An efficient method to evaluate hypersingular and supersingular integrals in boundary integral equations analysis

Engineering Analysis with Boundary Elements

Volumn 23, Issue 4, 1999, Pages 317-326

  Karami, G ^a   Derakhshan, D ^a  

^a SHIRAZ UNIVERSITY   (Iran)

Author keywords

Boundary integral analysis; Hypersingular and supersingular integrals; Polar transformation domain

Indexed keywords

ALGORITHMS; BOUNDARY ELEMENT METHOD; COMPUTATIONAL METHODS; DIFFERENTIATION (CALCULUS); INTEGRATION; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS;

BOUNDARY INTEGRAL ANALYSIS; HYPERSINGULAR INTEGRALS; POLAR TRANSFORMATION DOMAIN; SUPERSINGULAR INTEGRALS;

INTEGRAL EQUATIONS;

EID: 0033116850     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0955-7997(98)00085-x     Document Type: Article

References (17)

1. Hartmann F. Computing C-matrix in non-smooth boundary points. In: Brebbia CA, editor. New developments in boundary element methods. London: Butterworths, 1980:367-871.
2. Nishimura N., Kobayashi S. A regularized boundary integral equation method for elastodynamic crack problems. Comput Mech. 4:1989;367-871.
3. Polch E., Cruse T.A., Huang C.J. Traction BIE solution for flat cracks. Comput Mech. 2:1987;253-267.
4. Guiggiani M., Casalini P. Direct computation of Cauchy principal value integral in advanced boundary element. Int J Numer Meth Engng. 24:1987;1711-1720.
5. Guiggiani M., Gigante A. A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method. J Appl Mech Trans ASME. 57:1990;906-915.
6. Guiggiani M., Krishnasamy G., Rudolphi T.J., Rizzo F.J. A general algorithm for the numerical solution of hypersingular boundary integral equations. Trans ASME. 59:1992;604-614.
7. Rudolphi T.J. The use of simple solution in the regularization of hypersingular boundary integral equations. Math Comput Model. 15:1991;269-278.
8. Bialecki R., Dallner R., Kulin G. New application of the hypersingular equations in the boundary element method. Comput Meth Appl Mech Engng. 103:1993;399-416.
9. Bonnet M, Bui HD. Regularization of the displacement and traction BIE for 3D elastodynamics using indirect methods. In: Kane JH, Maier G, Tosaka, Atluri SN, editors. Advances in boundary element techniques. Berlin: Springer, 1993:1-29.
10. Gray L.J., Soucie C.S. A hermite interpolation algorithm for hypersingular boundary integrals. Int J Numer Meth Engng. 17:1990;2357-2367.
11. Toh K.C., Mukherjee S. Hypersingular and finite part integral in the boundary element method. Int J Solid Struct. 17:1994;2299-2312.
12. Kellogg OD. Foundation of potential theory. New York: Frederick Ungar, 1929.
13. Guiggiani M. Hypersingular boundary integral equation have additional free term. Comput Mech. 16:1995;245-248.
14. Mantic V., Paris R. Existence and evaluation of the two free terms in the hypersingular boundary integral equation of potential theory. Engng Anal Boundary Elements. 16:1996;253-260.
15. Young A. A single-domain boundary element method for 3-D elastostatic crack analysis using continuous elements. Int J Numer Meth Engng. 39:1996;1265-1293.
16. Brebbia CA, Dominquez J. Boundary elements, an introductory course. Southampton: Computational Mechanics Publications, 1989.
17. Karami G. A boundary element method for two-dimensional contact problems, vol. 59. Berlin: Springer, 1989:42-49.