基于曲率离散的几何非线性空间梁单元

齐朝晖; 方慧青; 张志刚; 王刚

doi:10.3879/j.issn.1000-0887.2014.05.004

基于曲率离散的几何非线性空间梁单元

doi: 10.3879/j.issn.1000-0887.2014.05.004

大连理工大学工业装备结构分析国家重点实验室, 辽宁大连 116024

基金项目: 国家自然科学基金（11372057）

详细信息

作者简介:
齐朝晖（1964—），男，辽宁大连人，教授，博士生导师(通讯作者. E-mail: zhaohuiq@dlut.edu.cn)

中图分类号: O342
计量
- 文章访问数: 2171
- HTML全文浏览量: 240
- PDF下载量: 1034
- 被引次数: 0
出版历程
- 收稿日期: 2014-02-26
- 修回日期: 2014-04-10
- 刊出日期: 2014-05-15

Geometric Nonlinear Spatial Beam Elements With Curvature Interpolations

State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China（11372057）

摘要

摘要: 以绝对坐标为节点参数的梁单元在结构的几何非线性分析和多柔体系统动力学中都有广泛的应用前景.其中一种具有代表性的单元为基于精确几何模型的梁单元，但它的构造过程涉及对节点转动矢量的插值，由此引起了很多数值求解方面的困难.由Shabana提出的绝对坐标梁单元，其节点参数中不含转动矢量，从而避免了对转角的插值，但却为此大幅度地增加了节点参数.以大变形梁虚功率方程为理论基础，先通过单元的形心曲线插值得到端面曲率及其对弧长的变化率，进而对单元域内的曲率进行插值，提出了一种既可避免转动矢量插值同时又不增加节点参数的空间梁单元，可用于梁的大变形几何非线性分析.数值算例验证了该单元的合理性.
- 空间梁单元 /
- 多柔体系统 /
- 几何非线性 /
- 曲率插值
Abstract: Beam elements with absolute nodal coordinates played an important role in the geometric nonlinear analysis of structures and dynamics of flexible multibody systems. One of such elements was the beam element based on the exact geometric beam model, in which the process of obtaining internal nodal forces involved interpolations of rotational angles, resulting in some numerical difficulties. Another such element proposed by Shabana, avoided the angular interpolations by replacing the nodal rotation parameters with many newly introduced nodal parameters. In accordance with the exact virtual power equations for beams with large deformations and the relationships between tangents of the beam centroid line and curvatures of the beam sections, a new spatial beam element with absolute nodal coordinates was presented. The nodal parameters of the presented element are the same with those of the element based on the exact geometric beam model, but the internal forces can be obtained without angular interpolations. Numerical examples verify its validity through comparison with the analytical results.
- spatial beam element /
- flexible multibody system /
- geometric nonlinearity /
- curvature interpolation

HTML全文

参考文献(16)

[1]	Kwak H-G, Kim D-Y, Lee H-W. Effect of warping in geometric nonlinear analysis of spatial beams[J].Journal of Constructional Steel Research,2001,57(7): 729-751.
[2]	Pai P F, Anderson T J, Wheater E A. Large-deformation tests and total-Lagrangian finite-element analyses of flexible beams[J].International Journal of Solids and Structures,2000,37(21): 2951-2980.
[3]	Hsiao K M, Lin J Y, Lin W Y. A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams[J].Computer Methods in Applied Mechanics and Engineering,1999,169(1/2): 1-18.
[4]	Teh L H, Clarke M J. Co-rotational and Lagrangian formulations for elastic three-dimensional beam finite elements[J].Journal of Constructional Steel Research,1998,48(2/3): 123-144.
[5]	Wu S-C, Haug E J. Geometric non-linear substructuring for dynamics of flexible mechanical systems[J].International Journal for Numerical Methods in Engineering,1988,26(10): 2211-2226.
[6]	Simo J C. A finite strain beam formulation. the three-dimensional dynamic problem—part Ⅰ[J].Computer Methods in Applied Mechanics and Engineering,1985,49(1): 55-70.
[7]	Simo J C, Vu-Quoc L. A three-dimensional finite-strain rod model—part Ⅱ: computational aspects[J].Computer Methods in Applied Mechanics and Engineering,1986,58(1): 79-116.
[8]	Beléndez T, Neipp C, Beléndez A. Large and small deflections of a cantilever beam[J].European Journal of Physics,2002,23(3): 371-379.
[9]	Banerjee A, Bhattacharya B, Mallik A K. Large deflection of cantilever beams with geometric non-linearity: analytical and numerical approaches[J].International Journal of Non-Linear Mechanics,2008,43(5): 366-376.
[10]	Yakoub R Y, Shabana A A. Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications[J].Journal of Mechanical Design,2001,123(4): 614-621.
[11]	Sopanen J T, Mikkola A M. Description of elastic forces in absolute nodal coordinate formulation[J].Nonlinear Dynamics,2003,34(1/2): 53-74.
[12]	Romero I. A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations[J].Multibody System Dynamics,2008,20(1): 51-68.
[13]	Jonker J B, Meijaard J P. A geometrically non-linear formulation of a three-dimensional beam element for solving large deflection multibody system problems[J].International Journal of Non-Linear Mechanics,2013,53: 63-74.
[14]	Reissner E. On one-dimensional finite-strain beam theory: the plane problem[J].Zeitschrift für angewandte Mathematik und Physik ZAMP,1972,23(5): 795-804.
[15]	Reissner E. On one-dimensional large-displacement finite-strain beam theory[J].Studies in Applied Mathematics,1973,52(2): 87-95.
[16]	Mattiasson K. Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals[J].International Journal for Numerical Methods in Engineering,1981,17(1): 145-153.