Stochastic meshless analysis of elastic-plastic cracked structures

Computational Mechanics

Volumn 32, Issue 3, 2003, Pages 199-213

  Rao, B N ^a   Rahman, S ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Element free galerkin method; J integral; Mesh free method; Probabilistic fracture mechanics; Probability of failure; Sensitivity of J integral

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; CRACKS; ELASTOPLASTICITY; FINITE DIFFERENCE METHOD; FRACTURE MECHANICS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MONTE CARLO METHODS; RANDOM PROCESSES; RELIABILITY; SENSITIVITY ANALYSIS;

ELEMENT FREE GALERKIN METHOD; FIRST ORDER RELIABILITY METHOD; J-INTEGRAL; MESH FREE METHOD; PROBABILISTIC FRACTION MECHANICS; PROBABILITY OF FAILURE; STOCHASTIC MESHLESS ANALYSIS;

GALERKIN METHODS;

EID: 1242343849     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-003-0475-7     Document Type: Article

References (39)

1. Provan JW (1987) Probabilistic Fracture Mechanics and Reliability. Martinus Nijhoff Publishers, Dordrecht, The Netherlands
2. Grigoriu M, Saif MTA, El-Borgi S, Ingraffea A (1990) Mixed-mode fracture initiation and trajectory prediction under random stresses. Int. J. Fracture 45: 19-34
3. Besterfield GH, Liu WK, Lawrence MA, Belytschko T (1991) Fatigue crack growth reliability by probabilistic finite elements. Comput. Meth. Appl. Mech. Eng. 86: 297-320
4. Besterfield GH, Lawrence MA, Belytschko T (1990) Brittle fracture reliability by probabilistic finite elements. ASCE J. Eng. Mech. 116(3): 642-659
5. Rahman S (2001) Probabilistic fracture mechanics: J-estimation and finite element methods. Eng. Fracture Mech. 68: 107-125
6. Rahman S, Kim J-S (2001) Probabilistic fracture mechanics for nonlinear structures. Int. J. Pressure Vessels and Piping 78(4): 261-269
7. Rahman S (1995) A stochastic model for elastic-plastic fracture analysis of circumferential through-wall-cracked pipes subject to bending. Eng. Fracture Mech. 52(2): 265-288
8. Dillstrom P (2000) ProSINTAP - A probabilistic program implementing the SINTAP assessment procedure. Eng. Fracture Mech. 67: 647-668
9. Rahman S, Chen G, Firmature R (2000) Probabilistic analysis of off-center cracks in cylindrical structures. Int. J. Pressure Vessels and Piping 77(1): 3-16
10. Belytschko T, Lu YY, Gu L (1995) Crack propagation by element-free Galerkin methods. Eng. Fracture Mech. 51(2): 295-315
11. Belytschko T, Tabbara M (1996) Dynamic fracture using element-free Galerkin methods. Int. J. Numer. Meth. Eng. 39: 923-938
12. Fleming M, Chu YA, Moran B, Belytschko T, Lu YY, Gu L (1997) Enriched element-free Galerkin methods for crack-tip fields. Int. J. Numer. Meth. Eng. 40: 1483-1504
13. Sukumar N, Moran B, Belytschko T (1998) The natural element method in solid mechanics. Int. J. Numer. Meth. Eng. 43: 839-887
14. Kaljevic I, Saigal S (1997) An improved element free Galerkin formulation. Int. J. Numer. Meth. Eng. 40: 2953-2974
15. Rao BN, Rahman S (2000) An efficient meshless method for fracture analysis of cracks. Comput. Mech. 26: 398-408
16. Rao BN, Rahman S (2001) A coupled meshless-finite element method for fracture analysis of cracks. Int. J. Pressure Vessels and Piping 78(9): 647-657
17. Rao BN, Rahman S (2002) Probabilistic fracture mechanics by Galerkin meshless methods - Part I: rates of stress-intensity factors. Comput. Mech. 28(5): 351-364
18. Rahman S, Rao BN (2002) Probabilistic fracture mechanics by Galerkin meshless methods - Part II: reliability analysis. Comput. Mech. 28(5): 365-374
19. Rao BN, Rahman S (2003) Meshfree analysis of cracks in isotropic functionally graded materials. Eng. Fracture Mech. 70(1): 1-27
20. Rao BN, Rahman S (2002) An enriched meshless method for nonlinear fracture mechanics. Proceedings of 2002 ASME Pressure Vessels and Piping Conference, Vancouver, BC, Canada, (also submitted to International Journal of Numerical Methods in Engineering)
21. Hutchinson JW (1968) Singular behavior at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids 16: 13-31
22. Rice JR, Rosengren GF (1968) Plane strain deformation near a crack tip in a power hardening material. J. Mech. Phys. Solids 16: 1-13
23. Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Mathematics of Computation 37: 141-158
24. Chen JS, Wang HP (2000) New boundary condition treatments in meshfree computation of contact problems. Computer Meth. Appl. Mech. Eng. 187(3-4): 441-468
25. Anderson TL (1995) Fracture mechanics: fundamentals and applications. 2nd Edition, CRC Press
26. Hutchinson JW (1968) Singular behavior at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids 16: 13-31
27. Rice JR, Rosengren GF (1968) Plane strain deformation near a crack tip in a power hardening material. J. Mech. Phys. Solids 16: 1-13
28. Pan J, Shih CF (1992) Elastic-plastic analysis of combined mode I, II and III crack-tip fields under small-scale yielding conditions. Int. J. Solids and Struct. 29: 2795-2814
29. Betegon C, Hancock JW (1991) Two-parameter characterization of elastic-plastic crack fields. J. Appl. Mech. 58: 104-113
30. Parks DM (1992) Advances in characterization of elastic-plastic crack-tip fields. Topics in Fracture and Fatigue, Springer-Verlag, New York
31. O'Dowd NP, Shih CF (1991) Family of crack-tip fields characterized by a triaxiality parameter: Part I - structure of fields. J. Mech. Phys. Solids 39(8): 989-1015
32. O'Dowd NP, Shih CF (1992) Family of crack-tip fields characterized by a triaxiality parameter: Part I - fracture applications. J. Mech. Phys. Solids 40(8): 939-963
33. Shih CF (1983) Tables of Hutchinson-Rice-Rosengren singular field quantities. MRL E-147, Materials Research Laboratory, Brown University
34. Rahman S, Ghadiali N, Paul D, Wilkowski G (1995) Probabilistic pipe fracture evaluations for leak-rate-detection applications. NUREG/CR-6004, US Nuclear Regulatory Commission, Washington, DC
35. Madsen HO, Krenk S, Lind NC (1986) Methods of structural safety. Prentice-Hall, Inc., Englewood Cliffs, New Jersey
36. Lim OK, Arora JS (1986) An active set RQP algorithm for optimum design. Comput. Meth. Appl. Mech. Eng. 57: 51-65
37. Arora JS (1989) Introduction to optimum design. McGraw-Hill, New York
38. ABAQUS (2002) User's guide and theoretical manual, Version 6.1, Hibbitt, Karlsson, and Sorenson, Inc., Pawtucket, Rhode Island
39. Chen G, Rahman S (2001) Shape sensitivity and reliability analyses in nonlinear fracture mechanics. Proceedings of 10th International Congress on Fracture, Honolulu, Hawaii