Flux and traction boundary elements without hypersingular or strongly singular integrals

International Journal for Numerical Methods in Engineering

Volumn 48, Issue 1, 2000, Pages 111-135

  Dominguez, J ^a   Ariza, M P ^a   Gallego, R ^b  

^a UNIVERSIDAD DE SEVILLA   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

Boundary elements; Hypersingular boundary integral equation; Three dimensional integral representation

Indexed keywords

INTEGRAL EQUATIONS; INTEGRATION; LAPLACE TRANSFORMS;

COLLOCATION POINTS; CONTINUOUS ELEMENTS; DISCRETIZATION; HYPERSINGULAR BOUNDARY INTEGRAL EQUATIONS;

BOUNDARY ELEMENT METHOD;

EID: 0034187454     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000510)48:1<111::AID-NME870>3.0.CO;2-Y     Document Type: Article

References (29)

1. Cruse TA. Boundary-integral equation method for three-dimensional elastic fracture mechanics analysis. Report. No. AFOSR-TR-75-0813, 1975; 13-20.
2. Burton AJ, Miller GF. The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proceedings of the Royal Society of London 1971; A323:201-210.
3. Sladek V, Sladek J. Transient elastodynamic three-dimensional problems in cracked bodies. Applied Mathematical Modelling 1984; 8:2-10.
4. Nishimura N, Kobayashi D. An improved boundary integral equation method for crack problems. In Proceedings IUTAM Symposium on Advanced Boundary Element Methods. Cruse TA (ed.). Springer: Berlin, 1987.
5. Budreck DE, Achenbach JD. Scattering from three-dimensional planar cracks by the boundary integral equation method. Journal of Applied Mechanics 1988; 55:405-412.
6. Krishnasamy G, Rizzo FJ, Rudophi TJ. Hypersingular boundary integral equation: their occurrence, interpretation, regularization and computation. In Developments in Boundary Element Methods, vol. 7, Banerjee PK, Kobayashi S (eds). Elsevier: London, 1992.
7. Tanaka M, Sladek V, Sladek J. Regularization techniques applied to boundary element methods. Applied Mechanics Reviews 1994; 47:457-499.
8. Martin PA, Rizzo FJ. On boundary integral equations for crack problems. Proceedings of the Royal Society 1989; A421:341-355.
9. Martin PA, Rizzo FJ. Hypersingular integrals: how smooth must the density be?. International Journal for Numerical Methods in Engineering 1996; 39:687-704.
10. Krishnasamy G, Schmerr LW, Rudolphi TJ, Rizzo FJ, Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering. Journal of Applied Mechanics ASME 1990; 57:404-414.
11. Martin PA, Rizzo FJ, Cruse TA. Smoothness-relaxation strategies for singular and hypersingular integral equations. International Journal for Numerical Methods in Engineering 1998; 42:885-906.
12. Huang Q, Cruse TA. On the non-singular traction BIE in elasticity. International Journal for Numerical Methods in Engineering 1994; 37:2041-2072.
13. Cruse TA, Richardson JD. Nonsingular somigliama stress identities in elasticity. International Journal for Numerical Methods in Engineering 1996; 39:3273-3304.
14. Richardson JD, Cruse RA, Huang Q. On the validity of conforming BEM algorithms for hypersingular boundary integral equations. Computational Mechanics 1997; 20:213-220.
15. Martha LF, Gray LJ, Ingraffea AR. Three-dimensional fracture simulation with a single-domain direct boundary element formulation. International Journal for Numerical Methods in Engineering 1992; 35:1907-1921.
16. Sladek V, Sladek J, Tanaka M. Numerical solution of nonsingular BIE for crack problems. In Boundary Elements XIV, vol. 2, Brebbia CA, Dominguez J, Paris F (eds). Vol. 2. Computational Mechanics Publications: Southampton, 1992.
17. Young A. A single-domain boudary element method for 3-D elastostatic crack analysis using cotinuous elements. International Journal for Numerical Methods in Engineering 1992; 39:1265-1293.
18. Portela A, Aliabadi MH, Rooke DP. The dual boundary element method: effective implementation for crack problems. International Journal for Numerical Methods in Engineering 1992; 33:1269-1287.
19. Mi Y, Aliabadi MH. Dual boundary element method for three-dimensional fracture mechanics analysis. Engineering Analysis with Boundary Elements 1992; 10:161-171.
20. Gallego R, Dominguez J. Hypersingular BEM for transient elastodynamics. International Journal for Numerical Methods in Engineering 1996; 39:1681-1705.
21. Rudolphi TJ. The use of simple solutions in the regularization of hypersingular boundary integral equations. Mathematical and Computer Modelling 1991; 15:269-278.
22. Rudolphi TJ, Krishnasamy G, Schmerr LW, Rizzo FJ. On the use of strongly singular integral equations for crack problems. In Boundary Elements X. Brebbia CA, (ed.). Computational Mechanics Publications: Southampton, 1988.
23. Guiggiani M, Krishnasamy G, Rudolphi TJ, Rizzo FJ. A general algorithm for the numerical solution of hypersingular boundary integral equations. Journal of Applied Mechanics ASME 1992; 59:604-614.
24. Mantic V. On computing boundary limiting values of boundary integrals with strongly singular and hypersingular kernels in 3D BEM for elastostatics. Engineering Analysis with Boundary Elements 1994; 13:115-134.
25. Aliabadi MH, Hall WS, Phemister TG. Taylor expansions for singular kernels in boundary element method. International Journal for Numerical Methods in Engineering 1985; 21:2221-2236.
26. Bonnet M, Bui HD. Regularization of the displacement and traction BIE for 3D elastodynamics using indirect methods. In Advances in B.E. Techniques, Kane JH, Maier G, Tosaka N, Atluri SN (eds). Springer: Berlin, 1992.
27. Sneddon IN. The distribution of stress in the nieghbourhood of a crack in an elastic solid. Proceedings of the Royal Society of London, Series A 1976; 187:229-260.
28. Irwin GR. Crack-extension force for a part-trough crack in a plate. Transactions of ASNME, Series E, Journal of Applied Mechanics 1962; 29:651-654.
29. Kassir MK, Sih GC, Three-dimensional stress distribution around an elliptical crack under arbitrary loadings, Transactions of ASME, Series E, Journal of Applied Mechanics 1966; 33:601-611.