| Summary: | 博士 === 國立臺灣科技大學 === 機械工程系 === 98 === This study presents plane elasticity problems of the three-phase elliptical media subjected to an arbitrary singularity point. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, both the displacements and stresses are derived explicitly in terms of the Muskhelishvili’s complex potentials. The external loadings considered in this study include an arbitrary concentration load, dislocation and a uniform load. The image forces acting on the dislocation are calculated through the Peach-Koehler formula.
The series solution can be simplified to an exact one to satisfy boundary condition of an elliptical hole (or rigid inclusion) for the single elliptical inhomogeneity problem. The interaction between a screw dislocation and elliptical inhomogeneity is also discussed for different materials and geometry in this study. Besides, the derived singularity solution can be served as Green’s function to investigate the crack problem of the corresponding problem. From the numerical results, the equilibrium position and subsequent stability of the dislocation are determined and the magnitude or direction of dislocation’s movement is discussed in detail.
In order to verify the effectiveness and accuracy of this proposed method, the solution of the present three-phase composite is reduced to the one for the corresponding biomaterial and single material problems, or degenerated into circle from elliptic ones. The comparison of our results with the known exact one shows that our approach is accurate and effective.
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