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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/98428 http://hdl.handle.net/10220/12437 |
| _version_ | 1826111646665277440 |
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| author | Zohoor, H. Abedinnasab, Mohammad H. Yoon, Yong-Jin |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Zohoor, H. Abedinnasab, Mohammad H. Yoon, Yong-Jin |
| author_sort | Zohoor, H. |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T02:53:51Z |
| format | Journal Article |
| id | ntu-10356/98428 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:53:51Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-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. |
| spellingShingle | Zohoor, H. Abedinnasab, Mohammad H. Yoon, Yong-Jin Exact formulations of non-linear planar and spatial Euler-Bernoulli beams with finite strains |
| title | 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_short | 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 |
| url | https://hdl.handle.net/10356/98428 http://hdl.handle.net/10220/12437 |
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