Analytical evaluation and application of the singularities in boundary element method

Engineering Analysis with Boundary Elements

Volumn 29, Issue 3, 2005, Pages 241-256

  Wang, John ^a   Tsay, Ting Kuei ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Boundary element method; Cut off wall; Numerical boundary layer; Singularities

Indexed keywords

BOUNDARY LAYERS; CONFORMAL MAPPING; CRACKS; GREEN'S FUNCTION; INTEGRAL EQUATIONS; INTEGRATION; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING;

BOUNDARY ELEMENTS; CUT-OFF WALLS; NUMERICAL BOUNDARY LAYERS; SINGULARITIES;

BOUNDARY ELEMENT METHOD;

EID: 15844399373     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2004.12.008     Document Type: Article

References (40)

1. V. Sladek, and J. Sladek Singular integrals in boundary element methods 1998 Computational Mechanics Publications UK
2. M. Guiggiani The evaluation of Cauchy principal value integrals in the boundary element method - a review Math Comput Modell 15 1991 175
3. M. Guiggiani, G. Krishnasamy, T.J. Rudolphi, and F.J. Rizzo A general algorithm for the numerical solution of hypersingular boundary integral equations Trans ASME 59 1992 604
4. J.A. Liggett, and P.L.-F. Liu The boundary integral equation method for porous media flow 1983 Allen & Unwin Ltd UK
5. M. Hang, and K. Norio Domain supplemental approach to avoid boundary layer effect of BEM in elasticity Eng Anal Bound Elem. 23 1999 281
6. H.B. Chen, P. Lu, M.G. Huang, and F.W. Williams An effective method for finding values on and near boundaries in the elastic BEM Comput Struct 69 1998 421
7. H. Kisu, and T. Kawahara Boundary element analysis system based on a formulation with relative quantity Proceedings of BEM10 conference 1988 Computational Mechanics Publications Southampton
8. P.R. Johnston, and D. Elliott Error estimation of quadrature rules for evaluating singular integrals in boundary element problems Int J Numer Meth Eng 48 2000 949
9. A. Nagarajan, and S. Mukherjee A mapping method for numerical evaluation of two-dimensional integrals with 1/r singularity Comput Mech 12 1993 19
10. T.C. Charles On bicubic transformation for the numerical evaluation of Cauchy principal value integrals Commun Numer Meth Eng 9 1993 307
11. M.S. Krishna, and M. Tanaka On non-linear transformations for accurate numerical evaluation of weakly singular boundary integrals Int J Numer Meth Eng 50 2001 2007
12. E.D. Lutz, and L.J. Gray Analytic evaluation of singular boundary integrals without CPV Commun Numer Meth Eng 9 1993 909
13. M. Tanaka, V. Sladek, and J. Sladek Regularization techniques applied to boundary methods Appl Mech Rev 47 10 1994 457
14. L.J. Gray, and E. Lutz On the treatment of corners in the boundary element method J Comput Appl Math 32 1990 369
15. P.R. Heyliger, and T.J. Rudolphi Evaluation of field singularities by an iterative boundary-element method Commun Numer Meth Eng 9 1993 337
16. O.P. Gupta, and S.S. Babu Error analysis in applying a boundary element method for three-dimensional steady state potential problems Comput Struct 58 1996 289
17. M.T. Liang, J.T. Chen, and S.S. Yang Error estimation for boundary element method Eng Anal Bound Elem 23 1999 257
18. J.T. Chen, and H.-K. Hong Dual boundary integral equations at a corner using contour approach around singularity Adv Eng Softw 21 1994 169
19. L.J. Gray, and L.L. Mamme Hypersingular integrals at a corner Eng Anal Bound Elem 11 1993 327
20. Chen JT. On a dual representation model and its applications to computational mechanics. PhD Thesis, Taiwan University; 1994.
21. A.R. Ingraffea, G. Blandford, and J.A. Liggett Automatic modeling of mixed-mode fatigue and quasi-static crack propagation using the boundary element method Proc 14th Natl Symp Fract Mech 971 1983 1407
22. H.-K. Hong, and J.T. Chen Derivation of integral equations on elasticity ASCE, J Eng Mech 114 6 1988 1028
23. J.T. Chen, and H.K. Hong On the dual integral representation of boundary value problem in Laplace equation BE Abstracts 4 3 1993 114
24. A. Poterla, M.H. Aliabadi, and D.P. Rooke The dual boundary element method: effective implementation for crack problems Int J Numer Meth Eng 33 1992 1269
25. S.L. Crouch Solution of plane elasticity problems by DD method Int J Numer Meth Eng 10 1976 301
26. L.J. Gray, D. Maroudas, M.N. Enmark, and E.F. D'Azevedo Approximation Green's functions in boundary integral analysis Eng Anal Bound Elem 23 1999 267
27. J.T. Chen Singular BIE/BEM Proceedings of BEM Conference, Section D 1998 NCHC Publications Taiwan
28. J.T. Chen, and H.-K. Hong Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series Appl Mech Rev, ASME 52 1 1999 17
29. C. Detournay On a Cauchy integral element method for potential flow with corner singularities Computational engineering with boundary elements 1990 Southampton; Boston: Computational Mechanics Publications p. 119
30. C. Detournay A Cauchy integral element method for boundary singularities Boundary element technology VII 1992 Southampton; UK: Boston, Mass: Computational Mechanics Publications p. 801
31. N. Papamichael, and C.A. Kokkinos Two numerical methods for the conformal mapping of simply-connected domains Comput Meth Appl Mech Eng 28 1981 285
32. N. Papamichael, and C.A. Kokkinos Numerical conformal mapping of exterior domains Comput Meth Appl Mech Eng 31 1982 189
33. N. Papamichael, and M.K. Warby The treatment of corner and pole-type singularities in numerical conformal mapping techniques J Comput Appl Math 14 1986 163
34. Lutz ED. Singular and nearly singular integrals. PhD Thesis, Cornell University; 1991.
35. B.O. Peirce, and M.F. Ronald A short table of integrals 1956 Ginn & Co. Boston
36. D. Lefeber Solving problems with singularities using boundary elements 1989 Computational Mechanics Publications UK and Boston, MA
37. S.R. Karur, and P.A. Ramachandran Orthogonal collocation in the nonconforming boundary element method J Comput Phys 121 1995 373
38. T.K. Tsay, and F.S. Hsu Numerical grid generation of an irregular region Int J Numer Meth Eng 40 1997 343
39. M. Hang, and K. Norio A general algorithm for accurate computation of field variables and its derivatives near the boundary in BEM Eng Anal Bound Elem 25 10 2001 833
40. J. Whiteman, and N. Papamichael Treatment of harmonic mixed boundary problems by conformal transformation methods Appl Math Phys 23 1972 655