轴向拉伸细长杆的非线性力学模型

马刚; 孙丽萍; 艾尚茂; 王宏伟

doi:10.3879/j.issn.1000-0887.2015.04.004

轴向拉伸细长杆的非线性力学模型

doi: 10.3879/j.issn.1000-0887.2015.04.004

哈尔滨工程大学船舶工程学院, 哈尔滨 150001

基金项目: 黑龙江省科学基金（QC2014C049）；中央高校基本科研业务费专项资金（HEUCFD1402；HEUCFD1424）；高等学校博士学科点专项科研基金新教师类资助课题（20132304120008）；高等学校学科创新引智计划（B07019）

详细信息

作者简介:
马刚（1984—），男，山东人，讲师，博士(通讯作者. Tel: +86-451-82569359;E-mail: magang@hrbeu.edu.cn).

中图分类号: O342
计量
- 文章访问数: 1158
- HTML全文浏览量: 47
- PDF下载量: 1525
- 被引次数: 0
出版历程
- 收稿日期: 2014-09-24
- 修回日期: 2014-12-01
- 刊出日期: 2015-04-15

A Nonlinear Mechanical Model for Extensible Slender Rods

College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, P.R.China

Funds: The National Natural Science Foundation of China;The National Basic Research Program of China (973 Program)

摘要

摘要: 聚酯系泊缆是深海工程中具备一定抗弯刚度、易拉伸变形的细长杆件结构.聚酯缆的轴向变形属大拉伸范畴，分析中应当区分变形前后状态，特别是缆索长度的改变使得基于小拉伸假设的细长杆模型需要予以改进.因此，基于Garrett细长杆模型，应用总体坐标和斜率取代Euler-Bernoulli(欧拉伯努利)梁元的转角，解决缆索在空间中大转动变形的几何非线性问题；使用轴向拉伸变形前后物质点对应的方法，借助单元两个节点和一个中点，以及3个二次多项式形函数描述轴向拉伸变形下细长杆元的运动微分方程.通过与轴向拉伸悬臂梁的对比分析，验证了该拉伸杆元的收敛性和准确性.
- 轴向拉伸 /
- 细长杆 /
- 非线性 /
- 聚酯缆 /
- 大转动
Abstract: The polyester mooring line is a flexible rod liable to axial extension and bending deformation. Due to its large axial deformation in tension, the polyester line’s deformed configurations shall be distinguished from the undeformed ones, and the slender rod model based on the small extension hypothesis shall be improved in view of its nonnegligible length change. The global coordinates and slopes were used to replace the rotation angles in the Euler-Bernoulli beam to deal with the geometrically nonlinear problem of large spatial rotation based on Garrett’s slender rod theory. Then the point-to-point mapping method was proposed to correlate the 2 configurations before and after axial extension in the slender rod theory, with 2 element nodes, 1 intermediate point and 3 quadratic polynomial combined to derive the differential equations of motion for the slender rod element in tension. Through comparison between the numerical results and the analytical solution of an extensible cantilever beam example, convergence and accuracy of the proposed model are proved.
- axial extension /
- slender rod /
- nonlinear /
- polyester line /
- large rotation

HTML全文

参考文献(15)

[1]	连宇顺, 刘海笑, 黄维. 超深水混合缆绷紧式系泊系统非线性循环动力分析[J]. 海洋工程, 2013,31(3): 1-8.(LIAN Yu-shun, LIU Hai-xiao, HUANG Wei. Cyclic nonlinear analysis of ultra-deepwater hybrid mooring systems[J].The Ocean Engineering,2013,31(3): 1-8.(in Chinese))
[2]	王宏伟, 罗勇, 马刚, 胡开业. 深水半潜式钻井平台纤维材料系泊方案研究[J]. 船舶工程, 2010,32(3): 58-62.(WANG Hong-wei, LUO Yong, MA Gang, HU Kai-ye. Research on fiber material mooring scheme of the deepwater semi-submersible drilling platform[J].Ship Engineering,2010,32(3): 58-62.(in Chinese))
[3]	Tahar A, Kim M H. Coupled-dynamic analysis of floating structures with polyester mooring lines[J].Ocean Engineering,2008,35(17/18): 1676-1685.
[4]	Paulling J R, Webster W C. A consistent large-amplitude analysis of the coupled response of a TLP and tension system[C]//Proceedings of the Fifth International Offshore Mechanics and Arctic Engineering Symposium,Tokyo, 1986.
[5]	白兴兰, 黄维平. 深水钢悬链线立管非线性有限元静力分析[J]. 工程力学, 2011,28(4): 208-213.(BAI Xing-lan, HUANG Wei-ping. Static analysis of deepwater steel catenary riser using nonlinear finite element method[J].Engineering Mechanics,2011,28(4): 208-213.(in Chinese))
[6]	MA Gang, SUN Li-ping, WANG Hong-wei. Implementation of a visco-elastic model into slender rod theory for deepwater polyester mooring line[C]//International Conference on Ocean, Offshore and Arctic Engineering,San Francisco, California, 2014.
[7]	Webster W C, Lambrakos K, Kim Jang-whan, JING Xiao-ning. Rod dynamics with large stretch[C]//Proceedings of the ASME 〖STBX〗2012 31st International Conference on Ocean, Offshore and Arctic Engineering,Rio de Janeiro, Brazil, 2012.
[8]	Arcandra T. Hull/mooring/riser coupled dynamic analysis of a deepwater floating platform with polyester lines[D]. PhD Thesis. Texas: Texas A & M University, 2001.
[9]	王金龙, 段梦兰, 田凯. 海流作用下的深水懒波型立管形态研究[J]. 应用数学和力学, 2014,35(9): 959-967.(WANG Jin-long, DUAN Meng-lan, TIAN Kai. Research on the configuration of the deepwater steel lazy-wave riser under effects of ocean currents[J].Applied Mathematics and Mechanics,2014,35(9): 959-967.(in Chinese))
[10]	CHEN Xiao-hong, ZHANG Jun, Johnson P, Irani M. Dynamic analysis of mooring lines with inserted springs[J].Applied Ocean Research,2001,23(5): 277-284.
[11]	Gerstmayr J, Irschik H. On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach[J].Journal of Sound and Vibration,2008,318(3): 461-487.
[12]	齐朝晖, 方慧青, 张志刚, 王刚. 基于曲率离散的几何非线性空间梁单元[J]. 应用数学和力学, 2014,35(5): 498-509.(QI Zhao-hui, FANG Hui-qing, ZHANG Zhi-gang, WANG Gang. Geometric nonlinear spatial beam elements with curvature interpolation[J].Applied Mathematics and Mechanics,2014,35(5): 498-509.(in Chinese))
[13]	Garrett D L. Dynamic analysis of slender rods[J].Journal of Energy Resources Technology,1982,104(4): 302-306.
[14]	张志刚, 齐朝晖, 吴志刚. 基于曲率插值的大变形梁单元[J]. 应用数学和力学, 2013,34(6): 620-629.(ZHANG Zhi-gang, QI Zhao-hui, WU Zhi-gang. Large deformation beam element based on curvature interpolation[J].Applied Mathematics and Mechanics,2013,34(6): 620-629.(in Chinese))
[15]	古雅琦, 王海龙, 杨怀宇. 一种大变形几何非线性Euler-Bernoulli梁单元[J]. 工程力学, 2013,30(6): 11-15.(GU Ya-qi, WANG Hai-long, YANG Huai-yu. A large deformation geometric nonlinear Euler-Bernoulli beam element[J].Engineering Mechanics,2013,30(6): 11-15.(in Chinese))