Interaction between two cracks in circular positions in plane elasticity

In this thesis, the interaction between two cracks in circular positions in plane elasticity is formulated into a system of hyper singular integral equations by using thecomplex variable function method. The center of the cracks are placed at the edgeof a circle with radius R. The first crack is fixed on thex-axis while the second crackis located on the boundary of a circle with the varying angle, θ. By using the curved length coordinate method, the cracks are mapped into a straight line which require less collocation points, hence give faster convergence. With the help of particular quadrature rules, the unknown coefficients are solved numerically from the resulting system of hyper singular integral equations. The obtained unknown coefficients are then used for determining the stress intensity factor (SIF).Three different domains for the problems of two cracks in circular positions will be considered which is the varying angle of positions of the second crack, the length ratio of the second to the first crack, and the length ratio of the first crack to the radius of a circle. The results for the tested problem presented here agree with the previous reported results.

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