THIRD-ORDER GENERALISED BEAM THEORY AND CALCULATION METHOD

Zhao Rujiang

doi:10.6052/0459-1879-14-033

Volume 46 Issue 6

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Theoretical and Applied Mechanics > 2014 > 46(6): 987-993. > DOI: 10.6052/0459-1879-14-033 CSTR: 32045.14.0459-1879-14-033

Zhao Rujiang. THIRD-ORDER GENERALISED BEAM THEORY AND CALCULATION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(6): 987-993. DOI: 10.6052/0459-1879-14-033

Citation:

Zhao Rujiang. THIRD-ORDER GENERALISED BEAM THEORY AND CALCULATION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(6): 987-993. DOI: 10.6052/0459-1879-14-033

Citation:

Zhao Rujiang. THIRD-ORDER GENERALISED BEAM THEORY AND CALCULATION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(6): 987-993. DOI: 10.6052/0459-1879-14-033

PDF (1647 KB)

THIRD-ORDER GENERALISED BEAM THEORY AND CALCULATION METHOD

Zhao Rujiang

The Construction Command Center of Sino-Singapore Guangzhou Knowledge City, Guangzhou 510555, China

Received Date: June 02, 2014
Revised Date: August 19, 2014

Graphical Abstract

Abstract

Abstract

First-order Generalised Beam Theory (GBT) analysis can be used to describe the behaviour of prismatic structures by using deformation functions for bending, torsion and distortion in ordinary uncoupled differential equations. In second-order GBT, the differential equations then are involved with the effect of deviating forces. By derived the virtual works of two membrane stress terms into the GBT system, we can obtain the complete expansions of the third order GBT equation in the form of a series of large discretized iterated functions, which can be converted to sets of tangent stiffness matrices for further numerical analyses. By introducing the membrane stresses as the third order terms ^ijrkv_σ and ^ijrkv_τ and using advanced numerical techniques to find a complete solution, the third-order Generalised Beam Theory becomes a rigorous and efficient numerical tool to investigate large deflection behaviours in post-buckling of thin-walled structures.
- thin-walled members,
- third-order generalised beam theory,
- large discretized iterated functions

FullText(HTML)

References (18)

References

Schardt R. The Generalized Beam Theory. In: Proceedings of the Michael R. Horne Conference, University of Manchester, 1984: 469-475

Schardt R. Generalized beam theory—an adequate method for coupled stability problems. In: Thin-Walled Structures: Coupled Instabilities in Metal Structues, Part 1: 1994, 161-180

Davies JM, Leach P. First order generalised beam theory. Journal of Constructional Steel Research, 1994, 31(2-3): 187-220

Davies JM, Leach P, Heinz D. Second order generalised beam theory. Journal of Constructional Steel Research, 1994, 31(2-3): 221-241

Davies JM, Leach P. Experimental verification of the generalized beam theory applied to interactive buckling problems. Thin-Walled Structures, 1996, 25(1): 61-79

Davies JM, Jiang C. Design for distortional buckling. Journal of Constructional Steel Research, 1998, 46(n1-3): 174-175

Davies JM, Jiang C. Design of thin-walled purlins for distortional buckling. Thin-Walled Structures, 1997, 29(n1-4): 189-202

Simão P, Sim?es da SL. A unified energy formulation for the stability analysis of open and closed thin-walled members in the framework of the generalized beam theory. Thin-Walled Structures, 2004, 42(10): 1495-1517

Bebiano R, Silvestre N, Camotim D. GBT formulation to analyze the buckling behaviour of thin-walled members subjected to non-uniform bending. International Journal of Structural Stability and Dynamics, 2007, 7(1): 23-54

Basaglia C, Camotim D, Silvestre N. GBT-based local, distortional and global buckling analysis of thin-walled steel frames. Thin-Walled Structures, 2009, 47(11): 1246-1264

