A BEM formulation for anisotropic half-plane problems

Engineering Analysis with Boundary Elements

Volumn 20, Issue 3, 1997, Pages 185-195

  Pan, Ernian ^a   Chen, Chao Shi ^a   Amadei, Bernard ^a  

^a UCB 450   (United States)

Author keywords

Anisotropic elasticity; Body force of gravity; Boundary element method; Dual BEM; Fracture mechanics; Half plane Green's functions

Indexed keywords

ANISOTROPY; ELASTICITY; FRACTURE MECHANICS; GRAVITATION; GREEN'S FUNCTION; INTEGRAL EQUATIONS; STRESS INTENSITY FACTORS;

ANISOTROPIC HALF PLANE PROBLEMS;

BOUNDARY ELEMENT METHOD;

EID: 0031248838     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0955-7997(97)00081-7     Document Type: Article

References (47)

1. Mindlin, R.D. Stress distribution around a tunnel. Transactions of the American Society of Civil Engineers, 1940, 105, 1117-1153.
2. Mindlin, R. D. Stress distribution around a hole near the edge of a plate under tension. In Proc. of The Society for Experimental Stress Analysis. 1948, Vol. 5, 56-68.
3. Ling, C.B. On the stresses in a notched plate under tension. J. Math. Phys., 1947, 26, 284-289.
4. Srolovitz, D.J. On the stability of surfaces of stressed solids. Acta Metal., 1989, 37, 621-625.
5. Liao, J.J., Savage, W.Z. and Amadei, B. Gravitational stresses in anisotropic ridges and valleys with small slopes. J. Geophys. Res., 1992, 97, 3325-3336.
6. Gao, H. Stress concentration at slightly undulating surfaces. J. Mech. Phys. Solids, 1991, 39, 443-458.
7. Gao, H. Morphological instabilities along surfaces of anisotropic solids. In Modern Theory of Anisotropic Elasticity and Applications, ed. J. J. Wu, T. C. T. Ting & D. M. Barnett, SIAM, Philadelphia, 1991, pp. 139-150.
8. Savage, W.Z. and Swolfs, H.S. Tectonic and gravitational stress in long symmetric ridges and valleys. J. Geophys. Res., 1986, 91, 3677-3685.
9. Chiu, C. and Gao, H. Stress singularities along a cycloid rough surface. Int. J. Solids Structures, 1993, 30, 2983-3012.
10. Pan, E. and Amadei, B. Stress concentration at irregular surfaces of anisotropic half-spaces. Acta Mech., 1995, 113, 119-135.
11. Pan, E., Amadei, B. and Savage, W.Z. Gravitational and tectonic stresses in anisotropic rock with irregular topography. Int. J. Rock. Mech. Min. Sci. and Geomech. Abstr., 1995, 32, 201-214.
12. Zienkiewicz, O.C., Cheung, Y.K. and Stagg, K.G. Stresses in anisotropic media with particular reference to problems of rock mechanics. J. Strain Analysis, 1966, 1, 172-182.
13. Barla, G. Stresses around a single underground opening near a tension-free surface. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr., 1972, 9, 103-126.
14. Soliman, E., Duddeck, H. and Ahrens, H. Two- and three-dimensional analysis of closely spaced double-tube tunnels. Tunelling and Undergound Space Technology, 1993, 8, 13-18.
15. Eissa, E. A. Stress analysis of underground excavations in isotropic and stratified rock using the boundary element method. PhD thesis, Imperial College of Science and Technology, London, 1980.
16. Fainstein, G., Sidi, A., Israeli, M. & Tsur-Lavie, Y. Application of boundary integral equations to the solution of stresses around a shallow circular hole. In 28th US Symposium, on Rock Mechanics. 1987, pp. 745-754.
17. Carter, J.P. and Alehossein. H. Analysis of tunnel distortion due to an open excavation in jointed rock. Comp. Geotech., 1990, 9, 209-231.
18. Xiao, B. and Carter, J.P. Boundary element analysis of anisotropic rock masses. Eng. Analy. Boundary Elements, 1993, 11, 293-303.
19. Beer, G. and Poulsen, B.A. Analysis of infinitely long excavations using finite and boundary elements. Int. J. Numer. Anal. Meth. Geomech., 1994, 18, 417-426.
20. Telles, J.C.F. and Brebbia, C.A. Boundary element solution for half-plane problems. Int. J. Solids Structures, 1981, 17, 1149-1158.
21. Meek, J.L. and Dai, C. Boundary element modeling: Near surface excavations. Computer Meth. Appl. Mech. Eng., 1993, 102, 15-27.
