Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains

Using Hamilton’s principle, exact equations of motion for non-linear planar and spatial Euler–Bernoulli beams are derived. In the existing non-linear Euler–Bernoulli beam formulations, some elastic terms are dropped by differentiation from the incomplete Green–Lagrange strain tensor followed by negl...

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Main Authors: Zohoor, H., Abedinnasab, Mohammad H., Yoon, Yong-Jin
Other Authors: School of Mechanical and Aerospace Engineering
Format: Article
Language:English
Published: 2013
Online Access:https://hdl.handle.net/10356/98428
http://hdl.handle.net/10220/12437
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-984282020-03-07T13:22:18Z Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains Zohoor, H. Abedinnasab, Mohammad H. Yoon, Yong-Jin School of Mechanical and Aerospace Engineering Using Hamilton’s principle, exact equations of motion for non-linear planar and spatial Euler–Bernoulli beams are derived. In the existing non-linear Euler–Bernoulli beam formulations, some elastic terms are dropped by differentiation from the incomplete Green–Lagrange strain tensor followed by negligible elastic deformations of cross-sectional frame. On the other hand, in this article, the exact strain field concerning considerable elastic deformations of cross-sectional frame is used as a source in differentiations. As a result, the achieved closed-form equations are exact and more accurate than formerly reported equations in the literature. Moreover, the applicable dynamic model of inextensional beams which is fully accurate, yet simple has been shown. The planar and inextensional dynamic models have been compared with the existing dynamic models in the literature, and the proposed dynamic models demonstrate significant improvements in the numerical results. Finally, experiments on the carbon fibre rods verify the model presented for inextensional beams. 2013-07-29T04:21:08Z 2019-12-06T19:55:10Z 2013-07-29T04:21:08Z 2019-12-06T19:55:10Z 2012 2012 Journal Article Abedinnasab, M. H., Zohoor, H., & Yoon, Y.-J. (2012). Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains. Proceedings of the institution of mechanical engineers, part C : journal of mechanical engineering science, 226(5), 1225-1236. https://hdl.handle.net/10356/98428 http://hdl.handle.net/10220/12437 10.1177/0954406211420206 en Proceedings of the institution of mechanical engineers, part C : journal of mechanical engineering science © 2011 The Authors.
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
description Using Hamilton’s principle, exact equations of motion for non-linear planar and spatial Euler–Bernoulli beams are derived. In the existing non-linear Euler–Bernoulli beam formulations, some elastic terms are dropped by differentiation from the incomplete Green–Lagrange strain tensor followed by negligible elastic deformations of cross-sectional frame. On the other hand, in this article, the exact strain field concerning considerable elastic deformations of cross-sectional frame is used as a source in differentiations. As a result, the achieved closed-form equations are exact and more accurate than formerly reported equations in the literature. Moreover, the applicable dynamic model of inextensional beams which is fully accurate, yet simple has been shown. The planar and inextensional dynamic models have been compared with the existing dynamic models in the literature, and the proposed dynamic models demonstrate significant improvements in the numerical results. Finally, experiments on the carbon fibre rods verify the model presented for inextensional beams.
author2 School of Mechanical and Aerospace Engineering
author_facet School of Mechanical and Aerospace Engineering
Zohoor, H.
Abedinnasab, Mohammad H.
Yoon, Yong-Jin
format Article
author Zohoor, H.
Abedinnasab, Mohammad H.
Yoon, Yong-Jin
spellingShingle Zohoor, H.
Abedinnasab, Mohammad H.
Yoon, Yong-Jin
Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains
author_sort Zohoor, H.
title Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains
title_short Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains
title_full Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains
title_fullStr Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains
title_full_unstemmed Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains
title_sort exact formulations of non-linear planar and spatial euler-bernoulli beams with finite strains
publishDate 2013
url https://hdl.handle.net/10356/98428
http://hdl.handle.net/10220/12437
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