Use of “Simple solutions” in regularizing hypersingular boundary integral equations in elastoplasticity

Journal of Applied Mechanics, Transactions ASME

Volumn 65, Issue 1, 1998, Pages 39-45

  Poon, H ^a   Mukherjee, S ^b   Ahmad, M Fouad ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003034314     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.2789043     Document Type: Article

References (29)

1. Bonnet, M., 1995, “Regularized Direct and Indirect Symmetric Variational BIE Formulations for Three-Dimensional Elasticity,” Engineering Analysis with Boundary Elements, Vol. 15, pp. 93-102.
2. Bonnet, M., and Mukherjee, S., 1996, “Implicit BEM formulations for usual and sensitivity problems in elasto-plasticity using the consistent tangent operator concept,” International Journal of Solids and Structures, Vol. 33, pp. 4461-4480.
3. Bonnet, M., Poon, H., and Mukherjee, S., 1998, “Hyper singular formulation for boundary strain evaluation in the context of a CTO-based implicit BEM scheme for small strain elasto-plasticity,” submitted for publication.
4. Cruse, T. A., and Vanburen, W„ 1971, “Three-Dimensional Elastic Stress Analysis of a Fracture Specimen with an Edge Crack,” International Journal of Fracture Mechanics, Vol. 7, pp. 1-15.
5. Cruse, T. A., and Richardson, J. D., 1996, “Non-singular Somigliana Stress Identities in Elasticity,” International Journal of Numerical Methods in Engineering, Vol. 39, pp. 3273-3304.
6. Ghosh, N., Rajiyah, H., Ghosh, S., and Mukherjee, S., 1986, “A New Boundary Element Method Formulation for Linear Elasticity,” ASME Journal of Applied Mechanics, Vol. 53, pp. 69-76.
7. Gray, L. J., Martha, L. F., and Ingraffea, A. R., 1990, “Hyper singular Integrals in Boundary Element Fracture Analysis,” International Journal of Numerical Methods in Engineering, Vol. 29, pp. 1135-1158.
8. Gray, L. J., Balakrishna, C., and Kane, J. H., 1995, “Symmetric Galerkin Fracture Analysis,” Engineering Analysis with Boundary Elements, Vol. 15, pp. 103-109.
9. Gray, L. J., and Paulino, G. H., 1997, “Symmetric Galerkin Boundary Integral Formulation for Interface and Multi-Zone Problems,” International Journal of Numerical Methods in Engineering, Vol. 40, pp. 3085-3101.
10. Gray, L. J., and Paulino, G. H., 1998, “Crack Tip Interpolation, Revisited,” SIAM Journal on Applied Mathematics, in press.
11. Guiggiani, M., Krishnasamy, K., Rudolphi, T. J., and Rizzo, F. J., 1992, “A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations,” ASME Journal of Applied Mechanics, Vol. 59, pp. 604-614.
12. Huber, O., Dallner, R., Partheymuller, P., and Kuhn, G., 1996, “Evaluation of the stress tensor in 3-D elastopiasticity by direct solving of hypersingular integrals,” International Journal of Numerical Methods in Engineering, Vol. 39, pp. 2555-2573.
13. Kleiber, M., Hien, T. D., and Postek, E., 1994, “Incremental finite-element sensitivity analysis for non-linear mechanics applications,” International Journal of Numerical Methods in Engineering, Vol. 37, pp. 3291-3308.
14. Krishnasamy, G., Schmerr, L. W., Rudolphi, T. J., and Rizzo, F. J., 1990, “Hypersingular Boundary Integral Equations: Some Applications in Acoustics and Elastic Wave Scattering,” ASME Journal of Applied Mechanics, Vol. 57, pp. 404-414.
15. Krishnasamy, G., Rizzo, F. J., and Rudolphi, T. J., 1992, “Hypersingular Boundary Integral Equations: Their Occurrence, Interpretation, Regularization and Computation,” Developments in Boundary Element Methods, Vol. 7, P. K. Banerjee and S. Kobayashi, eds., Elsevier Applied Science, London, pp. 207-252.
16. Leitao, V., Aliabadi, M. H., and Rooke, D. P., 1995, “The dual boundary element formulation for elastoplastic fracture mechanics,” International Journal of Numerical Methods in Engineering, Vol. 38, pp. 315-333.
17. Lutz, E. D., Ingraffea, A. R., and Gray, L. J., 1992, “Use of simple solutions for boundary integral methods in elasticity and fracture analysis,” International Journal of Numerical Methods in Engineering, Vol. 35, pp. 1737-1751.
18. Martin, P. A., and Rizzo, F. J., 1996, “Hyper singular Integrals: How Smooth Must the Density Be?,” International Journal of Numerical Methods in Engineering, Vol. 39, pp. 687-704.
19. Menon, G., 1996, “Hyper singular Error Estimates in Boundary Element Methods,” M.S. thesis, Cornell University, Ithaca, NY.
20. Menon, G., Paulino, H., and Mukherjee, S., 1998, “Analysis of Hypersingular Residual Error Estimates in Boundary Element Methods for Potential Problems,” Computer Methods in Applied Mechanics and Engineering, in press.
21. Paulino, G. H., 1995, “Novel Formulations of the Boundary Element Method for Fracture Mechanics and Error Estimation,” Ph.D. dissertation, Cornell University, Ithaca, NY.
22. Paulino, G. H., Gray, L. J., and Zarkian, V., 1996, “Hyper singular Residuals-A New Approach for Error Estimation in the Boundary Element Method,” International Journal of Numerical Methods in Engineering, Vol. 39, pp. 2005-2029.
23. Polch, E. Z., Cruse, T. A., and Huang, C. J., 1987, “Traction BIE solutions for flat cracks,” Computational Mechanics, Vol. 2, pp. 253-267.
24. Poon, H., 1996, “Numerical Solutions of Some Problems in Elasto-Plasticity With Finite and Boundary Element Methods,” Ph.D. Thesis, Cornell University, Ithaca, NY.
25. Poon, H., Mukherjee, S., and Bonnet, M., 1998, “Numerical implementation of a CTO-based implicit approach for the BEM solution of usual and sensitivity problems in elasto-plasticity,” Engineering Analysis With Boundary Elements, in press.
26. Simo, J. C., and Taylor, R. L., 1985, “Consistent tangent operators for rate-independent elastopiasticity,” Computer Methods in Applied Mechanics and Engineering, Vol. 48, pp. 101-118.
27. Sladek, J., and Sladek, V., 1986, “Computation of Stresses by BEM in 2-D Elasto statics,” Acta Technica CSAV, Vol. 31, pp. 523-531.
28. Tanaka, M., Sladek, V., and Sladek, J., 1994, “Regularization Techniques Applied to Boundary Element Methods,” ASME Applied Mechanics Reviews, Vol. 47, pp. 457-499.
29. Zhang, Q., Mukherjee, S., and Chandra, A., 1992, “Shape design sensitivity analysis for geometrically and materially nonlinear problems by the boundary element method,” International Journal of Solids and Structures, Vol. 29, pp. 2503-2525.