|Table of Contents|

[1] Zeng Sen, Chen Shaofeng, Wang Huanding, Qu Ting, et al. Finite element analysis of spatial curved beam in large deformation [J]. Journal of Southeast University (English Edition), 2010, 26 (4): 591-596. [doi:10.3969/j.issn.1003-7985.2010.04.019]
Copy

Finite element analysis of spatial curved beam in large deformation()
大变形空间曲梁有限元分析
Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
26
Issue:
2010 4
Page:
591-596
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2010-12-30

Info

Title:
Finite element analysis of spatial curved beam in large deformation
大变形空间曲梁有限元分析
Author(s):
Zeng Sen1;  Chen Shaofeng2;  Wang Huanding1;  Qu Ting1
1 School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China
2 School of Science and Engineering on Communications, Harbin Institute of Technology, Harbin 150090, China
曾森1;  陈少峰2;  王焕定1;  曲婷1
1哈尔滨工业大学土木工程学院, 哈尔滨150090; 2 哈尔滨工业大学交通科学与工程学院, 哈尔滨150090
Keywords:
spatial curved beams;  total Lagrangian incremental formulation;  updated Lagrangian incremental formulation;  geometrical nonlinearity;  isoparametric curve
空间曲梁;  全拉格朗日增量格式;  修正拉格朗日增量格式;  几何非线性;  等参数曲线
PACS:
O342
DOI:
10.3969/j.issn.1003-7985.2010.04.019
Abstract:
For the purpose of carrying out the large deformation finite element analysis of spatial curved beams, the total Lagrangian(TL)and the updated Lagrangian(UL)incremental formulations for arbitrary spatial curved beam elements are established with displacement vector interpolation, which is improved from component interpolation of the straight beam displacement. A strategy of replacing the actual curve with the isoparametric curve is used to expand the applications of the UL formulation. The examples indicate that the process of establishing the curved beam element is correct, and the accuracy with the curved beam element is obviously higher than that with the straight beam element. Generally, the same level of computational accuracy can be achieved with 1/5 as many curved beam elements as otherwise with straight beam elements.
为了进行空间曲梁大变形有限元分析, 将直梁单元位移分量插值的思想改进为位移矢量插值用以建立曲梁单元的位移场, 分别建立了适用于任意曲线形式的全拉格朗日和修正拉格朗日增量格式空间曲梁有限元列式.通过采用等参数曲线代替实际曲线的策略, 使得修正拉格朗日增量格式曲梁单元可以应用于更广泛的场合.算例对比结果表明, 曲梁单元的建立过程正确, 曲梁单元的精度要明显高于直梁单元.一般情况下, 仅用直梁单元数量1/5的曲梁单元就可以达到相同的计算精度.

References:

[1] Ojalvo I U, Newman M. Buckling of naturally curved and twisted beams [J]. Journal of the Engineering Mechanics Division, ASCE, 1968, 94(EM5):1067-1087.
[2] Rosen A, Rand O. Numerical model of the nonlinear behavior of curved rods [J]. Compt Struct, 1986, 22(5): 785-799.
[3] Bauchau O A, Hong C H. Nonlinear composite beam theory [J]. Journal of Applied Mechanics, 1988, 55(3):156-163.
[4] Pai P F, Nayfeh A H. A fully nonlinear theory of curved and twisted composite rotor blades accounting for warpings and three-dimensional stress effects [J]. Int J Solids Structures, 1994, 31(9): 1309-1340.
[5] Vlasov V Z. Thin-walled elastic beams [M]. 2nd ed. Jerusalem: Israel Program for Scientific Translation, 1961: 173-181.
[6] Yang Y B, Kuo S R. Effect of curvature on stability of curved beams [J]. J Struct Engrg, 1987, 113(6): 1185-1202.
[7] Timoshenko S P, Gere J M. Theory of elastic stability [M]. 2nd ed. New York: McGraw Hill Book Co. Inc, 1961: 154-157.
[8] Clough R W, Penzien J. Dynamics of structures [M]. 2nd ed. Berkeley, CA, USA: Computers & Structures Inc, 1995: 200-210.
[9] Yang Y B, Lin S P, Leu L J. Solution strategy and rigid element for nonlinear analysis of elastically structures based on updated Lagrangian formulation [J]. Engineering Structures, 2007, 29(6):1189-1200.
[10] Teh L H, Clarke M J. Corotational and Lagrangian formulations for elastic three-dimensional beam finite elements [J]. Journal of Constructional Steel Research, 1998, 48(2/3): 123-144.
[11] Williams F W. An approach to the non-linear behavior of the members of a rigid jointed plane framework with finite deflections [J]. The Quarterly Journal of Mechanics and Applied Mathematics, 1964, 17(4): 451-469.

Memo

Memo:
Biographies: Zeng Sen(1983—), male, graduate;Wang Huanding(corresponding author), male, professor, hdwhrb@hit.edu.cn.
Foundation item: The Major Research Plan of the National Natural Science Foundation of China(No.90715021).
Citation: Zeng Sen, Chen Shaofeng, Wang Huanding, et al. Finite element analysis of spatial curved beam in large deformation[J].Journal of Southeast University(English Edition), 2010, 26(4):591-596.
Last Update: 2010-12-20