| In this thesis,the problems for interfacial cracks are studied. The main achievments are as follows:(1) The foundamental solutions are re-derived for three-dimensional two-phased thransversely isotropic piezoelectric media. They are more convenient to be used.(2) By using of the foundamental solutions and the Somigliana identity,the hyper-singular integral-differential equations for interfacial cracks in three-dimensional transversely isotropic piezoelectric media are obtained. If the materials are homogeneous,the equations reduce to the displacement discontinuity-potential discontinuity boundary intergral equations in three-dimensional piezoelectric media.(3) The boundary element method for the hyper-singular integral-differential equations of the interfacial crack are realized in three-dimensional piezoelectric media.(4) Several important problems in fracture mechanics are analysed by the established displacement discontinuity boundary element method. The interaction problems for two elliptic cracks are carefully studied:the energe release rate for two interfacial cracks and the stress intensity factor for two cracks in homogeneous media are,respectively,given.
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