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a b s t r a c tA general solution to a reinforced elliptic hole embedded in an infinite matrix subjected to a remote uniform load is provided in this paper. Investigations on the present elasticity problem are rather tedious due to the presence of material inhomogeneities and complex geometric configurations. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the displacement and stresses in a reinforcement layer and the matrix are derived explicitly in a series form. Some numerical results are provided to investigate the effects of the material combinations and geometric configurations on the interfacial stresses. The results show that there exists an optimum design of a reinforcement layer such that both the magnitude of stress concentration and the interfacial stresses could be fairly reduced.

This paper presents a novel efficient procedure to analyze the two-phase confocally elliptical inclusion embedded in an unbounded matrix under antiplane loadings. The antiplane loadings considered in this paper include a point force and a screw dislocation or a far-field antiplane shear. The analytical continuation method together with an alternating technique is used to derive the general forms of the elastic fields in terms of the corresponding problem subjected to the same loadings in a homogeneous body. This approach could lead to some interesting simplifications in solution procedures, and the derived analytical solution for singularity problems could be employed as a Green's function to investigate matrix cracking in the corresponding crack problems. Several specific solutions are provided in closed form, which are verified by comparison with existing ones. Numerical results are provided to show the effect of the material mismatch, the aspect ratio, and the loading condition on the elastic field due to the presence of inhomogeneities.

An exact solution is given for the stress field in a three-phase composite cylinder induced by a uniform heat flow applied at infinity. Based on the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and stress functions are derived explicitly in each medium of a three-phase composite cylinder. It is discovered that the stress in the inclusion is always linearly proportional to the coordinate z. Comparison is made with the special case of a two-phase composite cylinder, which shows that our results presented here are exact and general.

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