TY - JOUR

T1 - Clifford algebra valued boundary integral equations for three-dimensional elasticity

AU - Liu, Li Wei

AU - Hong, Hong Ki

N1 - Funding Information:
This research was supported by National Science Council of Taiwan (NSC 102-2221-E-002-128 and NSC 102-2811-E-002-031 ) and Ministry of Science and Technology of Taiwan (MOST 103-2218-E-002-018 and MOST 104-2218-E-002-026-MY3 ).
Publisher Copyright:
© 2017 Elsevier Inc.

PY - 2018/2

Y1 - 2018/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85038210814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038210814&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2017.09.031

DO - 10.1016/j.apm.2017.09.031

M3 - Article

AN - SCOPUS:85038210814

VL - 54

SP - 246

EP - 267

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

ER -