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A spectral theory formulation for elastostatics by means of tensor spherical harmonics

Khorshidi, A ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1007/s10659-012-9395-0
  3. Publisher: 2013
  4. Abstract:
  5. Consider a set of (N+1)-phase concentric spherical ensemble consisting of a core region encased by a sequence of nested spherical layers. Each phase is spherically isotropic and is functionally graded (FG) in the radial direction. Determination of the elastic fields when the outermost spherical surface is subjected to a nonuniform loading and the constituent phases are subjected to some prescribed nonuniform body force and eigenstrain fields is of interest. When the outermost layer is an unbounded medium with zero eigenstrain and body force fields, then an N-phase multi-inhomogeneous inclusion problem is realized. Based on higher-order spherical harmonics, presenting a three-dimensional strain formulation with a robust form of compatibility equations, a spectral theory of elasticity in the spherical coordinate system is developed. Application of the established spectral theory leads to the exact closed-form solution when the elastic moduli of each phase vary as power-law functions of radius
  6. Keywords:
  7. Exact closed-form elastic fields ; Inclusion problem ; Functionally graded materials (FGMs) ; Multi-inhomogeneous inclusion ; Tensor spherical harmonics ; Body forces ; Closed form solutions ; Compatibility equation ; Constituent phasis ; Core region ; Eigen-strain ; Elastic fields ; Functionally graded ; Functionally graded material (FGMs) ; Higher-order ; 3D spectral analysis ; Nonuniform loadings ; Power-law functions ; Radial direction ; Spectral theory ; Spherical coordinate systems ; Spherical harmonics ; Spherical surface ; Spherically isotropic ; Three-dimensional strains ; Elasticity ; Harmonic analysis ; Spectrum analysis ; Spheres ; Tensors ; Loading
  8. Source: Journal of Elasticity ; Volume 111, Issue 1 , 2013 , Pages 67-89 ; 03743535 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs10659-012-9395-0