Please wait a minute...
浙江大学学报(工学版)
浙江大学学报(工学版)
土木工程     
悬臂梁固定端不同位移边界条件下解的对比
杨连枝1,2, 张亮亮2,3, 余莲英2, 尚兰歌2, 高阳2, 王敏中4
1. 北京科技大学 土木与环境工程学院, 北京 100083; 2. 中国农业大学 理学院, 北京 100083; 3. 中国农业大学 工学院, 北京 100083; 4. 北京大学 力学与空天技术系, 北京 100871
Comparison of solutions from different displacement boundary conditions at fixed end of cantilever beams
YANG Lian-zhi1,2, ZHANG Liang-liang2,3, YU Lian-ying2, SHANG Lan-ge2, GAO Yang2, WANG Min-zhong4
1. Civil and Environmental Engineering School, University of Science and Technology Beijing, Beijing 100083, China; 2. College of Science, China Agricultural University, Beijing 100083, China; 3. College of Engineering, China Agricultural University, Beijing 100083, China; 4. Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, China
 全文: PDF(702 KB)   HTML
摘要：

为了获得不同的悬臂梁固定端位移边界处理方式对结果的影响,针对悬臂梁承受3种载荷的情况：自由端受切向力,上表面受均布载荷和线性分布载荷,给出悬臂梁固定端利用传统边界条件和最小二乘法处理边界时,Timoshenko梁理论、Levinson梁理论和弹性力学理论的解析解,与有限元计算结果对比.结果表明,Timoshenko梁理论采用传统位移边界和最小二乘法处理边界的结果一致,采用最小二乘法处理边界获得的Levinson梁理论和弹性力学理论的解明显优于传统位移确定方法,且这种优势随着载荷阶次的增加而越加明显.
Abstract:

To obtain the influence of different displacement boundary conditions for the fixed end on analytical solutions of a cantilever beam, three load cases for a cantilever beam were investigated, which were a transverse shear force at the free end, a uniformly distributed load at the top surface, and a linearly distributed load at the top surface, respectively. Analytical solutions were given for Levinson theory, Timoshenko theory, and the elastic theory by using the conventional displacement boundary condition and the boundary condition through least squares method at the fixed end of the beam, and were compared with the solutions by  finite element method. It is shown that the solutions from Timoshenko theory by using both the conventional displacement boundary condition and the condition through least squares method are the same; Levinson theory and the elastic theory by using the boundary condition through least squares method provide better results than those by using the conventional boundary condition. With an increase in the order of the load, the superiority becomes more and more obvious．
出版日期: 2014-11-01
:  TU 391  
基金资助:

国家自然科学基金资助项目(11472299,11172319)；中央高校基本科研业务费专项资金资助项目(2011JS046，2013BH008)；教育部新世纪优秀人才支持计划项目(NCET-13-0552)；非线性力学国家重点实验室开放基金和国家大学生科研创新项目
通讯作者: 高阳，男，教授，博导     E-mail: gaoyangg@gmail.com
作者简介: 杨连枝(1982-)，女，讲师，从事固体弹性理论分析. E-mail: ylz_xiaozhu@126.com
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章　　

引用本文:

杨连枝, 张亮亮, 余莲英, 尚兰歌, 高阳, 王敏中. 悬臂梁固定端不同位移边界条件下解的对比[J]. 浙江大学学报(工学版), 10.3785/j.issn.1008-973X.2014.11.007.

YANG Lian-zhi, ZHANG Liang-liang, YU Lian-ying, SHANG Lan-ge, GAO Yang, WANG Min-zhong. Comparison of solutions from different displacement boundary conditions at fixed end of cantilever beams. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 10.3785/j.issn.1008-973X.2014.11.007.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2014.11.007    或    http://www.zjujournals.com/eng/CN/Y2014/V48/I11/1955

