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Regularization of the Boundary Integrals in the Bem Analysis of 3D Potential Problems

Published online by Cambridge University Press:  20 December 2012

Y. C. Shiah ,
M. R. Hematiyan  and
Y. H. Chen
Y. C. Shiah*
Affiliation:
Program of Mechanical and Aeronautical Engineering, Feng Chia University, Taichung, Taiwan 40724, R.O.C.
M. R. Hematiyan
Affiliation:
Department of Mechanical Engineering, Shiraz University, Shiraz, Iran
Y. H. Chen
Affiliation:
Department of Computer Science and Information Management, Providence University, Taichung, Taiwan 43301, R.O.C.
*
*Corresponding author ([email protected])
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Abstract

In the conventional boundary element analysis, near-singularities are present in the associated boundary integral equation for problems involving ultra-thin media. For this case, any conventional numerical schemes will fail to yield proper values for the integrals. In this paper, the boundary integrals of the boundary element method for 3D potential problems are fully regularized by the technique of integration by parts under the local coordinate system. The fully regularized integrands are expressed as very explicit formulations that can be easily programmed into a computer code. Numerical tests carried out for a typical case have verified the accuracy of the approach for any orders of small distance between the source and the element under integration.

Keywords

Boundary element methodRegularization of boundary integrals3D potential problems
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 3 , September 2013 , pp. 385 - 401
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

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References

REFERENCES

1.Kayhani, M. H., Norouzi, M. and Amiri Delouei, A., “A General Analytical Solution for Heat Conduction in Cylindrical Multilayer Composite Laminates,” International Journal of Thermal Sciences, 52, pp. 73–82 (2012).Google Scholar
2.Haji-Sheikh, A., Amos, Donald E., and Beck, J. V., “Axial Heat Conduction in a Moving Semi-Infinite Fluid,” International Journal of Heat and Mass Transfer, 51, pp. 4651–4658 (2008).Google Scholar
3.Ma, C.-C. and Chang, S.-W., “Analytical Exact Solutions of Heat Conduction Problems for Anisotropic Multi-Layered Media,” International Journal of Heat and Mass Transfer, 47, pp. 1643–1655 (2004).Google Scholar
4.Rizzo, F. J., “An Integral Equation Approach to Boundary Values Problems of Classical Elastostatics,” Quarterly of Applied Mathematics, 40, pp. 83–95 (1967).Google Scholar
5.Lauricella, G., Sur Pintégration De Péquation Relative A Pequilibre Des Plaques Élastiques Encastrées, Acta Math., 32 (in French).Google Scholar
6.Massonnet, C. E., Numerical Use of Integral Procedures, Stress Analysis, Zienkiewicz, O.C. and Holister, Z.S., eds., John Wily and Sons, London U.K. (1965).Google Scholar
7.Kupradze, V. D., Potential Methods in the Theory of Elasticity. Translated From Russian by Israel Program for Scientific Translation, Jerusalem, Israel., (1963).Google Scholar
8.Hong, H.-K. and Chen, J.-T., “Derivations of Integral Equations of Elasticity,” Journal of Engineering Mechanics, ASCE, 114, pp. 1028–1044 (1988).Google Scholar
9.Zozulya, V. V., “Divergent Integrals in Elastostatics: Regularization in 3-D Case,” CMES: Computer Modeling in Engineering & Sciences, 70, pp. 253–349 (2010).Google Scholar
10.Chen, J. T. and Hong, H-K., “Review of Dual Boundary Element Methods with Emphasis on Hypersingular Integrals and Divergent Series,” Applied Mechanics Reviews, 52, pp. 17–33 (1999).Google Scholar
11.Guz, A. N. and Zozulya, V. V., “Fracture Dynamics with Allowance for a Crack Edges Contact Interaction,” International Journal of Nonlinear Sciences and Numerical Simulation, 2, pp. 173–233 (2001).Google Scholar
12.Tanaka, M., Sladek, V. and Sladek, J., “Regulariza-tion Techniques Applied to Boundary Element Methods,” Applied Mechanics Reviews, 47, pp. 457–499 (1994).Google Scholar
13.Granados, J. J. and Gallego, R., “Regularization of Nearly Hypersingular Integrals in the Boundary Element Method,” Engineering Analysis with Boundary Elements, 25, pp. 165–184 (2001).Google Scholar
14.Tomioka, S. and Nishiyama, S., “Analytical Regu-larization of Hypersingular Integral for Helmholtz Equation in Boundary Element Method,” Engineering Analysis with Boundary Elements, 34, pp. 393–404 (2010).Google Scholar
15.de Lacerda, L. A. and Wrobel, L. C., “Hypersingular Boundary Integral Equation for Axisymmetric Elasticity,” International Journal for Numerical Methods in Engineering, 52, pp. 1337–1354 (2001).Google Scholar
16.Shiah, Y. C. and Shi, Y.-X., “Heat Conduction Across Thermal Barrier Coatings of Anisotropic Substrates,” International Communications in Heat and Mass Transfer, 33, pp. 827–835 (2006).Google Scholar
17.Shiah, Y. C., Chen, Y. H. and Kuo, W. S., “Analysis for the Interlaminar Stresses of Thin Layered Composites Subjected to Thermal Loads,” Composites Science and Technology, 67, pp. 2485–2492 (2007).Google Scholar
18.Chen, J. T., Kuo, S. R., Chen, W. C. and Liu, L. W., “On the Free Terms of the Dual BEM for the Two and Three-Dimensional Laplace Problems,” Journal of Marine Science and Technology, 8, pp. 8–15 (2000).Google Scholar
19.Brookfield, G., “Factoring Quartic Polynomials: A Lost Art,” Mathematics Magazine, 80, pp. 67–70 (2007).Google Scholar
20.http://en.wikipedia.org/wiki/Quartic_function.Google Scholar