Finite parts of singular and hypersingular integrals with irregular boundary source points

Engineering Analysis with Boundary Elements

Volumn 24, Issue 10, 2000, Pages 767-776

  Mukherjee, S ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS;

BOUNDARY INTEGRAL EQUATIONS; CAUCHY PRINCIPAL VALUES; HYPERSINGULAR INTEGRALS;

STRUCTURAL ANALYSIS;

EID: 0034517270     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(00)00059-X     Document Type: Article

References (50)

1. Krishnasamy G., Rizzo F.J., Rudolphi T.J. Hypersingular boundary integral equations: their occurrence, interpretation, regularization and computation. Banerjee P.K., Kobayashi S. Developments in boundary element methods - 7. 1992;207-252 Elsevier Applied Science, London.
2. Tanaka M., Sladek V., Sladek J. Regularization techniques applied to boundary element methods. ASME Appl Mech Rev. 47:1994;457-499.
3. Paulino GH.,Novel formulations of the boundary element method for fracture mechanics and error estimation. PhD dissertation. Cornell University, Ithaca, NY, 1995.
4. Chen J.T., Hong H.K. Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. ASME Appl Mech Rev. 52:1999;17-33.
5. Guiggiani M., Krishnasamy G., Rudolphi T.J., Rizzo F.J. A general algorithm for the numerical solution of hypersingular boundary integral equations. ASME J Appl Mech. 59:1992;604-614.
6. Wilde A.J., Aliabadi M.H. Direct evaluation of boundary stresses in the 3D BEM of elastostatics. Commun Numer Meth Engng. 14:1998;505-517.
7. Zhao Z.Y., Lan S.R. Boundary stress calculation - a comparison study. Comput Struct. 71:1999;77-85.
8. Chati M.K., Mukherjee S. Evaluation of gradients on the boundary using fully regularized hypersingular boundary integral equations. Acta Mech. 135:1999;41-45.
9. Krishnasamy G., Schmerr L.W., Rudolphi T.J., Rizzo F.J. Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering. ASME J Appl Mech. 57:1990;404-414.
10. Cruse T.A. Boundary element analysis in computational fracture mechanics. 1988;Kluwer, Dordrecht.
11. Gray L.J., Martha L.F., Ingraffea A.R. Hypersingular integrals in boundary element fracture analysis. Int J Numer Meth Engng. 29:1990;1135-1158.
12. Lutz E.D., Ingraffea A.R., Gray L.J. Use of simple solutions for boundary integral methods in elasticity and fracture analysis. Int J Numer Meth Engng. 35:1992;1737-1751.
13. Gray L.J., Paulino G.H. Crack tip interpolation revisited. SIAM J Appl Math. 58:1998;428-455.
14. Bonnet M. Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity. Engng Anal Bound Elem. 15:1995;93-102.
15. Gray L.J., Balakrishna C., Kane J.H. Symmetric Galerkin fracture analysis. Engng Anal Bound Elem. 15:1995;103-109.
16. Gray L.J., Paulino G.H. Symmetric Galerkin boundary integral formulation for interface and multizone problems. Int J Numer Meth Engng. 40:1997;3085-3101.
17. Gray L.J., Paulino G.H. Symmetric Galerkin boundary integral fracture analysis for plane orthotropic elasticity. Comput Mech. 20:1997;26-33.
18. Mukherjee S, Chati MK, Shi X. Evaluation of nearly singular integrals in boundary element contour and node methods for three-dimensional linear elasticity. Int J Solids Struct 2000;37:7633-54.
19. Phan A.-V., Mukherjee S., Mayer J.R.R. The hypersingular boundary contour method for two-dimensional linear elasticity. Acta Mech. 130:1998;209-225.
20. Mukherjee S., Mukherjee Y.X. The hypersingular boundary contour method for three-dimensional linear elasticity. ASME J Appl Mech. 65:1998;300-309.
21. Chati MK, Paulino GH, Mukherjee S. The meshless standard and hypersingular boundary node methods - applications to error estimation and adaptivity in three-dimensional problems. Int J Numer Meth Engng 2000 (in press).
22. Paulino G.H., Gray L.J., Zarkian V. Hypersingular residuals-a new approach for error estimation in the boundary element method. Int J Numer Meth Engng. 39:1996;2005-2029.
23. Menon G. Hypersingular error estimates in boundary element methods. MS thesis. Cornell University, Ithaca, NY, 1996.