Silvestre N, Camotim D, Silva NF. Generalized beam theory revisited: from the kinematical assumptions to the deformation mode determination. International Journal of Structural Stability and Dynamics, 2011, 11(5): 969-997

Basaglia C, Camotim D, Silvestre N. Post-buckling analysis of thin-walled steel frames using generalised beam theory (GBT). Thin-Walled Structures, 2013, 62: 229-242

Basaglia C, Camotim D. Buckling, postbuckling, strength, and DSM design of cold-formed steel continuous lipped channel beams. Journal of Structural Engineering, 2013, 139(5): 657-668

Camotim D, Basaglia C. Buckling analysis of thin-walled steel structures using generalized beam theory (GBT): state-of-the-art report. Steel Construction, 2013, 6(2): 117-131

De Miranda S, Gutiérrez A, Miletta R, et al. A generalized beam theory with shear deformation. Thin-Walled Structures, 2013, 67: 88-100

Miosga G. Vorwiegend längsbeanspruchte dünnwandige prismatische Stäbe and Platten mit endlichen elastichen Verformungen. Dissertation, Technische Hochschule Darmstadt, 1976

Davies JM, Chiu R. Flange curling in slender sections. In: Proc. 4th International Conference on Thin-Walled Structures. ICTWS 04, Loughborough University, UK, 2004: IOP Publishing Ltd, 2004: 39

Lecce M, Rasmussen KJR. Nonlinear flange curling in wide flange sections. Journal of Constructional Steel Research, 2008, 64(7-8): 779-784

[1]	Chen Wei, Fang Yaochu, Sun Bing, Peng Linxin. MESHLESS ANALYSIS OF LINEAR BENDING AND FREE VIBRATION OF FUNCTIONALLY GRADED CARBON NANOTUBE-REINFORCED COMPOSITE PLATE ON ELASTIC FOUNDATION BASED ON IMPROVED REDDY TYPE THIRD-ORDER SHEAR DEFORMATION THEORY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(6): 1355-1370. DOI: 10.6052/0459-1879-23-040
[2]	Gao Shan, Shi Donghua, Guo Yongxin. DISCRETE MOMENTUM CONSERVATION LAW OF GEOMETRICALLY EXACT BEAM IN HAMEL'S FRAMEWORK[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1712-1719. DOI: 10.6052/0459-1879-21-092
[3]	Hou Shujuan, Liang Huiyan, Wang Quanzhong, Han Xu. STUDY ON NONLINEAR ELASTIC HOMOGENIZATION WITH ITERATIVE METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 837-846. DOI: 10.6052/0459-1879-18-039
[4]	Ji Chunning, Liu Danqing, Xu Dong. LARGE EDDY SIMULATION OF SAND RIPPLE EVOLUTION USING DISCRETE PARTICLE METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(4): 613-623. DOI: 10.6052/0459-1879-14-254
[5]	Wang Qishen, Zhang Lihua, Wang Dajun. SOME QUALITATIVE PROPERTIES OF MODESOF DISCRETE SYSTEM OF BEAM WITH OVERHANG[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(6): 1071-1074. DOI: 10.6052/0459-1879-12-023
[6]	Z.-Q. Wang Jincheng Zhao. Restrained torsion theory of open thin-walled beams and its application[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 963-967. DOI: 10.6052/0459-1879-2011-5-lxxb2011-063
[7]	Yufeng Xing, Yang Yang. A bending moment beam eigenelement with piecewise shape functions[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(2): 222-228. DOI: 10.6052/0459-1879-2008-2-2007-263
[8]	Jinyang Liu, Jiazhen Hong. Nonlinear formulation for flexible multibody system with large deformation[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(1): 111-119. DOI: 10.6052/0459-1879-2007-1-2006-113
[9]	UNITED PROOF FOR QUALITATIVE PROPERTIES OF DISCRETE AND CONTINUOUS SYSTEMS OF VIBRATING ROD AND BEAM[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(1): 99-102. DOI: 10.6052/0459-1879-1997-1-1995-201
[10]	A STUDY ON THE COMPUTATION EFFICIENCY OF MARCHING/ITERATING ALGORITHM[J]. Chinese Journal of Theoretical and Applied Mechanics, 1994, 26(4): 503-507. DOI: 10.6052/0459-1879-1994-4-1995-574

