A quasi-dual function method for extracting edge stress intensity functions

SIAM Journal on Mathematical Analysis

Volumn 35, Issue 5, 2004, Pages 1177-1202

  Costabel, Martin ^a   Dauge, Monique ^a   Yosibash, Zohar ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Dual singularities; Edge singularities; Stress intensity factors

Indexed keywords

EID: 4644275727     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141002404863     Document Type: Article

References (36)

1. B. ANDERSSON, U. FALK, AND I. BABUŠKA, Reliable determination of edge and vertex stress intensity factors in three-dimensional elastomechanics, in Proceedings of the 17th Congress of the International Council of the Aeronautical Sciences, Stockholm, 1990, ICAS-90-4.9.2, AIAA, Washington, D.C., 1990, pp. 1730-1746.
2. I. BABUŠKA AND A. MILLER, The post-processing approach in the finite element method. Part II: The calculation of the stress intensity factors, Internat. J. Numer. Methods Engrg., 20 (1984), pp. 1111-1129.
3. A. BEAGLES AND A.-M. SÄNDIG, Singularities of rotationally symmetric solutions of boundary value problems for the Lamé equations, ZAMM Z. Angew. Math. Mech., 71 (1991), pp. 423-431.
4. H. BLUM, On the approximation of linear elliptic systems on polygonal domains, in Singularities and Constructive Methods for Their Treatment (Oberwolfach, 1983), Lecture Notes in Math. 1121, Springer-Verlag, Berlin, pp. 28-37.
5. H. BLUM, Numerical treatment of corner and crack singularities, in Finite Element and Boundary Element Techniques from Mathematical and Engineering Point of View, CISM Courses and Lectures 301, Springer-Verlag, Vienna, 1988, pp. 171-212.
6. H. BLUM AND M. DOBROWOLSKI, On finite element methods for elliptic equations on domains with corners, Computing, 28 (1982), pp. 53-63.
7. M. BOURLARD, M. DAUGE, M.-S. LUBUMA, AND S. NICAISE, Coefficients of the singularities for elliptic boundary value problems on domains with conical points. III. Finite element methods on polygonal domains, SIAM J. Numer. Anal., 29 (1992), pp. 136-155.
8. M. BOURLARD, M. DAUGE, AND S. NICAISE, Error estimates on the coefficients obtained by the singular function method, Numer. Funct. Anal. Optim., 10 (1989), pp. 1077-1113.
9. M. COSTABEL AND M. DAUGE, General edge asymptotics of solutions of second order elliptic boundary value problems. I and II, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), pp. 109-184.
10. M. COSTABEL AND M. DAUGE, Crack singularities for general elliptic systems, Math. Nachr., 235 (2002), pp. 29-49.
11. M. COSTABEL, M. DAUGE, AND R. DUDUCHAVA, Asymptotics without logarithmic terms for crack problems, Comm. Partial Differential Equations, 28 (2003), pp. 869-926.
12. M. COSTABEL, M. DAUGE, AND Y. LAFRANCHE, Fast semi-analytic computation of elastic edge singularities, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 2111-2134.
13. M. COSTABEL AND E. P. STEPHAN, An improved boundary element Galerkin method for three-dimensional crack problems, Integral Equations Operator Theory, 10 (1987), pp. 467-504.
14. M. DAUGE, Elliptic Boundary Value Problems in Corner Domains. Smoothness and Asymptotics of Solutions, Lecture Notes in Math. 1341, Springer-Verlag, Berlin, 1988.
15. M. DAUGE, S. NICAISE, M. BOURLARD, AND J. M.-S. LUBUMA, Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. 1. Résultats généraux pour le problème de Dirichlet, RAIRO Model. Math. Anal. Numér., 24 (1990), pp. 27-52.
16. M. DAUGE, S. NICAISE, M. BOURLARD, AND J. M.-S. LUBUMA, Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. II. Quelques opérateurs particuliers, RAIRO Modél. Math. Anal. Numér., 24 (1990), pp. 343-367.
