初始扭转欧拉梁有限元力学模型研究

陈昌宏; 黄莺; 单建

doi:10.13204/j.gyjz2011205017

初始扭转欧拉梁有限元力学模型研究

doi: 10.13204/j.gyjz2011205017

1.
1. 西北工业大学力学与土木建筑学院西安 710129;
2.
2. 西安建筑科技大学土木工程学院西安 710055;
3.
3. 东南大学土木工程学院南京 210096

基金项目:

西北工业大学基础研究基金资助项目;国家自然科学基金资助项目(50678036)

详细信息

作者简介:
陈昌宏，男，1980年出生，博士，讲师。

中图分类号: TU311
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- 文章访问数: 161
- HTML全文浏览量: 18
- PDF下载量: 360
- 被引次数: 0
出版历程
- 收稿日期: 2011-11-23
- 刊出日期: 2012-05-20

THE FINITE ELEMENT MODEL STUDY ON THE PRE- TWISTED EULER BEAM

1.
1. Institute of Mechanics and Civil Engineering,Northwestern Polytechnical University,Xi'an 710129,China;
2.
2. College of Civil Engineering,Xi'an University of Architecture and Technology,Xi'an 710055,China;
3.
3. College of Civil Engineering,Southeast University,Nanjing 210096,China

摘要

摘要: 基于传统欧拉直梁力学模型,对初始扭转欧拉梁有限元模型进行系统的分析与研究。采用2节点12个自由度模型,单元轴向位移插值函数采用2节点拉格朗日插值函数,梁截面横向弯曲位移u,v仍采用三次式位移模式。绕梁轴扭转角位移函数z同轴向位移函数一样采用2节点拉格朗日插值函数。首先基于作者先前文献中初始扭转梁的弯曲正应变关系,导出初始扭转欧拉梁单元刚度矩阵。最后,通过矩形截面初始扭转悬臂梁算例,并与ANSYS三维实体有限元分析结果进行对比分析,表明建立的初始扭转欧拉梁单元刚度矩阵具有良好的精度。
- 初始扭转 /
- 欧拉梁 /
- 有限元 /
- 刚度矩阵 /
- ANSYS
Abstract: Based on the traditional mechanical model of straight beam,the paper makes a systematic analysis and research on the pre-twisted Euler beam finite element numerical model.The paper uses two-node model of 12 degrees of freedom,axial displacement interpolation function using 2-node Lagrange interpolation function,beam transverse bending displacements (u and v) still use the cubic displacement,bending with torsion angle displacement function using cubic polynomial displacement function.Firstly,based on the author previous literature on the flexure strain relationship,the paper deduces the element stiffness matrix of the pre-twisted beam.Finally,by calculating the pre- twisted rectangle section beam example,and contrasting three-dimensional solid finite element using ANSYS,the comparative analysis results show that pre-twisted Euler beam element stiffness matrix has good accuracy．
- pre-twisted /
- Euler beam /
- finite element /
- stiffness matrix /
- ANSYS

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参考文献(8)

L D. Certain Problems of the Theory of Rectilinear，Naturally Twisted Beams[J]. Soviet Applied M Magomaev Echanics，1985，21(9): 901-908.

[2] Barnett J F. A Bridge for the Bridges [C] ∥ Conference Proceedings for Bridges 1999. American: ISBN，0-9665201-1-4. 1999.

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[4] 陈昌宏，单建，黄莺. 初始扭转矩形梁力学性能研究[J]. 工业建筑，2009，39(4):54-57.

[5] 陈昌宏，单建，黄莺. 初始扭转轴压杆弹性弯扭屈曲性能研究[J]. 工程力学，2009，26(6):166-171.

[6] 陈省身，陈维桓. 微分几何讲义[M]. 第二版. 北京:北京大学出版社，2001:14-17.

[7] E Petrov，M Geradin. Finite Element Theory for Curved and Twisted Beams Based on Exact Solutions for Three Dimensional Solids[J]. Part 1: Beam Concept and Geometrically Exact Nonlinear Formulation，Part 2: Anisotropic and Advanced Beam Models，Computer Methods in Applied Mechanics and Engineering，1998，(165): 43-127.

[8] 张志涌. 精通 MATLAB6. 5[M]. 北京:北京航空航天大学出版社，2003:225-227.

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