1］ WANG C M, REDDY J N. Shear deformable beams and plates relations wiht classical solutions ［M］. New York: Elsevier, 2000: 117．
［2］ TIMOSHENKO S P. On the correction for shear of the differential equation for transverse vibration of prismatic bars \[J\]. Philosophical Magazine Series 6, 1921, 41: 744-746.
［3］ LEVINSON M. A new rectangular beam theory ［J］. Journal of Sound and Vibration, 1981, 74(1): 81-87.
［4］ TIMOSHENKO S P, GOODIER J C. Theory of elasticity ［M］. New York: McGraw-Hill, 1970: 44-45.
［5］ GERE J M, Goodno B J. Mechanics of Materials (8th edition) ［M］. USA: Cengage Learning, 2012: 730-735．
［6］ 于涛, 仲政. 均布载荷作用下功能梯度悬臂梁弯曲问题的解析解［J］.固体力学学报, 2006, 27(1): 15-20．
YU Tao, ZHONG Zheng. A general solution of a clamped functionally graded cantilever-beam under uniform loading ［J］. Acta Mechanica Solida Sinica, 2006, 27(1): 15-20．
［7］ 杨永波, 石志飞, 陈盈. 线性分布载荷作用下梯度功能压电悬臂梁的解［J］. 力学学报, 2004, 36(3): 305-310．
YANG Yong-bo, SHI Zhi-fei, CHEN Ying. Piezoelectric cantilever actuator subjected to a linearly distributed loading ［J］. Acta Mechanica Sinica, 2004, 36(3): 305-310．
［8］ SHI Zhi-Fei, CHEN Ying. Functionally graded piezoelectric cantilever beam ［J］. Archive of Applied Mechanics, 2004, 74: 237-247．
［9］ HUANG De-jin, DING Hao-Jiang, CHEN Wei-Qiu. Analysis of functionally graded and laminated piezoelectric cantilever actuators subjected to constant voltage［J］. Smart Materials and Structures, 2008, 17: 065002．
［10］ 王敏中. 关于“平面弹性悬臂梁剪切挠度问题［J］. 力学与实践,2004,26(6)：66-68．
WANG Min-zhong. About “Problems on the shear deflection of a planer elastic cantilever beam” ［J］. Mechanics in Engineering, 2004, 26(6): 66-68．
［11］ 黄文彬.平面弹性悬臂梁剪切挠度问题［J］.力学与实践,1997,19(2): 61-62．
HUANG Wen-bin. Problems on the shear deflection of a planer elastic cantilever beam ［J］. Mechanics in Engineering, 1997, 19(2): 61-62．
［12］ 黄文彬.平面弹性悬臂梁剪切挠度的进一步研究［J］.力学与实践, 1998, 20(5): 65．
HUANG Wen-bin. Further study on the shear deflection of a planer elastic cantilever beam ［J］ . Mechanics in Engineering, 1998, 20(5):65．
［13］ 唐玉花,王鑫伟.关于“平面弹性悬臂梁剪切挠度问题”的进一步研究［J］.力学与实践,2008,30:97-99．
TANG Yu-hua, WANG Xin-wei. Further study on “Problems on the shear deflection of a planer elastic cantilever” ［J］. Mechanics in Engineering, 2008, 30: 97-99．
［14］ COWPER G R. The shear coefficients in Timoshenkos beam theory ［J］. ASME Journal of Applied Mechanics, 1966, 33: 335-340.
[1] 杨章, 童根树, 张磊. 对称布置2根单侧加劲肋的有效刚度[J]. 浙江大学学报(工学版), 2016, 50(8): 1446-1455.
[2] 相阳, 罗永峰, 廖冰, 沈祖炎. 球面网壳地震动输入与振型响应的相关性[J]. 浙江大学学报(工学版), 2016, 50(6): 1040-1047.
[3] 欧阳丹丹, 付波, 童根树. 矩形钢管截面延性等级和板件宽厚比相关关系[J]. 浙江大学学报(工学版), 2016, 50(2): 271-281.
[4] 童根树,杨章,张磊. 钢板剪力墙单侧加劲肋的有效抗弯刚度[J]. 浙江大学学报(工学版), 2015, 49(11): 2151-2158.
[5] 王佼姣, 石永久, 王元清, 潘鹏, 牧野俊雄, 齐雪. 低屈服点钢材LYP100循环加载试验[J]. 浙江大学学报(工学版), 2015, 49(8): 1401-1409.
[6] 陆金钰,唐屹,舒赣平,王恒华. 不等高开缝钢板剪力墙滞回性能分析[J]. 浙江大学学报(工学版), 2014, 48(11): 1968-1975.
[7] 程华强,罗尧治,许贤. 自适应张弦梁结构的非线性内力控制[J]. 浙江大学学报(工学版), 2014, 48(7): 1155-1161.
[8] 张磊, 罗桂发, 童根树. 人字撑-钢框架弹塑性抗侧性能的精细化研究[J]. J4, 2013, 47(10): 1815-1823.
[9] 肖南, 王海, 陈华鹏, 张飞林. 大气腐蚀下网架结构症状可靠度及寿命预测[J]. J4, 2013, 47(8): 1373-1378.
[10] 王振宇,张劲帆,方成,刘国华,蒋建群. 半刚性节点初始刚度的组件式计算模型[J]. J4, 2012, 46(11): 1998-2006.
[11] 张磊,童根树. 薄壁构件整体稳定性的有限元模拟[J]. J4, 2011, 45(3): 531-538.
[12] 金阳, 童根树. 考虑翼缘约束的工字形截面腹板的弹性屈曲[J]. J4, 2009, 43(10): 1883-1891.