A simple method for determining large deflection states of arbitrarily curved planar elastica
The paper discusses a relatively simple method for determining large deflection states of arbitrarily curved planar elastica, which is modeled by a finite set of initially straight flexible segments. The basic equations are built using Euler–Bernoulli and large displacement theory. The problem is so...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/105250 |
| _version_ | 1826212867830972416 |
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| author | Sitar, Matej Kosel, Franc Brojan, Miha |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Sitar, Matej Kosel, Franc Brojan, Miha |
| author_sort | Sitar, Matej |
| collection | MIT |
| description | The paper discusses a relatively simple method for determining large deflection states of arbitrarily curved planar elastica, which is modeled by a finite set of initially straight flexible segments. The basic equations are built using Euler–Bernoulli and large displacement theory. The problem is solved numerically using Runge–Kutta–Fehlberg integration method and Newton method for solving systems of nonlinear equations. This solution technique is tested on several numerical examples. From a comparison of the results obtained and those found in the literature, it can be concluded that the developed method is efficient and gives accurate results. The solution scheme displayed can serve as reference tool to test results obtained via more complex algorithms. |
| first_indexed | 2024-09-23T15:39:43Z |
| format | Article |
| id | mit-1721.1/105250 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:39:43Z |
| publishDate | 2016 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1052502022-09-29T15:19:23Z A simple method for determining large deflection states of arbitrarily curved planar elastica Sitar, Matej Kosel, Franc Brojan, Miha Massachusetts Institute of Technology. Department of Mechanical Engineering Brojan, Miha The paper discusses a relatively simple method for determining large deflection states of arbitrarily curved planar elastica, which is modeled by a finite set of initially straight flexible segments. The basic equations are built using Euler–Bernoulli and large displacement theory. The problem is solved numerically using Runge–Kutta–Fehlberg integration method and Newton method for solving systems of nonlinear equations. This solution technique is tested on several numerical examples. From a comparison of the results obtained and those found in the literature, it can be concluded that the developed method is efficient and gives accurate results. The solution scheme displayed can serve as reference tool to test results obtained via more complex algorithms. 2016-11-07T23:09:14Z 2016-11-07T23:09:14Z 2013-10 2013-03 2016-08-18T15:27:03Z Article http://purl.org/eprint/type/JournalArticle 0939-1533 1432-0681 http://hdl.handle.net/1721.1/105250 Sitar, Matej, Franc Kosel, and Miha Brojan. “A Simple Method for Determining Large Deflection States of Arbitrarily Curved Planar Elastica.” Archive of Applied Mechanics 84.2 (2014): 263–275. en http://dx.doi.org/10.1007/s00419-013-0798-6 Archive of Applied Mechanics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag Berlin Heidelberg application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Sitar, Matej Kosel, Franc Brojan, Miha A simple method for determining large deflection states of arbitrarily curved planar elastica |
| title | A simple method for determining large deflection states of arbitrarily curved planar elastica |
| title_full | A simple method for determining large deflection states of arbitrarily curved planar elastica |
| title_fullStr | A simple method for determining large deflection states of arbitrarily curved planar elastica |
| title_full_unstemmed | A simple method for determining large deflection states of arbitrarily curved planar elastica |
| title_short | A simple method for determining large deflection states of arbitrarily curved planar elastica |
| title_sort | simple method for determining large deflection states of arbitrarily curved planar elastica |
| url | http://hdl.handle.net/1721.1/105250 |
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