Clifford algebra valued boundary integral equations for three-dimensional elasticity

Li Wei Liu, Hong Ki Hong

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Applications of Clifford analysis to three-dimensional elasticity are addressed in the present paper. The governing equation for the displacement field is formulated in terms of the Dirac operator and Clifford algebra valued functions so that a general solution is obtained analytically in terms of one monogenic function and one multiple-component spatial harmonic function together with its derivative. In order to solve numerically the three-dimensional problems of elasticity for an arbitrary domain with complicated boundary conditions, Clifford algebra valued boundary integral equations (BIEs) for multiple-component spatial harmonic functions at an observation point, either inside the domain, on the boundary, or outside the domain, are constructed. Both smooth and non-smooth boundaries are considered in the construction. Moreover, the singularities of the integrals are evaluated exactly so that in the end singularity-free BIEs for the observation point on the boundary taking values on Clifford numbers can be obtained. A Clifford algebra valued boundary element method (BEM) based on the singularity-free BIEs is then developed for solving three-dimensional problems of elasticity. The accuracy of the Clifford algebra valued BEM is demonstrated numerically.

Original languageEnglish
Pages (from-to)246-267
Number of pages22
JournalApplied Mathematical Modelling
Volume54
DOIs
Publication statusPublished - 2018 Feb

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

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