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Analytical exact solutions of a fundamental anti-plane interaction problem for a reinforced elliptical hole embedded in an infinite matrix with an arbitrarily oriented crack located in the matrix under a remote uniform shear load are provided in this paper. Investigations on the present anti-plane problem are tedious due to the presence of material in-homogeneities and geometric discontinuities. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the stress function in the coated layer and the matrix are derived explicitly in a closed form. By applying the existing solutions for dislocation functions, the integral equations for a line crack are formulated and the mode-III stress intensity factors are obtained numerically. Several numerical examples are given to demonstrate the effects of geometrical parameters and material property combinations on the strength of the anti-plane stress singularity.

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