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Isogeometric Analysis of the Dual Boundary Element Method for the Laplace Problem With a Degenerate Boundary

Published online by Cambridge University Press:  23 September 2019

J. H. Kao ,
K. H. Chen ,
J. T. Chen Open the ORCID record for J. T. Chen [Opens in a new window]  and
S. R. Kuo
J. H. Kao
Affiliation:
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan
K. H. Chen
Affiliation:
Department of Civil Engineering, National Ilan University, Ilan, Taiwan
J. T. Chen*
Affiliation:
Department of Harbor and River Engineering, Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung, Taiwan Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan
S. R. Kuo
Affiliation:
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan
*
*Corresponding author ([email protected])
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Abstract

In this paper, we develop the isogeometric analysis of the dual boundary element method (IGA-DBEM) to solve the potential problem with a degenerate boundary. The non-uniform rational B-Spline (NURBS) based functions are employed to interpolate the geometry and physical function. To deal with the rank-deficiency problem due to the degenerate boundary, the hypersingular integral equation is introduced to promote the full rank for the influence matrix in the dual BEM. Finally, three numerical examples are given to verify the accuracy of our proposed method. Both circular and square domains subjected to the Dirichlet boundary condition are considered. The engineering problem containing a degenerate boundary is considered, e.g., a seepage flow problem with a sheet pile. Numerical results of the IGA-DBEM agree well with these of the exact solution and the original dual boundary element method.

Keywords

Dual BEMIsogeometric analysisNURBSDegenerate boundaryLaplace equation
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 1 , February 2020 , pp. 35 - 46
Copyright
Copyright © 2019 The Society of Theoretical and Applied Mechanics 

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