Element free Galerkin method of composite beams with partial interaction

Composite beam with partial interaction behaviour has ignited many studies, not just on its mechanics but also on solutions of its one-dimensional partial differential equation. Inadequate solution by available analytical methods for this high order differential equation has demanded for numerical a...

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Main Author:	Ahmad, Dzulkarnain
Format:	Thesis
Language:	English
Published:	2013
Subjects:	TA Engineering (General) Civil engineering (General)
Online Access:	http://eprints.utm.my/id/eprint/37969/1/DzulkarnainAhmadPFKA2013.pdf
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id	my-utm-ep.37969
record_format	uketd_dc
spelling	my-utm-ep.379692018-04-12T05:38:51Z Element free Galerkin method of composite beams with partial interaction 2013-08 Ahmad, Dzulkarnain TA Engineering (General). Civil engineering (General) Composite beam with partial interaction behaviour has ignited many studies, not just on its mechanics but also on solutions of its one-dimensional partial differential equation. Inadequate solution by available analytical methods for this high order differential equation has demanded for numerical approach and therefore Element Free Galerkin (EFG) method is applied for the first time in this present work. The work consists of three parts; first is the formulation of Galerkin weak form and assemblage of the EFG discrete equilibrium equation. One-dimensional formulation of the weak form is performed by adopting the variational approach and the discrete equation, which is in matrix form and written using the Matlab programming code. Subsequently in second part, the EFG formulation is developed for both the slip and uplift models, where the former adopted equal curvature deflection assumption while the latter considered the unequal curvature. The proposed EFG formulation gives comparable results in both models, after been validated by established analytical solutions, thus signify its application in partial interaction problems. The third part provides numerical tests result on EFG numerical parameters such as size of support domain, polynomial basis and quadrature points with seven different types of weight functions for this composite beams behaviour. Conclusively, Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation results, compares to other weight functions. The capability of the EFG formulation was also studied in terms of its application on free vibration problem and various composite beam cross-sections. Results from the numerical tests deduced the demand for optimised parameters value as the parameters are highly reliant on user-defined value. Additionally, the research supports the need for more efficient EFG code’s algorithm, stiffness matrix, shape function formulation and background integration methods, in approximating the higher order differential equation which refers to dynamics analysis. 2013-08 Thesis http://eprints.utm.my/id/eprint/37969/ http://eprints.utm.my/id/eprint/37969/1/DzulkarnainAhmadPFKA2013.pdf application/pdf en public phd doctoral Universiti Teknologi Malaysia, Faculty of Civil Engineering Faculty of Civil Engineering
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	TA Engineering (General) Civil engineering (General)
spellingShingle	TA Engineering (General) Civil engineering (General) Ahmad, Dzulkarnain Element free Galerkin method of composite beams with partial interaction
description	Composite beam with partial interaction behaviour has ignited many studies, not just on its mechanics but also on solutions of its one-dimensional partial differential equation. Inadequate solution by available analytical methods for this high order differential equation has demanded for numerical approach and therefore Element Free Galerkin (EFG) method is applied for the first time in this present work. The work consists of three parts; first is the formulation of Galerkin weak form and assemblage of the EFG discrete equilibrium equation. One-dimensional formulation of the weak form is performed by adopting the variational approach and the discrete equation, which is in matrix form and written using the Matlab programming code. Subsequently in second part, the EFG formulation is developed for both the slip and uplift models, where the former adopted equal curvature deflection assumption while the latter considered the unequal curvature. The proposed EFG formulation gives comparable results in both models, after been validated by established analytical solutions, thus signify its application in partial interaction problems. The third part provides numerical tests result on EFG numerical parameters such as size of support domain, polynomial basis and quadrature points with seven different types of weight functions for this composite beams behaviour. Conclusively, Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation results, compares to other weight functions. The capability of the EFG formulation was also studied in terms of its application on free vibration problem and various composite beam cross-sections. Results from the numerical tests deduced the demand for optimised parameters value as the parameters are highly reliant on user-defined value. Additionally, the research supports the need for more efficient EFG code’s algorithm, stiffness matrix, shape function formulation and background integration methods, in approximating the higher order differential equation which refers to dynamics analysis.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Ahmad, Dzulkarnain
author_facet	Ahmad, Dzulkarnain
author_sort	Ahmad, Dzulkarnain
title	Element free Galerkin method of composite beams with partial interaction
title_short	Element free Galerkin method of composite beams with partial interaction
title_full	Element free Galerkin method of composite beams with partial interaction
title_fullStr	Element free Galerkin method of composite beams with partial interaction
title_full_unstemmed	Element free Galerkin method of composite beams with partial interaction
title_sort	element free galerkin method of composite beams with partial interaction
granting_institution	Universiti Teknologi Malaysia, Faculty of Civil Engineering
granting_department	Faculty of Civil Engineering
publishDate	2013
url	http://eprints.utm.my/id/eprint/37969/1/DzulkarnainAhmadPFKA2013.pdf
_version_	1747816515255664640

Element free Galerkin method of composite beams with partial interaction

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