九发, 王同光, 王枭. 大型风力机的几何非线性动态响应研究[J]. 振动与冲击, 2016, 35(14):182-187.
Cao Jiufa,Wang Tongguang,Wang Xiao.Geometric nonlinear dynamics response of large-scale wind turbine[J].Journal of Vibration and Shock,2016,35(14):182-187.
[13] 徐荣桥. 结构分析的有限元法与MATLAB程序设计[M]. 北京:人民交通出版社, 2006.
Xu Rongqiao , Finite element Method in Structural Analysis and Matlab Programming[M]. Beijing: China Communications Press, 2006.
[14] Daryi L. Logan. A First Course in the Finite Element Method[M], SI Edition, Fifth Edition. New York: Cengage Learning, 2012.
[15] 王涛. 斜拉桥拉索的索-梁相关振动研究. [D]. 成都:西南交通大学, 2014.
Wang Tao. The Investigation on Cable-beam vibration of the Cable in Cable-Stayed Bridge.[D]. Chengdu: Southwest Jiaotong University, 2014.
[16] 王新敏. ANSYS结构动力分析与应用[M]. 北京:人民交通出版, 2014.
Wang Xinmin. Structural Dynamic Analysis and Application with ANSYS[M]. Beijing: China Communications Press, 2014.
[17] Nayfeh A.H, Mook D.T. Nonlinear Oscillations[M]. New York: Wiley Press, 1984.