考虑横向和扭转剪切变形的空间薄壁梁单元

王晓峰; 杨庆山

doi:10.6052/0459-1879-12-218

考虑横向和扭转剪切变形的空间薄壁梁单元

王晓峰^,,
杨庆山

北京交通大学土建学院,北京100044

基金项目: 国家自然科学基金资助项目(51278049,90815021,51078026).

详细信息

通讯作者:
王晓峰,讲师,主要研究方向:薄壁结构和薄膜结构.E-mail:wangxiaof@bjtu.edu.cn

中图分类号: TU323.3
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出版历程
- 收稿日期: 2012-08-05
- 修回日期: 2012-09-06
- 刊出日期: 2013-03-17

A NEW SPATIAL THIN-WALLED BEAM ELEMENT INCLUDING TRANSVERSE AND TORSIONAL SHEAR DEFORMATION

Wang Xiaofeng^,,
Yang Qingshan

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

Funds: The project was supported by the National Natural Science Foundation of China (51278049, 90815021, 51078026).

摘要

摘要: 基于Timoshenko梁及Benscoter薄壁杆件理论,建立了考虑剪切变形、弯扭耦合以及翘曲剪应力影响的空间任意开闭口薄壁截面梁单元. 通过引入单元内部结点,对弯曲转角和翘曲角采用三节点Lagrange独立插值的方法,考虑了剪切变形和翘曲剪应力的影响并避免了横向剪切锁死问题;借助载荷作用下薄壁梁的截面运动分析,在位移和应变方程中考虑了弯扭耦合的影响. 通过数值算例将该单元的计算结果与理论解以及商用有限元软件和其他文献中的数值解进行对比和验证,结果对比表明该薄壁梁单元具有良好的精度和收敛性.
- 薄壁梁 /
- 任意开闭口截面 /
- 空间梁单元 /
- Benscoter理论 /
- 刚度矩阵
Abstract: Based on the Timoshenko and Benscoter's theory, a new spatial thin-walled beam element with an arbitrary open or closed cross section is proposed in this paper, accounting for the influences of shear deformation, flexural and torsional coupling and warping shear stress. With introduction of an interior node to the element, three-node interpolation functions are adopted for bending angles and warping angle to consider shear deformation and warping shear stress, and to avoid shear locking simultaneously. Through a kinematic description of the cross section of a deformed thin-walled beam under loads, the flexural-torsional coupling is included in the displacement and strain equations. In order to verify its accuracy and convergence, some numerical examples are analyzed and their results obtained from the present element are compared with theoretical solutions and numerical solutions of the commercial finite element software and other literatures. Comparisons indicate that the present element is free of shear locking and more accurate than those beam elements presented in other documents.
- thin-walled beam /
- arbitrary open or closed cross section /
- spatial beam element /
- Benscoter's theory /
- sti ness matrix

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参考文献(22)

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