Wave propagation in the presence of empty cracks in an elastic medium

Computational Mechanics

Volumn 38, Issue 3, 2006, Pages 183-199

  Mendes, P A ^a   Tadeu, A ^a  

^a UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

Boundary element method; Elastic scattering; Empty cracks; Traction boundary element method; Two and a half dimensional problem; Wave propagation

Indexed keywords

BOUNDARY ELEMENT METHOD; CRACKS; ELASTIC MODULI; ELECTRIC TRACTION; GEOMETRY; SCATTERING; THREE DIMENSIONAL;

ELASTIC SCATTERING; EMPTY CRACKS; TRACTION BOUNDARY ELEMENT METHOD (TBEM); TWO-AND-A-HALF-DIMENSIONAL PROBLEM;

WAVE PROPAGATION;

EID: 33744724297     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-005-0737-7     Document Type: Article

References (46)

1. Aliabadi MH (1997) Boundary element methods formulations in fracture mechanics. Appl Mech Rev 50:93-96
2. Aliabadi MH (1997) A new generation of boundary element methods in fracture mechanics. Int J Fracture 86:91-125
3. António J, Tadeu A (2002) 3D Seismic response of a limited valley via BEM using 2.5D analytical Green's functions for an infinite free-rigid layer. J Soil Dyn Earthquake Eng 22:659-673
4. Bouchon M, Aki K (1977) Discrete wave-number representation of seismic-source wave field. Bull Seism Soc Am 67:259-277
5. Budreck DE, Achenbach JD (1988) Scattering from three-dimensional planar cracks by the boundary integral equation method. J Appl Mech 55:405-412
6. Burton AJ, Miller GF (1971) The application of the integral equation method to the numerical solution of some exterior boundary value problems. Proc R Soc London Ser A 323:201-210
7. Chien CC, Rajiyah H, Atluri SN (1990) An effective method for solving the hypersingular integral equations in 3D acoustics. J Acoustic Soc Am 88(2):918-937
8. Cruse TA (1987) Boundary Element Analysis in Computational Fracture Mechanics. Kluwer Academic Publishers
9. Cruse TA, Richardson JD (1996) Nonsingular Somigliana stress identities in elasticity. Int J Numer Meth Eng 39:3273-3304
10. Dell'erba DN, Aliabadi MH, Rooke DP (1998) Dual boundary element method for three-dimensional thermoelastic crack problems. Int J Fracture 94:89-101
11. Dominguez J, Gallego R (1992) Time domain boundary element method for dynamic stress intensity factor computations. Int J Numer Meth Eng 33:635-647
12. Dominguez J, Ariza MP, Gallego R (2000) Flux and traction boundary elements without hypersingular or strongly singular integrals. Int J Numer Meth Eng 48:111-135
13. Fedelinski P, Aliabadi MH, Rooke DP (1994) The dual boundary element method: Ĵ-integral for dynamic stress intensity factors. Int J Fracture 65(4):369-381
14. Fedelinski P, Aliabadi MH, Rooke DP (1995) A sinlge-region time domain BEM for dynamic crack problems. Int J Solids Struct 32:3555-3571
15. Fedelinski P, Aliabadi MH, Rooke DP (1996) The Laplace transform DBEM for mixed-mode dynamic crack analysis. Comp Struct 59:1021-1031
16. Fedelinski P, Aliabadi MH, Rooke DP (1996) Boundary element formulations for the dynamic analysis of cracked structures. EABE - Eng Anal Bound Elem 17:45-56
17. Guiggiani M (1998) Formulation and numerical treatment of boundary integral equations with hypersingular kernels. Singular Integrals in Boundary Element Methods, Computational Mechanics Publications, Southampton (UK) & Boston (USA)
18. Kausel E, Roesset JM (1992) Frequency domain analysis of undamped systems. J Eng Mech ASCE 118(4):721-734
19. Lutz E, Ingraffea AR, Gray LJ (1992) Use of 'simple solutions' for boundary integral methods in elasticity and fracture analysis. Int J Numer Meth Eng 35:1737-1751
20. Manolis GD, Beskos DE (1988) Boundary Element Methods in Elastodynamics. Unwin Hyman (sold to Chapman and Hall), London
21. Mi Y, Aliabadi MH (1992) Dual boundary element method for three-dimensional fracture mechanics analysis. BABE - Eng Anal Bound Elem 10:161-171
