A general algorithm for multidimensional cauchy principal value integrals in the boundary element method

Journal of Applied Mechanics, Transactions ASME

Volumn 57, Issue 4, 1990, Pages 906-915

  Guiggiani, M ^a   Gigante, A ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPLIED MECHANICS; BOUNDARY ELEMENTS; CAUCHY PRINCIPAL VALUE; COMPUTER CODES; GENERAL METHOD; INTERNAL CELLS; NUMERICAL IMPLEMENTATION; NUMERICAL RESULTS; QUADRATURE FORMULA; SINGULAR INTEGRAL; SURFACE ELEMENTS;

COMPUTER GRAPHICS; MECHANICS; NUMERICAL METHODS;

BOUNDARY ELEMENT METHOD;

EID: 0001548771     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.2897660     Document Type: Article

References (31)

1. Aliabadi, M. H., Hall, W. S., and Phemister.T. G., 1985, “Taylor Expansions for Singular Kernels in the Boundary Element Method,” International Journal for Numerical Methods in Engineering, Vol. 21, pp. 2221-2236.
2. Bonnet, M., 1986, “Méthodes des Equations Intégrales Régularisées en Elastodynamique,” Ph.D. Thesis, Ecole Nat. des Ponts et Chaussees.
3. Bonnet, M., 1989, “Regular Boundary Integral Equations for Three-Dimensional Finite or Infinite Bodies With or Without Curved Cracks in Elastodynamics,” Boundary Element Techniques: Applications in Engineering, C. A. Brebbia and N. Zamani, eds., Computational Mechanics Publications, Southampton, U.K, pp. 171-188.
4. Brebbia, C. A., Telles, J. C. F., and Wrobel, L. C., 1984, Boundary Element Techniques, Springer-Verlag, Berlin.
5. Bui, H. D., 1978, “Some Remarks About the Formulation of Three-Dimensional Thermoelastoplastic Problems by Integral Equations,” International Journal of Solids and Structures, Vol. 14, pp. 935-939.
6. Bui, H. D., Loret, B., and Bonnet, M., 1985, “Régularisation des Équations Intégrales de I’élastostatique et de l’élastodynamique,” Compte Rendus Acad. Sci. Paris, t. 300, Série II, no. 14, pp. 633-636.
7. Casalini, P., and Guiggiani, M., 1988, “New Developments in the Boundary Element Method for Plane and Axisymmetric Elasticity,” Advanced Boundary Element Methods, T. A. Cruse, ed., Springer-Verlag, Berlin, pp. 81-91.
8. Cruse, T. A., 1987, “Recent Advances in Boundary Element Analysis Method,” Computer Methods in Applied Mechanics and Engineering, Vol. 62, pp. 227-244.
9. Cruse, T. A., 1988, Boundary Element Analysis in Computational Fracture Mechanics, Kluwer Academic Publishers, Dordrecht.
10. Gigante, A., 1989, “Sviluppo delMetodo Degli Elementi al Contorno Tramite la Definizione di Nuove Tecniche per la Valutazione di Integrali a Valor Principale,” (in Italian), Thesis, Universitá degli Studi di Pisa, Italy.
11. Guiggiani, M., 1988, letter to the editor, International Journal for Numerical Methods in Engineering, Vol. 26, pp. 1683-1684.
12. Guiggiani, M., 1990, “The Evaluation of Cauchy Principal Value Integrals in the Boundary Element Method-A Review,” Computers and Mathematics with Applications, Special Issue on BIEM/BEM, in press.
13. Guiggiani, M., and Casalini, P., 1987, “Direct Computation of Cauchy Principal Value Integrals in Advanced Boundary Elements,” International Journal for Numerical Methods in Engineering, Vol. 24, pp. 1711-1720.
14. Hartmann, F., 1980, “Computing C-Matrix in Non-Smooth Boundary Points,” New Developments in Boundary Element Methods, C. A. Brebbia, ed., Butterworths, London, pp. 367-379.
