The hypersingular boundary contour method for two-dimensional linear elasticity

Acta Mechanica

Volumn 130, Issue 3-4, 1998, Pages 209-225

  Phan, A V ^a   Mukherjee, S ^b   Mayer, J R R ^a  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; CONTINUUM MECHANICS; PROBLEM SOLVING; TWO DIMENSIONAL;

HYPERSINGULAR BOUNDARY CONTOUR METHOD;

ELASTICITY;

EID: 0031619329     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01184312     Document Type: Article

References (24)

1. Bonnet, M.: Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity. Eng. Anal. Bound. Elem. 15, 93-102 (1995).
2. Cruse, T. A., Richardson, J. D.: Non-singular Somigliana stress identities in elasticity. Int. J. Num. Meth. Eng. 39, 3273-3304 (1996).
3. Gray, L. J., Martha, L. F., Ingraffea, A. R.: Hypersingular integrals in boundary element fracture analysis. Int. J. Num. Meth. Eng. 29, 1135-1158 (1990).
4. Gray, L. J., Balakrishna, C., Kane, J. H.: Symmetric Galerkin fracture analysis. Eng. Anal. Bound. Elem. 15, 103-109 (1995).
5. Gray, L. J., Paulino, G. H.: Crack tip interpolation, revisited. SIAM J. Num. Anal. 58, 428-455 (1998).
6. Gray, L. J., Paulino, G. H.: Symmetric Galerkin boundary integral formulation for interface and multy-zone problems. Int. J. Num. Meth. Eng. 40, 3085-3101 (1997).
7. 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, 604-614 (1992).
8. Krishnasamy, G., Schmerr, L. W., Rudolphi, T. J., Rizzo, F. J.: Hypersingular boundary integral equations: some applications in acoustics and elastic wave scattering. ASME J. Appl. Mech. 57, 404-414 (1990).
9. Krishnasamy, G., Rizzo, F. J., Rudolphi, T. J.: Hypersingular boundary integral equations: their occurrence, interpretation, regularization and computation. In: Developments in boundary element methods, vol. 7 (Banerjee, P. K., Kobayashi, S., eds.), pp. 207-252. London: Elsevier 1992.
10. Lutz, E. D., Ingraffea, A. R., Gray, L. J.: Use of 'simple solutions' for boundary integral methods in elasticity and fracture analysis. Int. J. Num. Meth. Eng. 35, 1737-1751 (1992).
11. Martin, P. A., Rizzo, F. J.: Hypersingular integrals: how smooth must the density be? Int. J. Num. Meth. Eng. 39, 687-704 (1996).
12. Menon, G.: Hypersingular error estimates in boundary element methods. M. S. Thesis, Cornell University, Ithaca, 1996.
13. Menon, G., Paulino, G. H., Mukherjee, S.: Analysis of hypersingular residual error estimates for potential problems in boundary element methods. Comput. Meth. Appl. Mech. Eng. (in press).
14. Mukherjee, S.: Boundary element methods in creep and fracture. New York: Elsevier 1982.
15. Mukherjee, Y. X., Mukherjee, S., Shi, X., Nagarajan, A.: The boundary contour method for three-dimensional linear elasticity with a new quadratic boundary element. Eng. Anal. Bound. Elem. 20, 35-44 (1997).
16. Nagarajan, A., Lutz, E. D., Mukherjee, S.: A novel boundary element method for linear elasticity with no numerical integration for two-dimensional and line integrals for three-dimensional probems. ASME J. Appl. Mech. 61, 264-269 (1994).
17. Nagarajan, A., Lutz, E. D., Mukherjee, S.: The boundary contour method for three-dimensional linear elasticity. ASME J. Appl. Mech. 63, 278-286 (1996).
18. Paulino, G. H.: Novel formulations of the boundary element method for fracture mechanics and error estimation. Ph. D. dissertation, Cornell University, Ithaca, 1995.
19. Paulino, G. H., Gray, L. J., Zarkian, V.: Hypersingular residuals - A new approach for error estimation in the boundary element method. Int. J. Num. Meth. Eng. 39, 2005-2029 (1996).
20. Phan, A.-V., Mukherjee, S., Mayer, J. R. R.: The boundary contour method for two-dimensional linear elasticity with quadratic boundary elements. Comput. Mech. 20, 310-319 (1997).
21. Phan, A.-V., Mukherjee, S., Mayer, J. R. R.: A boundary contour formulation for design sensitivity analysis in two-dimensional linear elasticity. Int. J. Solids Struct. 35, 1981-1999 (1998).
22. Phan, A.-V., Mukherjee, S., Mayer, J. R. R.: Stresses, stress sensitivities and shape optimization for two-dimensional linear elasticity by the boundary contour method. Int. J. Num. Meth. Eng. (in press).
23. Rizzo, F. J.: An integral equation approach to boundary value problems of classical elastostatics. Q. Appl. Math. 25, 83-95 (1967).
24. Timoshenko, S. P., Goodier, J. N.: Theory of elasticity. New York: McGraw-Hill 1970.