24. Menon G., Paulino G.H., Mukherjee S. Analysis of hypersingular residual error estimates in boundary element methods for potential problems. Comput Meth Appl Mech Engng. 173:1999;449-473.
25. Paulino G.H., Gray L.J. Galerkin residuals for adaptive symmetric-Galerkin boundary element methods. ASCE J Engng Mech. 125:1999;575-585.
26. Rudolphi T.J. The use of simple solutions in the regularization of hypersingular boundary integral equations. Math Comput Modelling. 15:1991;269-278.
27. Cruse T.A., Richardson J.D. Non-singular Somigliana stress identities in elasticity. Int J Numer Meth Engng. 39:1996;3273-3304.
28. Poon H., Mukherjee S., Ahmad M.F. Use of simple solutions in regularizing hypersingular boundary integral equations in elastoplasticity. ASME J Appl Mech. 65:1998;39-45.
29. Mukherjee Y.X., Shah K., Mukherjee S. Thermoelastic fracture mechanics with regularized hypersingular boundary integral equations. Engng Anal Bound Elem. 23:1999;89-96.
30. Gray L.J., Manne L.L. Hypersingular integrals at a corner. Engng Anal Bound Elem. 11:1993;327-334.
31. Gray L.J., Lutz E.D. On the treatment of corners in the boundary element method. J Comp Appl Math. 32:1990;369-386.
32. Telles J.C.F., Prado A.A. Hypersingular boundary formulation for 2-D potential problems. Aliabadi M.H., Brebbia C.A. Advanced formulations in boundary element methods. 1993;191-213 Elsevier Applied Science/Computational Mechanics Publications, Southampton, UK. (chap. 6).
33. Chen J.T., Hong H.K. Dual boundary integral equations at a corner using contour approach around singularity. Adv Engng Software. 21:1994;169-178.
34. Guiggiani M. Hypersingular boundary integral equations have an additional free term. Comput Mech. 16:1995;245-248.
35. Mantic V., Paris F. Existence and evaluation of two free terms in the hypersingular boundary integral equation of potential theory. Engng Anal Bound Elem. 16:1995;253-260.
36. Hadamard J. Lectures on Cauchy's problem in linear partial differential equations. 1923;Yale University Press, New Haven, CT.
37. Martin P.A. End-point behavior of solutions to hypersingular integral equations. Proc R Soc London, A. 432:1991;301-320.
38. Toh K.-C., Mukherjee S. Hypersingular and finite part integrals in the boundary element method. Int J Solids Struct. 31:1994;2299-2312.
39. Hui C.Y., Mukherjee S. Evaluation of hypersingular integrals in the boundary element method by complex variable techniques. Int J Solids Struct. 34:1997;203-221.
40. Mukherjee S. CPV and HFP integrals and their applications in the boundary element method. Int J Solids Struct 2000;37:6623-34.
41. Martin P.A., Rizzo F.J., Cruse T.A. Smoothness-relaxation strategies for singular and hypersingular integral equations. Int J Numer Meth Engng. 42:1998;885-906.
42. Mukherjee S, Mukherjee YX. Error analysis and adaptivity in three-dimensional linear elasticity by the usual and hypersingular boundary contour method. Int J Solids Struct 2000;38:161-78.
43. Mukherjee S. On boundary integral equations for cracked and for thin bodies. Math Mech Solids. 2000;. (in press).
44. Ghosh N., Rajiyah H., Ghosh S., Mukherjee S. A new boundary element method formulation for linear elasticity. ASME J Appl Mech. 53:1986;69-76.
45. Kane J.H. Boundary element analysis in engineering continuum mechanics. 1994;Prentice Hall, Englewood Cliffs, NJ.
46. Rizzo F.J. An integral equation approach to boundary value problems of classical elastostatics. Qly Appl Math. 25:1967;83-95.
47. Cruse T.A. Numerical solutions in three-dimensional elastostatics. Int J Solids Struct. 5:1969;1259-1274.
48. Glushkov E., Glushkova N., Lapina O. 3-D elastic stress analysis at polyhedral corner points. Int J Solids Struct. 36:1999;1105-1128.
49. Zhang Q., Mukherjee S. Design sensitivity coefficients for linear elastic bodies with zones and corners by the derivative boundary element method. Int J Solids Struct. 27:1991;983-998.
50. Mukherjee Y.X., Mukherjee S., Shi X., Nagarajan A. The boundary contour method for three-dimensional linear elasticity with a new quadratic boundary element. Engng Anal Bound Elem. 20:1997;35-44.