A boundary spectral method for elastostatic problems with multiple spherical cavities and inclusions

Hamid R. Sadraie, Steven L Crouch, Sofia Mogilevskaya

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The problem of an infinite solid containing an arbitrary number of non-overlapping spherical cavities and inclusions with arbitrary sizes and locations is considered. The infinite solid and the spherical inclusions are made of different isotropic, linearly elastic materials. The spherical cavities are assumed to carry arbitrary tractions, and the spherical inclusions are assumed to be perfectly bonded to the infinite solid. The boundary and interfacial displacements and tractions are represented by truncated series of surface spherical harmonics. The problem involving multiple spherical features is replaced by a sequence of problems involving a single spherical feature via Schwarz's alternating method which accounts for the interactions in the course of an iterative process. Problems involving a single spherical feature are solved by employing the Papkovich-Neuber functions, and the interactions are evaluated by applying a least squares method. A robust scheme is introduced to control the total errors on the spherical boundaries and interfaces and to choose the number of terms in the series expansions. Several numerical examples are given to address the efficiency and the accuracy of the proposed method.

Original languageEnglish (US)
Pages (from-to)425-442
Number of pages18
JournalEngineering Analysis with Boundary Elements
Volume31
Issue number5
DOIs
StatePublished - May 1 2007

Keywords

  • Alternating method
  • Boundary spectral method
  • Elasticity
  • Least squares method
  • Spherical cavities and inclusions
  • Spherical harmonics

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