22. Dumir, P.C. and Mehta, A.K. Boundary element solution for elastic orthotropic half-plane problems. Computers and structures, 1987, 26, 431-438.
23. Pan, E. and Amadei, B. Fracture mechanics analysis of cracked 2-D anisotropic media with a new formulation of the boundary element method. Int. J. Fracture, 1996, 77, 161-174.
24. Pan, E. and Amadei, B. A 3-D boundary element formulation of anisotropic elasticity with gravity. Appl. Math. Modelling, 1996, 20, 114-120.
25. Aliabadi, M. H. and Rooke, D. P. Numerical Fracture Mechanics. Computational Mechanics Publications. 1991.
26. Hong, H.K. and Chen, J.T. Derivations of integral equations of elasticity. J. Eng. Mech., 1988, 114, 1028-1044.
27. Portela, A., Aliabadi, M.H. and Rooke, D.P. The dual boundary element method: Effective implementation for crack problems. Int. J. Numer. Meth. Eng., 1992, 33, 1269-1287.
28. Guimaraes, S. and Telles, J.C.F. On the hyper-singular boundary-element formulation for fracture-mechanics applications. Eng. Analy. Boundary elements, 1994, 13, 353-363.
29. Sollero, P. and Aliabadi, M.H. Anisotropic analysis of cracks in composite laminates using the dual boundary element method. Computers and Structures, 1995, 31, 229-234.
30. Aliabadi, M.H. Boundary element formulations in fracture mechanics. Appl. Mech. Rev., 1997, 50, 83-96.
31. Lee, J.S. Boundary element method for electroelastic interaction in piezoceramics. Eng. Anal. Bound. Elements, 1995, 15, 321-328.
32. Tsamasphyros, G. and Dimou, G. Gauss quadrature rules for finite part integrals. Int. J. Numer. Methods Eng., 1990, 30, 13-26.
33. Lekhnitskii, S. G. Theory of Elasticity of an Anisotropic Body. Holden Day, San Francisco, 1963.
34. Eshelby, J.D., Read, W.T. and Shockley, W. Anisotropic elasticity with applications to dislocations theory. Acta Metal., 1953, 1, 251-259.
35. Stroh, A.N. Dislocations and cracks in anisotropic elasticity. Philos. Mag., 1958, 7, 625-646.
36. Suo, Z. Singularities, interfaces and cracks in dissimilar anisotropic media. Proc. R. Soc. Lond., 1990, A427, 331-358.
37. Ting, T.C.T. Image singularities of Green's functions for anisotropic elastic half-spaces and bimaterials. Q. J. Mech. Appl. Math., 1992, 45, 119-139.
38. Ting, T.C.T. and Barnett, D.M. Image force on line dislocations in anisotropic elastic half-spaces with a fixed boundary. Int. J. Solids Structures, 1993, 30, 313-323.
39. Wei, L. and Ting, T.C.T. Explicit expressions of the Barnett-Lothe tensors for anisotropic materials. J. Elasticity, 1994, 36, 67-83.
40. Sollero, P., Aliabadi, M.H. and Rooke, D.P. Anisotropic analysis of cracks emanating from circular holes in composite laminates using the boundary element method. Eng. Fracture. Mech., 1994, 49, 213-224.
41. Amadei, B. and Pan, E. Gravitational stresses in anisotropic rock masses with inclined strata Int. J. Rock Mech. Min. Sci. and Geomech. Abstr., 1992, 29, 225-236.
42. Chen, Y.Z. Multiple circular hole problem for an elastic half-plane. Computers and Structures, 1994, 52, 1277-1281.
43. Noda, N.A. and Matsuo, T. Numerical solutions of singular integral equations having Cauchy-type singular kernel by means of expansion method. Int. J. Fracture, 1993, 63, 229-245.
44. Savin, G. N. Stress Concentration Around Holes. Pergamon Press, New York, 1961.
45. Portela, A., Aliabadi, M.H. and Rooke, D.P. Dual boundary element incremental analysis of crack propagation. Computers and Structures, 1993, 46, 237-247.
46. Wong, R.C.K. and Kaiser, P.K. Performance assessment of tunnels in cohersionless soils. J. Geotechnical Eng., 1991, 117, 1880-1901.
47. Haimson, B. C., Lee, C. F. & Huang, J. H. S. High horizontal stresses at Niagara Falls, their measurement, and the design of a new hydroelectric plant. In Proc. Int. Symp. Rock Stresses and Rock Stress Measurements, 1986, pp. 615-624.