Elastic and plastic bending of the beams by finite difference method (FDM)
The Euler-Bernoulli beam model has a wide range of applications to the real life; such as nano electro mechanical system switches in small scale up to the Eifel tower in large scale. Advantages of FDM like simpler mathematical concept and easier programming have made scientist to choose this numeric...
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| Format: | Thesis |
| Language: | English |
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2013
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| Online Access: | http://eprints.utm.my/78269/1/MohammadMahdiDavoudiMFKM20131.pdf |
| _version_ | 1796862818873507840 |
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| author | Davoudi, Mohammad Mahdi |
| author_facet | Davoudi, Mohammad Mahdi |
| author_sort | Davoudi, Mohammad Mahdi |
| collection | ePrints |
| description | The Euler-Bernoulli beam model has a wide range of applications to the real life; such as nano electro mechanical system switches in small scale up to the Eifel tower in large scale. Advantages of FDM like simpler mathematical concept and easier programming have made scientist to choose this numerical method to solve many state-of-the-art physical problems of partial differential equations (PDE). There are researches done by using this method in solving many problems; while, how the nodes at the boundaries can be treated in the best way is still unclear. Therefore, this study is subjected to obtaining the beam behavior with the material in two ranges of elastic and ideal plasticity. Firstly, different schemes of FDM are applied to the PDE of the beam in the elastic range for six cases. Afterwards, loading increases that the material goes to the ideal plastic range. In both ranges, validity of the results by comparing with the analytical solutions need to be studied. Finally, the best FD scheme to implement the boundary conditions are determined. Effect of the point load on FDM is investigated. Moreover, optimum value of the vital parameters like number of nodes, layers and load increments are extracted. Advantages of FDM like simpler mathematical concept and easier programming have made scientist to choose this numerical method to solve many state-of-the-art physical problems of PDE. There are researches done by using this method in solving many problems; while, how the nodes at the boundaries can be treated in the best way is still unclear. |
| first_indexed | 2024-03-05T20:17:21Z |
| format | Thesis |
| id | utm.eprints-78269 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-03-05T20:17:21Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | utm.eprints-782692018-08-03T08:46:52Z http://eprints.utm.my/78269/ Elastic and plastic bending of the beams by finite difference method (FDM) Davoudi, Mohammad Mahdi TJ Mechanical engineering and machinery The Euler-Bernoulli beam model has a wide range of applications to the real life; such as nano electro mechanical system switches in small scale up to the Eifel tower in large scale. Advantages of FDM like simpler mathematical concept and easier programming have made scientist to choose this numerical method to solve many state-of-the-art physical problems of partial differential equations (PDE). There are researches done by using this method in solving many problems; while, how the nodes at the boundaries can be treated in the best way is still unclear. Therefore, this study is subjected to obtaining the beam behavior with the material in two ranges of elastic and ideal plasticity. Firstly, different schemes of FDM are applied to the PDE of the beam in the elastic range for six cases. Afterwards, loading increases that the material goes to the ideal plastic range. In both ranges, validity of the results by comparing with the analytical solutions need to be studied. Finally, the best FD scheme to implement the boundary conditions are determined. Effect of the point load on FDM is investigated. Moreover, optimum value of the vital parameters like number of nodes, layers and load increments are extracted. Advantages of FDM like simpler mathematical concept and easier programming have made scientist to choose this numerical method to solve many state-of-the-art physical problems of PDE. There are researches done by using this method in solving many problems; while, how the nodes at the boundaries can be treated in the best way is still unclear. 2013-01 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/78269/1/MohammadMahdiDavoudiMFKM20131.pdf Davoudi, Mohammad Mahdi (2013) Elastic and plastic bending of the beams by finite difference method (FDM). Masters thesis, Universiti Teknologi Malaysia, Faculty of Mechanical Engineering. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:79545 |
| spellingShingle | TJ Mechanical engineering and machinery Davoudi, Mohammad Mahdi Elastic and plastic bending of the beams by finite difference method (FDM) |
| title | Elastic and plastic bending of the beams by finite difference method (FDM) |
| title_full | Elastic and plastic bending of the beams by finite difference method (FDM) |
| title_fullStr | Elastic and plastic bending of the beams by finite difference method (FDM) |
| title_full_unstemmed | Elastic and plastic bending of the beams by finite difference method (FDM) |
| title_short | Elastic and plastic bending of the beams by finite difference method (FDM) |
| title_sort | elastic and plastic bending of the beams by finite difference method fdm |
| topic | TJ Mechanical engineering and machinery |
| url | http://eprints.utm.my/78269/1/MohammadMahdiDavoudiMFKM20131.pdf |
| work_keys_str_mv | AT davoudimohammadmahdi elasticandplasticbendingofthebeamsbyfinitedifferencemethodfdm |