Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane

In this thesis, the triple Griffith cracks problems subjected to shear stress in an elastic half-plane with free traction boundary condition are formulated into hypersingular integral equation (HSIE) associated with the modified complex potential. Curved length coordinate method is utilized to tr...

Full description

Saved in:

Bibliographic Details
Main Author:	Husin, Nur Hazirah
Format:	Thesis
Language:	English
Published:	2020
Subjects:	Integral equations - Numerical solutions Fracture mechanics - Mathematics
Online Access:	http://psasir.upm.edu.my/id/eprint/90348/1/IPM%202020%2011%20ir.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-upm-ir.90348
record_format	uketd_dc
spelling	my-upm-ir.903482021-12-01T06:26:22Z Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane 2020-02 Husin, Nur Hazirah In this thesis, the triple Griffith cracks problems subjected to shear stress in an elastic half-plane with free traction boundary condition are formulated into hypersingular integral equation (HSIE) associated with the modified complex potential. Curved length coordinate method is utilized to transform the HSIEs for the various cracks configurations into the HSIEs for a straight crack on the real axis which requires less collocation points. With the suitable choices of collocation points on the cracks, the HSIEs is reduced to a system of linear equations. The system of HSIEs is solved numerically by adapting the appropriate quadrature rules and the unknown coefficients with M+1 collocation points are obtained. The obtained unknown coefficients will later be used in computing the stress intensity factors (SIFs). The nondimensional SIFs at all cracks tips for straight, inclined and circular arc cracks of various cracks configurations are analyzed. For the test problems, our results give good agreements with the existence results. Numerical results presented that the nondimensional SIFs are influenced by the inclined angle, crack opening angle and the distance of cracks to the boundary of half-plane. The influence vary for different cracks configurations. The higher the value of SIFs the weaker the material. Integral equations - Numerical solutions Fracture mechanics - Mathematics 2020-02 Thesis http://psasir.upm.edu.my/id/eprint/90348/ http://psasir.upm.edu.my/id/eprint/90348/1/IPM%202020%2011%20ir.pdf text en public masters Universiti Putra Malaysia Integral equations - Numerical solutions Fracture mechanics - Mathematics Nik Long, Nik Mohd Asri
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Nik Long, Nik Mohd Asri
topic	Integral equations - Numerical solutions Fracture mechanics - Mathematics
spellingShingle	Integral equations - Numerical solutions Fracture mechanics - Mathematics Husin, Nur Hazirah Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane
description	In this thesis, the triple Griffith cracks problems subjected to shear stress in an elastic half-plane with free traction boundary condition are formulated into hypersingular integral equation (HSIE) associated with the modified complex potential. Curved length coordinate method is utilized to transform the HSIEs for the various cracks configurations into the HSIEs for a straight crack on the real axis which requires less collocation points. With the suitable choices of collocation points on the cracks, the HSIEs is reduced to a system of linear equations. The system of HSIEs is solved numerically by adapting the appropriate quadrature rules and the unknown coefficients with M+1 collocation points are obtained. The obtained unknown coefficients will later be used in computing the stress intensity factors (SIFs). The nondimensional SIFs at all cracks tips for straight, inclined and circular arc cracks of various cracks configurations are analyzed. For the test problems, our results give good agreements with the existence results. Numerical results presented that the nondimensional SIFs are influenced by the inclined angle, crack opening angle and the distance of cracks to the boundary of half-plane. The influence vary for different cracks configurations. The higher the value of SIFs the weaker the material.
format	Thesis
qualification_level	Master's degree
author	Husin, Nur Hazirah
author_facet	Husin, Nur Hazirah
author_sort	Husin, Nur Hazirah
title	Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane
title_short	Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane
title_full	Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane
title_fullStr	Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane
title_full_unstemmed	Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane
title_sort	hypersingular integral equations for triple griffith cracks problems in an elastic half-plane
granting_institution	Universiti Putra Malaysia
publishDate	2020
url	http://psasir.upm.edu.my/id/eprint/90348/1/IPM%202020%2011%20ir.pdf
_version_	1747813616090873856

Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane

Similar Items