FEM Calculation of Space Timoshenko Beam of Large Deflection

doi:10.3969 /j.issn.1674-0696.2013.04.04

Journal of Chongqing Jiaotong University(Natural Science) ›› 2013, Vol. 32 ›› Issue (4): 564-568.DOI: 10.3969 /j.issn.1674-0696.2013.04.04

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FEM Calculation of Space Timoshenko Beam of Large Deflection

Liu Xiaohui¹，Wang Jialin¹，Yan Bo²

1.School of Civil Engineering ＆ Architecture，Chongqing Jiaotong University，Chongqing 400074，China;2.School of Ｒesources ＆ Environmental Science，Chongqing University，Chongqing 400044，China

Received:2012-12-18 Revised:2013-04-18 Online:2013-08-15 Published:2014-10-27

空间大挠度 Timoshenko 梁的有限元计算方法

刘小会¹,王家林¹,严波²

1.重庆交通大学土木建筑学院，重庆 400074；2.重庆大学资源及环境科学学院，重庆 400044

作者简介:刘小会(1981—),男,内蒙古包头人,讲师,博士,主要从事柔性结构行为分析的研究。E-mail:cqdxlxh@126.com。
基金资助:
国家自然科学基金重点项目( 51277186)

Abstract

Abstract: A variation principle for Timoshenko beams of large deflection with geometrical non-linearity is presented． And the space beam element stiffness matrix of large deflection can be deduced from this variation principle，considering the effect of the shear deformation． To improve the computational precision and efficiency for the large displacement and rotation of beam，a finite element method based on the moment-curvature relationship of beam section is presented． The method calculated by node coordinates of the beam element is applied to calculate the internal nodal forces． A nonlinear finite element code is then developed which considers the effects of large rotations，large displacements and shear deformations． Numerical examples are provided in order to verify the feasibility and effectivity of the presented method．

Key words: geometric non-linearity, large deflection, space beam, shear deformation

摘要： 解析了几何非线性的大挠度 Timoshenko 梁的变分原理，建立了考虑横向剪切应变的大挠度梁的空间单元刚度矩阵; 采用基于梁截面弯矩-曲率关系的宏观有限元方法，直接通过节点坐标系计算内部节点力，提高了大位移、大转动梁的计算精度及效率; 编制了考虑单元大转角、大位移和剪切变形影响的非线性有限元程序; 通过数值算例验证了该程序的可行性和有效性。

关键词: 几何非线性, 大挠度, 空间梁, 剪切变形

CLC Number:

U448.2

Liu Xiaohui，Wang Jialin，Yan Bo. FEM Calculation of Space Timoshenko Beam of Large Deflection[J]. Journal of Chongqing Jiaotong University(Natural Science), 2013, 32(4): 564-568.

刘小会，王家林，严波. 空间大挠度 Timoshenko 梁的有限元计算方法[J]. 重庆交通大学学报（自然科学版）, 2013, 32(4): 564-568.

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FEM Calculation of Space Timoshenko Beam of Large Deflection

空间大挠度 Timoshenko 梁的有限元计算方法

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