22. Pao YH, Mow CC (1973) Diffraction of Elastic Waves and Dynamic Stress Concentrations. Crane and Russak
23. Partridge PE, Brebbia CA, Wrobel LC (1992) The Dual Reciprocity Boundary Element Methods. CMP, Southampton
24. Portela A, Aliabadi MH, Rooke DP (1992) The dual boundary element method: effective implementation for crack problems. Int J Numer Meth Eng 33:1269-1287
25. Prosper D, Kausel E (2001) Wave scattering by cracks in laminated media. In: Atluri SN, Nishioka T, Kikuchi M (eds), CD: Advances in Computational Engineering and Sciences. Proceedings of the international Conference on Computational Engineering and Science ICES'01, Puerto Vallarta, Mexico, 19-25/08/2001. Tech Science Press
26. Prosper D (2001) Modeling and Detection of Delaminations in Laminated Plates. PhD Thesis, MIT, Cambridge
27. Pyl L, Clouteau D, Degrande G (2004) A weakly singular boundary integral equation inelastodynamics for heterogeneous domains mitigating ficticious eigenfrequencies. EABE - Eng Anal Bound Elem 28(12):1493-1513
28. Qian ZY, Han ZD, Ufimtsev P, Atluri SN (2004) Non-hyper-singular boundary integral equations for acoustic problems, implemented by the collocation-based boundary element method. CMES - Comput Model Eng 6(2): 133-144
29. Rudolphi TJ (1991) The use of simple solutions in the regularisation of hypersingular boundary integral equations. Math Comp Model 15:269-278
30. Sladek V, Sladek J (1984) Transient elastodynamic three-dimensional problems in cracked bodies. Appl Math Model 8:2-10
31. Sládek V, Sládek J (1987) A boundary integral equation method for dynamic crack problems. Eng Fracture Mech 27(3):269-277
32. SladekV, SladekJ,Tanaka M (1992)Numerical solution of nonsingular BIE for crack problems. In: Brebbia C A, Domínuez J, Paris F (eds) Boundary Elements XIV. vol. 2, Computational Mechanics Publications, Southampton
33. Sladek J, Sladek V (2000) Nonsingular traction BIEs for crack problems in elastodynamics. Comput Mech 25:590-599
34. Stamos AA, Beskos DE (1996) 3-D seismic response analysis of long lined tunnels in half-space. J Soil Dyn Earthquake Eng 15:111-118
35. Tadeu AJB (1992) Modelling and Seismic Imaging of Buried Structures. PhD Thesis, MIT, Cambridge
36. Tadeu A, Santos P, Kausel E (1999) Closed-form Integration of Singular Terms for Constant, Linear and Quadratic Boundary Elements - Part I: SH Wave Propagation. EABE - Eng Anal Bound Elem 23(8):671-681
37. Tadeu A, Santos P, Kausel E (1999) Closed-form Integration of Singular Terms for Constant, Linear and Quadratic Boundary Elements - Part II: SV-P Wave Propagation. EABE - Eng Anal Bound Elem 23(9):757-768
38. Tadeu A, Kausel E (2000) Green's Functions for Two-and-a-half Dimensional Elastodynamic Problems. J Eng Mech, ASCE 126(10): 1093-1097
39. Tadeu A, Godinho L, Santos P (2001) Performance of the BEM solution in 3D acoustic wave scattering. J Adv Eng Software 32:629-639
40. Tadeu A, António J, Kausel E (2002) 3D Scattering of waves by a cylindrical irregular cavity of infinite length in a homogeneous elastic medium. Comp Method Appl Mech Eng 191 (27-28): 3015-3033
41. Takakuda K (1983) Diffraction of plane harmonic waves by cracks. JSME 26(214): 487-493
42. Tanaka M, Sladek V, Sladek J (1994) Regularization techniques applied to boundary element methods. Appl Mech Rev 47:457-499
43. Watson JO (1995) Singular boundary elements for the analysis of cracks in plane strain. Int J Numer Meth Eng 38:2389-2411
44. Wu TW, Seybert AF, Wan GC (1991) On the numerical implementation of a Cauchy principal value integral to insure a unique solution for acoustic radiation and scattering. J Acoust Soc Am 90:554-560
45. Yan ZY, Hung KC, Zheng H (2003) Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship. J Acoust Soc Am 113(5):2674-2683
46. Young A (1992) A single-domain boundary element method for 3-D elastostatic crack analysis using continuous elements. Int J Numer Meth Eng 39:1265-1293