Kirchhoff plate modelling using finite element method

The Kirchhoff plate theory works well for thin plates where the real shear strains are small. In this study, the development of Kirchhoff plate theory using FEM is presented. The equilibrium condition of the problem defined as 2 0 2 2 2 2 2 � � � � � � � � � � � q y M x y M x Mxx xy yy is investigat...

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Main Author:	Ismail, Nazihah
Format:	Thesis
Language:	English
Published:	2010
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/26823/5/NazihahIsmailMFS2010.pdf
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id	my-utm-ep.26823
record_format	uketd_dc
spelling	my-utm-ep.268232017-09-19T04:08:03Z Kirchhoff plate modelling using finite element method 2010-12 Ismail, Nazihah QA Mathematics The Kirchhoff plate theory works well for thin plates where the real shear strains are small. In this study, the development of Kirchhoff plate theory using FEM is presented. The equilibrium condition of the problem defined as 2 0 2 2 2 2 2 � � � � � � � � � � � q y M x y M x Mxx xy yy is investigated in providing the appropriate boundary conditions, hence to the establishment of the FE formulation of the problem. The plate elements developed are the two-dimensional triangular element. To meet the convergence criteria, the quadratic interpolation function is adopted and the six nodes triangular element is developed. The deflection w takes the form of � , � 2 . 5 6 2 w x y ��1 �� 2 x �� 3 y �� 4 x �� xy �� y The numerical results of two neighbouring six nodes triangular elements are studied. These elements are considered to be interconnected at specified nodes which lie on the element boundaries where adjacent elements are considered to be connected. In each piece or element, the element shape function Ni , the stiffness matrix K , and the load vector fl are derived. The assemblage of these matrices together with the derivation of boundary vector fb will yield to an approximate solution for the displacement of the problem. The computational scheme is developed by using Matlab programming language on the Windows environment for computing the problem studied. 2010-12 Thesis http://eprints.utm.my/id/eprint/26823/ http://eprints.utm.my/id/eprint/26823/5/NazihahIsmailMFS2010.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Ismail, Nazihah Kirchhoff plate modelling using finite element method
description	The Kirchhoff plate theory works well for thin plates where the real shear strains are small. In this study, the development of Kirchhoff plate theory using FEM is presented. The equilibrium condition of the problem defined as 2 0 2 2 2 2 2 � � � � � � � � � � � q y M x y M x Mxx xy yy is investigated in providing the appropriate boundary conditions, hence to the establishment of the FE formulation of the problem. The plate elements developed are the two-dimensional triangular element. To meet the convergence criteria, the quadratic interpolation function is adopted and the six nodes triangular element is developed. The deflection w takes the form of � , � 2 . 5 6 2 w x y ��1 �� 2 x �� 3 y �� 4 x �� xy �� y The numerical results of two neighbouring six nodes triangular elements are studied. These elements are considered to be interconnected at specified nodes which lie on the element boundaries where adjacent elements are considered to be connected. In each piece or element, the element shape function Ni , the stiffness matrix K , and the load vector fl are derived. The assemblage of these matrices together with the derivation of boundary vector fb will yield to an approximate solution for the displacement of the problem. The computational scheme is developed by using Matlab programming language on the Windows environment for computing the problem studied.
format	Thesis
qualification_level	Master's degree
author	Ismail, Nazihah
author_facet	Ismail, Nazihah
author_sort	Ismail, Nazihah
title	Kirchhoff plate modelling using finite element method
title_short	Kirchhoff plate modelling using finite element method
title_full	Kirchhoff plate modelling using finite element method
title_fullStr	Kirchhoff plate modelling using finite element method
title_full_unstemmed	Kirchhoff plate modelling using finite element method
title_sort	kirchhoff plate modelling using finite element method
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2010
url	http://eprints.utm.my/id/eprint/26823/5/NazihahIsmailMFS2010.pdf
_version_	1747815519585566720

Kirchhoff plate modelling using finite element method

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