Analytic stress intensity factors for finite elastic disk using symplectic expansion

Engineering Fracture Mechanics

Volumn 76, Issue 12, 2009, Pages 1866-1882

  Leung, A Y T ^a   Xu, Xinsheng ^b   Zhou, Zhenhuan ^b   Wu, Y F ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Analytic stress intensity factors; Hamiltonian formulation; Mixed boundary conditions; Symplectic expansion

Indexed keywords

ANALYTIC METHOD; ANALYTIC STRESS INTENSITY FACTORS; DISCONTINUOUS BOUNDARY CONDITIONS; DISPLACEMENTS AND STRESS; EIGEN FUNCTION; ELASTIC DISK; EQUILIBRIUM EQUATION; HAMILTONIAN FORMULATION; LEAST SQUARE METHODS; MIXED BOUNDARY CONDITIONS; NEW RESULTS; POLAR COORDINATE; POST PROCESSING; SYMPLECTIC; SYMPLECTIC EXPANSION; T STRESS; VARIABLE SEPARATION;

BOUNDARY CONDITIONS; DISKS (STRUCTURAL COMPONENTS); HAMILTONIANS; MEATS; NONLINEAR CONTROL SYSTEMS; STRESS INTENSITY FACTORS;

ASPHALT PAVEMENTS;

EID: 67649213544     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2009.04.004     Document Type: Article

References (37)

1. Noda N.A., and Xu C.H. Controlling parameter of the SIFs for a planar interfacial crack in three-dimensional bimaterials. Int J Solids Struct 45 (2008) 1017-1031
2. Tweed J., and Rooke D.P. The SIFs of a radial crack in a finite elastic disc. Int J Engng Sci 10 (1972) 323-335
3. Tweed J., and Rooke D.P. The SIF of an edge crack in a finite elastic disc. Int J Engng Sci 11 (1973) 65-73
4. Tweed J., and Rooke D.P. The SIFs of a radial crack in a point loaded disc. Int J Engng Sci 11 (1973) 285-290
5. Gregory R.D. Circular disk containing a radial edge crack opened by a constant internal-pressure. Math Proc Cambridge Phil Soc 81 (1977) 497-521
6. Xu Y.L., and Delale F. SIFs for an internal or edge crack in a circular elastic disk subjected to concentrated or distributed loads. Engng Fract Mech 42 (1992) 757-787
7. Wu X.R., and Carlsson A.J. Weight functions and SIF solutions (1991), Pergamon Press, Oxford
8. Gregory R.D. Edge-cracked circular disk under symmetric pin-loading. Math Proc Cambridge Phil Soc 85 (1979) 523-538
9. Schneider G.A., and Danzer R. Calculation of the SIF of an edge crack in a finite elastic disc using the weight function method. Engng Fract Mech 34 (1989) 547-552
10. Wu X.R. The arbitrarily loaded single-edge cracked circular disk - accurate weight function solutions. Int J Fract 49 (1991) 239-256
11. Li J., Wang X., and Tan C.L. Weight functions for the determination of SIF and T-stress for edge-cracked plates with built-in ends. Int J Pres Ves Pip 81 (2004) 285-296
12. Wang Y.H., Tham L.G., Lee P.K.K., and Tsui Y. A boundary collocation method for cracked plates. Compos Struct 81 (2003) 2630-2632
13. Fett T. SIFs and T-stress for single and double-edge-cracked circular disks under mixed boundary conditions. Engng Fract Mech 69 (2002) 69-83
14. Morais A.B. Calculation of SIFs by the force method. Engng Fract Mech 74 (2007) 739-750
15. Tsang D.K.L., Oyadiji S.O., and Leung A.Y.T. Two-dimensional fractal-like finite element method for thermoelastic crack analysis. Int J Solids Struct 44 (2007) 7862-7876
16. Chang J., and Xu J.Q. The singular stress field and SIFs of a crack terminating at a bimaterial interface. Int J Mech Sci 49 (2007) 888-897
17. Mavrothanasis F.I., and Pavlou D.G. Mode-I SIF derivation by a suitable green's function. Engng Anal Bound Elem 31 (2007) 184-190
18. Song CM, Vrcelj Z. Evaluation of dynamic stress intensity factors and T-stress using the scaled boundary finite-element method. Enging Fract Mech 2008;75(8):1960-80.
19. Vigdergauz S. An effective method for computing the elastic field in a finite cracked disk. Engng Fract Mech 53 (1996) 545-556
20. Freese C.E., and Baratta F.I. Single edge-crack SIF solutions. Engng Fract Mech 73 (2006) 616-625
21. Fett T., and Bahr H.A. Mode I SIFs and weight functions for short plates under different boundary conditions. Engng Fract Mech 62 (1999) 593-606
22. Fett T. SIFs for edge-cracked plates under arbitrary loading. Fat Fract Engng Mater Struct 20 (1999) 301-305
23. Gross B, Sarwley JE, Brown WF. SIFs for single edge notch tension specimen by boundary collocation of a stress function, NASA Tech Note D-2395; 1964.
24. Belytschko T., and Black T. Elastic crack growth in finite elements with minimal meshing. Int J Numer Met Engng 46 (1999) 601-620
25. Zhong W.X. Plane elasticity in sectorial domain and the Hamiltonian system. Appl Math Mech 15 (1994) 1057-1066 [English Edition]
26. Zhong W.X., and Zhang H.W. Analytical formulas on plane crack element. J Mech Strength 17 (1995) 1-6 [in Chinese]
27. Zhang H.W., and Zhong W.X. Hamiltonian principle based stress singularity analysis near crack corners of multi-material junctions. Int J Solids Struct 40 (2003) 493-510
28. Xu X.S., Zheng X.G., Zhang H.W., and Zhong W.X. Hamiltonian Structure and wedge body in elasticity. Chin J Appl Mech 16 (1999) 140-145 [in Chinese]
29. Leung A.Y.T., Xu X.S., Gu Q., Leung C.T.O., and Zheng J.J. The boundary layer phenomena in 2D transversely isotropic piezoelectric media by exact symplectic expansion. Int J Numer Met Engng 69 (2007) 2381-2408
30. Xu XS, Leung AYT, Gu Q, Yang H, Zheng JJ. 3D symplectic expansion for piezoelectric media. Int J Numer Met Engng. 2008;74(12):1848-71.
31. Leung A.Y.T. Perturbed general eigensolutions. Commun Appl Numer Met 6 (1990) 401-409
32. Zhao L., and Chen W.-Q. On numerical calculation in symplectic approach, for elasticity problems. J Zhejiang Univ Sci A 9 5 (2008) 583-588
33. Leung A.Y.T., and Su R.K.L. Mode-I crack problems by fractal 2-level finite-element methods. Engng Fract Mech 48 6 (1994) 847-856
34. Leung A.Y.T., and Su R.K.L. Mixed-mode 2-dimensional crack problem by fractal 2-level finite-element method. Engng Fract Mech 51 6 (1995) 889-895
35. Leung A.Y.T., and Su R.K.L. Body-force linear elastic stress intensity factor calculation using fractal 2-level finite-element method. Engng Fract Mech 51 6 (1995) 879-888
36. Leung A.Y.T., and Su R.K.L. Two-level finite element study of axisymmetric cracks. Int J Fract 89 2 (1998) 193-203
37. Treifi M., Oyadiji S.O., and Tsang D.K.L. Computation of the stress intensity factors of sharp notched plates by the fractal-like finite element method. Int J Numer Meth Engng 77 4 (2009) 558-580