基于曲率插值的大变形梁单元

张志刚; 齐朝晖; 吴志刚

doi:10.3879/j.issn.1000-0887.2013.06.008

基于曲率插值的大变形梁单元

doi: 10.3879/j.issn.1000-0887.2013.06.008

¹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 116023;²大连理工大学航空航天学院,辽宁大连 116023

基金项目: 国家自然科学基金资助项目(10972044)

详细信息

作者简介:
张志刚（1984—），男，河南开封人，博士生（E-mail：zhigangzhang@foxmail.com）

中图分类号: O342
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- 文章访问数: 1965
- HTML全文浏览量: 169
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- 被引次数: 0
出版历程
- 收稿日期: 2012-12-07
- 修回日期: 2013-05-20
- 刊出日期: 2013-06-15

Large Deformation Beam Element Based on Curvature Interpolation

¹State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China;²School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

摘要

摘要: 线性梁单元的形函数在单元大转动时会引起虚假应变，不适用于几何非线性分析．传统的几何非线性梁单元由于位移插值和转角插值的相干性，常常引起剪切闭锁等问题．该文提出了一种平面大变形梁单元，通过单元域内的曲率插值以及曲率与节点位移之间的函数关系，将单元节点力和节点位移表示为节点曲率的函数．由于曲率插值本质上是对梁的应变进行插值，保证了单元任意刚体运动不会产生虚假的节点力；且将梁的截面形心位移表示为曲率的函数，避免了传统单元中的剪切闭锁问题．因而所提方法特别适用于梁的几何非线性分析．数值算例说明了所提方法的正确性和有效性.
- 曲率插值 /
- 几何非线性 /
- 平面梁单元 /
- 大变形
Abstract: The shape functions of linear beam element, which will cause the false strain when large rotation occurs, does not apply to geometric nonlinear analysis. Because of the coherence of the interpolation of the displacement and angle, traditional geometric nonlinear beam element is often caused by problems such as shear locking. A plane large deformation beam element was proposed, by use of the interpolation of curvature and the functional relationship between the curvature and nodal displacements . The element node forces and displacements were expressed as a function of the curvature. Essentially the interpolation of the beam curvature is strain interpolation，which ensures that the element rigid body motion does not produce false node force; the shear locking in traditional element is avoided because the beam centroid displacement is expressed as a function of curvature. Thus this method is especially suitable for geometry nonlinear analysis of the beam. The numerical examples show the truth and validity of the proposed method.
- curvature interpolation /
- geometric nonlinear /
- plane beam element /
- large displacement

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参考文献(13)

[1]	Xiao N, Zhong H. Nonlinear quadrature element analysis of planar frames based on geometrically exact beam theory[J].International Journal of NonLinear Mechanics,2012, 47(5): 481-488.
[2]	王世来，凌道盛. 适用于大变形分析的平面协调梁单元[J]. 浙江大学学报 (工学版), 2007, 41(5): 818822. (WANG Shi-lai, LING Dao-sheng. Fully conforming plane beam element for large deformation analysis[J]. Journal of Zhejiang University (Engineering Science), 2007, 41(5):818-822. (in Chinese))
[3]	Felippa C A, Haugen B. A unified formulation of smallstrain corotational finite elements—Ⅰ: theory[J].Computer Methods in Applied Mechanics and Engineering,2005, 194(21): 2285-2335.
[4]	吕和祥，朱菊芬. 大转动梁的几何非线性分析讨论[J]. 计算结构力学及其应用, 1995, 12(4): 485490. (Lū He-xiang, ZHU Ju-fen. Discussion of analyzing of geometric nonlinear beams with large rotations[J].Computational Structural Mechanics and Applications,1995, 12(4):485-490. (in Chinese))
[5]	蔡松柏，沈蒲生. 大转动平面梁有限元分析的共旋坐标法[J]. 工程力学, 2006, 23(s1): 76-80. (CAI Song-bai, SHEN Pu-sheng. Co-rotational procedure for finite element analysis of plane beam under large rotational displacement[J].Engineering Mechanics,2006, 23(s1):76-80. (in Chinese))
[6]	Li Z X. A co-rotational formulation for 3D beam element using vectorial rotational variables[J]. Computational Mechanics,2007, 39(3): 309-322.
[7]	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): 1-18.
[8]	罗晓明，齐朝晖，许永生，韩雅楠. 含有整体刚体位移杆件系统的几何非线性分析[J]. 工程力学, 2011, 28(2): 62-68. (LUO Xiao-ming, QI Zhao-hui, XU Yong-sheng, HAN Ya-nan. Geometric nonlinear analysis of truss systems with rigid body motions[J]. Engineering Mechanics,2011, 28(2):62-68 (in Chinese))
[9]	Haefner L, Willam K J. Large deflection formulations of a simple beam element including shear deformations[J]. Engineering Computations,1984, 1(4): 359-368.
[10]	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.
[11]	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.
[12]	Mattiasson K. Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals[J].International Journal for Numerical Methods in Engineering, 1981, 17(1): 145-153.
[13]	Nanakorn P, Vu L N. A 2D field-consistent beam element for large displacement analysis using the total Lagrangian formulation[J]. Finite Elements in Analysis and Design,2006, 42(14): 1240-1247.