Computation of generalized stress intensity factors for bonded elastic structures

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1. [1] I. Babu¡ka and A. Miller, The post-processing approach in the finite element method, Part 2: The calculation of stress intensity factors. Internat. J. Numer. Methods Engrg. 20 (1984) 1111-1129. Zbl0535.73053
2. [2] I. Babu¡ka, T. von Petersdorff and B. Andersson, Numerical treatment of vertex singularities and intensity factors for mixed boundary value problems for the Laplace equation in R3. SIAM J. Numer. Anal. 31 (1994) 1265-1288. Zbl0806.65107MR1293515
3. [3] 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) 136-155. Zbl0794.35015MR1149089
4. [4] H.F. Bueckner, A novel principle for the computation of stress intensity factors. ZAMM 50 (1970) 529-546. Zbl0213.26603MR272239
5. [5] H.F. Bueckner, Weight functions and fundamental fields for the penny-shaped and the half-plane crack in three-space. Internat. J. Solids and Structures 23 (1987) 57-93. Zbl0601.73102
6. [6] M. Costabel and M. Dauge, General edge asymptotics of solutions of second-order elliptic boundary value problems I, II. Proc. Roy. Soc. Edinburgh A 123 (1993) 109-155, 157-184. Zbl0791.35033MR1204855
7. [7] M. Costabel and M. Dauge, Computation of corner singularities in linear elasticity, in Boundary Value Problems and Integral Equations in Nonsmooth Domains, M. Costabel, M. Dauge, S. Nicaise Eds., Marcel Dekker Inc. (1995). Zbl0822.35040MR1301341
8. [8] M. Dobrowolski, Numerical Approximation of Elliptic Interface and Corner Problems. Habilitationsschrift, University of Bonn (1981). 
9. [9] G.C. Hsiao, B.N. Khoromskij and W.L. Wendland, Boundary integral operators and domain decomposition. Preprint 94-11, Mathematisches Institut A, Universität Stuttgart (1994). 
10. [10] G.C. Hsiao and W.L. Wendland, The Aubin-Nitsche Lemma for integral equations. J. Integral Equations 3 (1981) 299-315. Zbl0478.45004MR634453
11. [11] G.C. Hsiao and W.L. Wendland, Domain decomposition in boundary element methods, in Domain Decomposition Methods for Partial Differential Equations, R. Glowinski et al. Eds., SIAM (1991) 41-49. Zbl0766.65094MR1106449
12. [12] C. Hwu, C.J. Kao and L.E. Chang, Delamination fracture criteria for composite laminates. J. Composite Mat. 29 (1995) 1962-1987. 
13. [13] M.F. Kanninen and C.H. Popelar, Advanced Fracture Mechanics. Oxford University Press, New York (1985). Zbl0587.73140
14. [14] S.N. Karp and F.C. Karal, The elastic-field behaviour in the neighbourhood of a crack of arbitrary angle. Comm. Pure Appl. Math. 15 (1962) 413-421. Zbl0166.20705MR167026
15. [15] V.A. Kondrat'ev, Boundary problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc. 16 (1967) 209-292. Zbl0194.13405MR226187
16. [16] A. Kufner and A.-M. Sändig, Some Applications of Weighted Sobolev Spaces. Teubner, Leipzig (1987). Zbl0662.46034MR926688
17. [17] M. Lenczner, Méthode de calcul du coefficient de singularité pour la solution du problème de Laplace dans un domaine diédral. Math. Modell Numer. Anal. 27 (1993) 395-420. Zbl0784.65079MR1230828
18. [18] K.M. Liu, K.M. Lee and C.K. Pan, Numerical techniques for determining stress intensity and higher order factors using the finite difference methods, in Computational Mechanics '95 Vol. 2, S.N. Atluri et al. Eds., Springer Verlag, Berlin (1995). 
19. [19] V.G. Maz'ya and B.A. Plamenevsky, On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points. Math. Nachr. 76 (1977) 29-60. Zbl0359.35024MR601608
20. [20] V.G. Maz'ya and J. Rossmann, Über die Asymptotik der Lösungen elliptischer Randwertaufgaben in der Umgebung von Kanten. Math. Nachr. 138 (1988) 27-53. Zbl0672.35020MR975198
21. [21] S.A. Nazarov, Derivation of the variational inequality for small increase of mode-one crack. Mech. Solids 24 (1989) 145-152. 
22. [22] S.A. Nazarov and B.A. Plamenevsky, The Neumann problem for selfadjoint elliptic systems in a domain with piecewise-smooth boundary. Amer. Math. Soc. Transl. (2) 155 (1993) 169-206. Zbl0778.35033
23. [23] S.A. Nazarov and B.A. Plamenevsky, Elliptic Problems in Domains with Piecewise Smooth Boundaries. Walter de Gruyter, Berlin (1994). Zbl0806.35001MR1283387
24. [24] S. Nicaise and A.-M. Sändig, General interface problems I, II. Math. Methods Appl. Sci. 17 (1994) 395-429, 431-450. Zbl0824.35015MR1274152
25. [25] S. Nicaise and A.-M. Sändig, Transmission problems for the Laplace and elasticity operators: Regularity and boundary integral formulation. Math. Models Methods Appl. Sci. (to appear). Zbl0958.35023MR1702865
26. [26] J.R. Rice, Some remarks on elastic crack-tip stress fields. Internat. J. Solids and Structures 8 (1972) 751-758. Zbl0245.73083
27. [27] J.B. Rosser and N. Papamichael, A power series solution of a harmonic mixed boundary value problem. MRC Technical Summary Report number 1405 (1975). 
28. [28] 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 76 Suppl. 4 (1996) 181-184. Zbl0925.65117
29. [29] H. Schmitz, K. Volk and W. Wendland, Three-dimensional singularities of elastic fields near vertices. Numer. Methods Partial Differential Equations 9 (1993) 23-337. Zbl0771.73014MR1216118
30. [30] T.L. Shan and H.F. Bückner, The weight function theory for piecewise homogeneous isotropic notches in antiplane strain. J. Appl. Mech. 55 (1988) 596-603. Zbl0707.73055
31. [31] O. Steinbach, Gebietszerlegungsmethoden mit Randintegralgleichungen und effiziente numerische Lösungsverfahren für gemischte Randwertprobleme. Dissertation, Universität Stuttgart (1996). Zbl0863.65079MR1466967
32. [32] O. Steinbach, On the realization of boundary element methods for mixed boundary value problems. Preprint 98/07, SFB 404, Universität Stuttgart (1998). Zbl0968.65099MR1634286
33. [33] O. Steinbach and W.L. Wendland, Domain decomposition and preconditioning techniques in boundary element methods, in Boundary Element Topics, W.L. Wendland Ed., Springer Verlag, Berlin (1997) 473-492. Zbl0884.65113MR1655254
34. [34] B.A. Szabo and Z. Yosibash, Numerical analysis of singularities in two dimensions, Part 2: Computation of generalized flux/stress intensity factors. Internat. J. Numer. Methods Engrg. 39 (1996) 409-434. Zbl0855.73076MR1369913
35. [35] M.L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19 (1952) 526-528. 
36. [36] M.L. Williams, The stresses around a fault or crack in dissimilar media. Bull. Seismol. Soc. Amer. 49 (1959) 199-204. MR102211
37. [37] L.S. Xanthis, M.J.M. Bernal and C. Atkinson, The treatment of singularities in the calculation of stress intensity factors using the boundary integral equation method. Comput. Methods Appl. Mech. Engrg. 26 (1981) 285-304. Zbl0461.73066MR624326