Cited By

Cited by

Periodical cited type(18)

1.	时晓天，张桂茹，吕蒙，赵渊，高军. 结构变形对高超声速可变形减速器的动态稳定性影响分析. 航天返回与遥感. 2025(01): 11-20 .
2.	张鑫，王勋年. 正弦交流介质阻挡放电等离子体激励器诱导流场研究的进展与展望. 力学学报. 2023(02): 285-298 . 本站查看
3.	陈肇麟，陆政旭，肖天航，邓双厚. 局部振动对火星环境下薄翼型气动性能的影响. 北京航空航天大学学报. 2023(11): 2938-2950 .
4.	黄广靖，戴玉婷，杨超. 低雷诺数俯仰振荡翼型等离子体流动控制. 力学学报. 2021(01): 136-155 . 本站查看
5.	李钊，杨广珺，蒋锋. 随积冰历程的机翼蒙皮载荷实验研究. 实验流体力学. 2021(03): 9-15 .
6.	阳鹏宇，张鑫，赖庆仁，车兵辉，陈磊. 机翼尺度效应对等离子体分离流动控制特性的影响. 力学学报. 2021(12): 3321-3330 . 本站查看
7.	马东立，张良，杨穆清，夏兴禄，王少奇. 超长航时太阳能无人机关键技术综述. 航空学报. 2020(03): 34-63 .
8.	刘惠祥，何国毅，王琦. 蜻蜓滑翔时柔性褶皱前翅气动特性分析. 力学学报. 2019(01): 94-102 . 本站查看
9.	赵炜，高德亮，黄江流，尹航，周俊忠. 低雷诺数下速度对流场结构的影响研究. 沈阳航空航天大学学报. 2019(06): 14-21 .
10.	李冠雄，马东立，杨穆清，郭阳. 低雷诺数翼型局部振动非定常气动特性. 航空学报. 2018(01): 118-130 .
11.	李国强，张卫国，陈立，聂博文，张鹏，岳廷瑞. 风力机叶片翼型动态试验技术研究. 力学学报. 2018(04): 751-765 . 本站查看
12.	于晓东，袁腾飞，李代阁，曲航，郑旭航. 极端工况双矩形腔静压推力轴承动态特性. 力学学报. 2018(04): 899-907 . 本站查看
13.	李国强，陈立，黄霞. 横摆振荡翼型动态气动掠效应试验研究. 力学学报. 2018(05): 977-989 . 本站查看
14.	刘强，刘强，白鹏，李锋. 不同雷诺数下翼型气动特性及层流分离现象演化. 航空学报. 2017(04): 27-39 .
15.	王人凤，尤云祥，陈科，段金龙. 两自由度舵-轴系统振动三维效应修正模型. 力学学报. 2017(04): 920-928 . 本站查看
16.	朱玉杰，孙振生，张炜，张世英. 低Reynolds数翼型绕流主动控制技术. 气体物理. 2017(06): 18-27 .
17.	朱正，招启军，王博. 剪刀式尾桨涡流干扰机理和气动特性研究. 力学学报. 2016(04): 886-896 . 本站查看
18.	王睿，熊鹰，王展智. 混合式CRP面元法计算对比. 力学学报. 2016(06): 1425-1436 . 本站查看

Other cited types(8)

Get Citation

PDF

XML

Article Metrics

Article views (1615) PDF downloads (1217) Cited by(26)

THIRD-ORDER GENERALISED BEAM THEORY AND CALCULATION METHOD