A general algorithm for the numerical evaluation of nearly singular boundary integrals of various orders for two- and three-dimensional elasticity

Computational Mechanics

Volumn 29, Issue 4-5, 2002, Pages 277-288

  Ma, H ^a   Kamiya, N ^b  

^a SHANGHAI UNIVERSITY   (China)

^b NAGOYA UNIVERSITY   (Japan)

Author keywords

Boundary element method; Distance transformation; Elasticity; Nearly singular integrals; Numerical integration

Indexed keywords

ALGORITHMS; BOUNDARY ELEMENT METHOD; ELASTICITY; INTEGRAL EQUATIONS; INTEGRATION; MATHEMATICAL TRANSFORMATIONS;

BOUNDARY INTEGRALS;

COMPUTATIONAL METHODS;

EID: 0036814988     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0340-0     Document Type: Article

References (28)

1. Brebbia C.A., Telles J.C.F., Wrobel L.C. (1984) Boundary element techniques - theory and applications in engineering. Springer, Berlin, Heidelberg New York.
2. Mukherjee S. (1982) Boundary element methods in creep and fracture. Applied Science, London.
3. Tanaka M., Matsumoto T., Nakamura M. (1991) Boundary element method (in Japanese). Baifukan Press, Tokyo.
4. Cristescu M., Loubignac G. (1978) Gaussian quadrature formulars for functions with singularities in 1/R over triangles and quadrangles. In: Brebbia C.A. (ed), Recent advances in boundary element methods. Pentech Press, London, pp. 375-390.
5. Cruse T.A., Aithal R. (1993) Non-singular boundary integral equation implementation. Int. J. Numer. Methods Eng. 36: 237-254.
6. Liu Y.J. (1998) Analysis of shell-like structures by the boundary element method based on 3-D elasticity: formulation and verification. Int. J. Numer. Methods Eng. 41: 541-558.
7. Krishnasamy G., Rizzo F.J., Liu Y.J. (1994) Boundary integral equations for thin bodies. Int. J. Numer. Methods Eng. 37: 107-121.
8. Dirgautara T., Aliabadi M.H. (2000) Crack growth analysis of plates loaded by bending and tension using dual boundary element method. Int. J. Fracture 105: 27-74.
9. Aliabadi M.H., Martin D. (2000) Boundary element hypersingular formulation for elasto-plastic contact problems. Int. J. Numer. Methods Eng. 48: 995-1014.
10. Zhang D., Rizzo F.I., Rudolphi T.J. (1999) Stress intensity sensitivities via hypersingular boundary integral equations. Comput. Mech. 23: 389-396.
11. Aliabadi M.H., Hall W.S. (1985) Taylor expansions for singular kernels in the boundary element method. Int. J. Numer. Methods Eng. 21: 2221-2236.
12. Cerrolaza M., Alarcon E. (1989) A bi-cubic transformation of the Cauchy principal value integrals in boundary methods. Int. J. Numer. Methods Eng. 28: 987-999.
13. Doblare M., Gracia L. (1997) On non-linear transformations for the integration of weakly-singular and Cauchy principal value integrals. Int. J. Numer. Methods Eng. 40: 3325-3358.
14. Johnston P.R. (1999) Application of sigmoidal transformations to weakly singular and nearly-singular boundary element integrals. Int. J. Numer. Methods Eng. 45: 1333-1348.
15. Telles J.C.F. (1987) A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals. Int. J. Numer. Methods Eng. 24: 959-973.
16. Sladek N., Sladek J., Tanaka M. (1993) Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity. Int. J. Numer. Methods Eng. 36: 1609-1628.
17. Liu Y.J., Rudolphi T.J. (1999) New identities for fundamental solutions and their applications to non-singular boundary element formulations. Comput. Mech. 24: 286-292.
18. Lin Y.J. (2000) On the simple solution and non-singular nature of the BIE/BEM-a review and some new results. Eng. Anal. Boundary Elements 24: 789-795.
19. Krishnasamy G., Schmerr L.W., Rudolphi T.J., Rizzo F.J. (1990) Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering. ASME J. Appl. Mech. 57: 404-414.
20. Ma H., Kamiya N. (1999) Domain supplemental approach to avoid boundary layer effect of BEM in elasticity. Eng. Anal. Boundary Elements 23: 281-284.
21. Ma H., Kamiya N. (2001) A general algorithm for accurate computation of field variables and its derivatives near boundary in BEM. Eng. Anal. Boundary Elements 25: 843-849.
22. Granados J.J., Gallego R. (2001) Regularization of nearly hypersingular integrals in the boundary element method. Eng. Anal. Boundary Elements 25: 165-184.
23. Ma H., Kamiya N. (1998) Boundary-type integral formulation of domain variables for three-dimensional initial strain problems. JSCE J. Appl. Mech. 1: 355-364.
24. Guiggiani M., Gigante A., (1990) A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method. ASME J. Appl. Mech. 57: 906-915.
25. Guiggiani M., Krishnasamy G., Rudolphi T.J., Rizzo F.J., (1992) A general algorithm for the numerical solution of hypersingular boundary integral equations. ASME J. Appl. Mech. 59: 604-614.
26. Guiggiani M., Casalini P. (1987) Direct computation of Cauchy principal value integrals in advanced boundary elements. Int. J. Numer. Methods Eng. 24: 1711-1720.
27. Mukherjee S. (2000) Finite parts of singular and hypersingular integrals with irregular boundary source points, Eng. Anal. Boundary Elements 24: 767-776.
28. Martin P.A., Rizzo F.J. (1996) Hypersingular integrals: how smooth must the density be? Int. J. Numer. Methods Eng. 39: 687-704.