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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Main Author:	Davoudi, Mohammad Mahdi
Format:	Thesis
Language:	English
Published:	2013
Subjects:	TJ Mechanical engineering and machinery
Online Access:	http://eprints.utm.my/id/eprint/78269/1/MohammadMahdiDavoudiMFKM20131.pdf
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id	my-utm-ep.78269
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spelling	my-utm-ep.782692018-08-03T08:46:52Z Elastic and plastic bending of the beams by finite difference method (FDM) 2013-01 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 http://eprints.utm.my/id/eprint/78269/ http://eprints.utm.my/id/eprint/78269/1/MohammadMahdiDavoudiMFKM20131.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:79545 masters Universiti Teknologi Malaysia, Faculty of Mechanical Engineering Faculty of Mechanical Engineering
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	TJ Mechanical engineering and machinery
spellingShingle	TJ Mechanical engineering and machinery Davoudi, Mohammad Mahdi Elastic and plastic bending of the beams by finite difference method (FDM)
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.
format	Thesis
qualification_level	Master's degree
author	Davoudi, Mohammad Mahdi
author_facet	Davoudi, Mohammad Mahdi
author_sort	Davoudi, Mohammad Mahdi
title	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_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_sort	elastic and plastic bending of the beams by finite difference method (fdm)
granting_institution	Universiti Teknologi Malaysia, Faculty of Mechanical Engineering
granting_department	Faculty of Mechanical Engineering
publishDate	2013
url	http://eprints.utm.my/id/eprint/78269/1/MohammadMahdiDavoudiMFKM20131.pdf
_version_	1747817948472410112

Elastic and plastic bending of the beams by finite difference method (FDM)

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