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 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.

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