15. Hartmann, F., 1981, “The Somigliana Identity on Piecewise Smooth Surfaces,” J. of Elasticity, Vol. 11, pp. 403-423.
16. Lachat, J. C, and Watson, J. O., 1976, “Effective Numerical Treatment of Boundary Integral Equations: A Formulation for Three-Dimensional Elasto- statics,” International Journal for Numerical Methods in Engineering, Vol. 10, pp. 991-1005.
17. Matsumoto, T., and Yuuki, R., 1988, “Accurate Boundary Element Analysis of Two-dimensional Elasto-Plastic Problems,” Boundary Element Methods in Applied Mechanics, M. Tanaka and T. A. Cruse, eds., Pergamon Press, Oxford, pp. 205-214.
18. Mikhlin, S. G., 1965, Multidimensional Singular Integrals and Integral Equations, Pergamon Press, Oxford.
19. Mukherjee, S., and Chandra, A., 1988, “A Boundary Element Formulation for Design Sensitivities in Materially Nonlinear Problems,” Boundary Element Methods in Applied Mechanics, M. Tanaka and T. A. Cruse, eds., Pergamon Press, Oxford.
20. Nishimura, N., and Kobayashi, S., 1989, “A Boundary Integral Equation Method for Consolidation Problems,” InternationalJournal of Solids and Structures, Vol. 25, pp. 1-21.
21. Okada, H., Rajiyah, H., and Atluri, S. N., 1988, “A Novel Displacement Gradient Boundary Element Method for Elastic Stress Analysis With High Accuracy,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 55, pp. 786-794.
22. Okada, H., Rajiyah, H., and Atluri, S. N., 1989, “Non-Hyper-Singular Integral-Representations for Velocity (Displacement) Gradients in Elastic/Plastic Solids (Small or Finite Deformations),” Computational Mechanics, Vol. 4, pp. 165-175.
23. Parreira, P., and Guiggiani, M., 1989, “On the Implementation of the Galerkin Approach in the Boundary Element Method,” Computers and Structures, Vol. 33, pp. 269-279.
24. Rizzo, F. J., and Shippy, D. J., 1986, “A Boundary Element Method for Axisymmetric Elastic Bodies,” Developments in Boundary Element Methods-4, P. K. Banerjee and J. O. Watson, eds., Elsevier Applied Science Publishers, Barking, Essex, England, pp. 67-90.
25. Rizzo, F. K., Shippy, D. J., and Rezayat, M., 1985, “A Boundary Integral Equation Method for Radiation and Scattering of Elastic Waves in Three Dimensions,” International Journal for Numerical Methods in Engineering, Vol. 21, pp. 115-129.
26. Sarihan, V., and Mukherjee, S., 1982, “Axisymmetric Viscoplastic Deformation by the Boundary Element Method,” International Journal of Solids and Structures, Vol. 18, pp. 1113-1128.
27. Telles, J. C. F., 1983, The Boundary Element Method Applied to Inelastic Problems, Springer-Verlag, Berlin.
28. Telles, J. C. F., and Brebbia, C. A., 1979, “On the Application of the Boundary Element Method to Plasticity,” Applied Mathematical Modelling, Vol. 3, pp. 466-470.
29. Telles, J. C. F., and Brebbia, C. A., 1981, “The Boundary Element Method in Plasticity,” Applied Mathematical Modelling, Vol. 5, pp. 275-281.
30. Theocaris, P. S., Ioakimidis, N. I., and Kazantzakis, J. G., 1980, “On the Numerical Evaluation of Two-Dimensional Principal Value Integrals,” International Journal for Numerical Methods in Engineering, Vol. 15, pp. 629-634.
31. Zhang, Ch., and Achenbach, I. D., 1989, “A New Boundary Integral Equation Formulation for Elastodynamic and Elastostatic Crack Analysis,” ASME JOURNAL OF APPLIED MECHANICS, Vol. 56, pp. 284-290.