17. P. DESTUYNDER AND M. DJAOUA, Estimation de l'erreur sur le coefficient de la singularité de la solution d'un problème elliptique sur un ouvert avec coin, RAIRO Anal. Numér., 14 (1980), pp. 239-248.
18. P. GRISVARD, Singularités en élasticité, Arch. Ration. Mech. Anal., 107 (2) (1989), pp. 157-180.
19. B. HEINRICH, S. NICAISE, AND B. WEBER, Elliptic interface problems in axisymmetric domains. II. The Fourier-finite-element approximation of non-tensorial singularities, Adv. Math. Sci. Appl., 10 (2000), pp. 571-600.
20. M. LENCZNER, Méthode de calcul du coefficient de singularité pour la solution du problème de Laplace dans un domaine diédral, RAIRO Modél. Math. Anal. Numér., 27 (1993), pp. 395-420.
21. V. MAZ'YA AND B. PLAMENEVSKII, On the coefficients in the asymptotics of solutions of elliptic boundary-value problems near conical points, Soviet Math. Dokl., 15 (1974), pp. 1570-1575.
22. V. MAZ'YA AND B. PLAMENEVSKII, On the coefficients in the asymptotics of solutions of elliptic boundary value problems near the edge, Soviet Math. Dokl., 17 (1976), pp. 970-974.
23. V. G. MAZ'YA AND B. A. PLAMENEVSKII, Coefficients in the asymptotics of the solutions of an elliptic boundary value problem in a cone, J. Soviet Math., 9 (1978), pp. 750-764.
24. p estimates of solutions of elliptic boundary value problems in a domain with edges, Trans. Moscow Math. Soc., 1 (1980), pp. 49-97.
25. V. G. MAZ'YA AND B. A. PLAMENEVSKII, On the coefficients in the asymptotic of solutions of the elliptic boundary problem in domains with conical points, Amer. Math. Soc. Transl. (2), 123 (1984), pp. 57-88.
26. V. G. MAZ'YA AND J. ROSSMANN, Über die Lösbarkeit und die Asymptotik der Lösungen elliptischer Randwertaufgaben in Gebieten mit Kanten. III, preprint P-MATH-31/84, Akad. Wiss. DDR, Inst. Math., Berlin, 1984.
27. V. G. MAZ'YA AND J. ROSSMANN, Über die Asymptotik der Lösungen elliptischer Randwertaufgaben in der Umgebung von Kanten, Math. Nachr., 138 (1988), pp. 27-53.
28. M.-A. MOUSSAOUI, Sur l'approximation des solutions du problème de Dirichlet dans un ouvert avec coins, in Singularities and Constructive Methods for Their Treatment (Oberwolfach, 1983), Springer-Verlag, Berlin, pp. 199-206.
29. A. RöSSLE, Corner singularities and regularity of weak solutions for the two-dimensional Lamé equations on domains with angular corners, J. Elasticity, 60 (2000), pp. 57-75.
30. J. ROSSMANN AND A.-M. SÄNDIG, Formulas for the coefficients in the asymptotics of solutions of boundary value problems for second order systems near edges, ZAMM Z. Angew. Math. Mech., 76 (1996), pp. 181-184.
31. E. P. STEPHAN AND M. COSTABEL, A boundary element method for three-dimensional crack problems, in Innovative Numerical Methods in Engineering (Atlanta, GA, 1986), Computational Mechanics, Southampton, 1986, pp. 351-360.
32. G. STRANG AND G. J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffe, NJ, 1973.
33. B. A. SZABÓ AND Z. YOSIBASH, Numerical analysis of singularities in two dimensions. I. Computation of eigenpairs, Internat. J. Numer. Methods Engrg., 38 (1995), pp. 2055-2082.
34. B. A. SZABÓ AND Z. YOSIBASH, Numerical analysis of singularities in two dimensions. II. Computation of generalized flux/stress intensity factors, Internat. J. Numer. Methods Engrg., 39 (1996), pp. 409-434.
35. Z. YOSIBASH, Computing singular solutions of elliptic boundary value problems in polyhedral domains using the p-FEM, Appl. Numer. Math. 33 (2000), pp. 71-93.
36. Z. YOSIBASH, R. ACTIS, AND B. SZABÓ, Extracting edge flux intensity functions for the Lapla-cian, Internat. J. Numer. Methods Engrg., 53 (2002), pp. 225-242.