Clifford algebra valued boundary integral equations for three-dimensional elasticity
| Autor: | Hong-Ki Hong, Li Wei Liu |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
Algebra of physical space Mathematical analysis Clifford algebra Boundary (topology) Dirac algebra 02 engineering and technology Clifford analysis Dirac operator 01 natural sciences 010101 applied mathematics Geometric algebra symbols.namesake 020303 mechanical engineering & transports 0203 mechanical engineering Modeling and Simulation symbols Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | Applied Mathematical Modelling. 54:246-267 |
| ISSN: | 0307-904X |
| DOI: | 10.1016/j.apm.2017.09.031 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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