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Spectral Analysis of the Elastic Fields Associated With a Spherical Multi-Inhomogeneous Inclusion

Khorshidi, Alireza | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42346 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammadi Shoja, Hossein
  7. Abstract:
  8. Determination of the elastic fields associated with a spherical multiply-coated inhomogeneous inclusion is a problem of great interest among researchers. In this work a set consisting of N+1 concentric spherical domains is considered. Each domain is either isotropic or spherically isotropic and is functionally graded (FG) in the radial direction. The outermost spherical surface is subjected to nonuniform loading and the constituent phases are subjected to some prescribed nonuniform body force and eigenstrain fields. When the outermost domain is an unbounded medium with zero eigenstrain and body force fields then an N-phase multi-inhomogeneous inclusion problem is realized for which the treatments proposed in this study still applies. To date, the solution of the above-defined boundary value problem does not exist in the literature. Based on the higher-rank spherical harmonics, the spectral theory of elasticity and the spectral equivalent inclusion method in the spherical coordinate system are developed. Application of the spectral theory of elasticity leads to the exact closed-form solution when the elastic moduli of each phase vary as power-law functions of radius. On the other hand, the spherical multi-inhomogeneous inclusion problem with homogeneous phases may be exactly solved by the spectral equivalent inclusion method. For variation of the elastic moduli of the constituent phases other than what stated above, both theories provide highly accurate results. For further illustration of the robustness of the current theories, some previously intractable problems will be treated by the present methods
  9. Keywords:
  10. Spherical Harmonics ; Eshelby Tensor ; Three Dimentional Spectral Analysis ; Spherically Isotropic ; Exact Close-Form Elastic Fields ; Multi-Inhomogeneity

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