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Mixed Boundary Value Problems in Transversely Isotropic Materials

Eskandari, Morteza | 2010

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40861 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammadi Shodja, Hossein
  7. Abstract:
  8. By virtue of a robust and efficient method, the solution of triple and quadruple integral equations which are the keys of various mixed boundary value problems corresponding to half-space and full-space media is addressed. These multiple integral equations are reduced to a well-known Fredholm integral equation of the second kind. In order to write the governing integral equations of the problem, Green’s functions play an important role. Therefore, Green’s functions of homogeneous and non-homogeneous transversely isotropic media in the form of line integrals including Bessel functions are obtained. Three interesting mixed boundary value problems in transversely isotropic materials are considered: (i) rigid disk inclusion embedded between two dissimilar transversely isotropic half-spaces; (ii) an energetically consistent annular crack in a transversely isotropic piezoelectric medium; and (iii) axisymmetric interaction of an annular crack and a penny-shaped crack in a piezoelectric solid. For each problem, the governing integral equations are written and utilizing the presented method the solution of these problems is obtained. For verification, the obtained results for special cases are compared with the available works in the literature. It should be noted that with the aid of the provided method, various mixed boundary value problems in transversely isotropic media can be solved
  9. Keywords:
  10. Green Function ; Mixed Boundary Value Problem ; Transversely Isotropic ; Annular Crack ; Fredholm Integral Equation

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