On singular integral equations and fundamental solutions of poroelasticity

International Journal of Solids and Structures

Volumn 35, Issue 34-35, 1998, Pages 4521-4555

  Cheng, A H D ^a   Detournay, E ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; BOUNDARY ELEMENT METHOD; ELASTICITY; GALERKIN METHODS; GREEN'S FUNCTION; INTEGRAL EQUATIONS; STRESS ANALYSIS;

POROELASTICITY; SINGULAR INTEGRAL EQUATIONS;

POROUS MATERIALS;

EID: 0032338381     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(98)00082-1     Document Type: Article

References (50)

1. Altiero N. J., Gavazza S. D. Journal of Elasticity. 10:1980;1.
2. Badmus T., Cheng A. H.-D., Grilli S. International Journal of Numerical Methods in Engineering. 36:1993;67.
3. Banerjee, P. K. and Butterfield, R. (1981) Boundary Element Methods in Engineering Science. McGraw-Hill.
4. Banerjee P. K., Butterfield R., Tomlin G. R. Int. J. Num. Anal. Meth. Geomech. 5:1981;15.
5. Becache E., Nedelec J. C., Nishimura N. Journal of Elasticity. 31:1993;25.
6. Bilby B. A. and Eshelby, J. D. (1968) Dislocations and the theory of fracture. In : Fracture, ed. H. Liebowitz, pp. 99-182. Academic Press.
7. Biot M. A. Journal of Applied Physics. 12:1941;155.
8. Biot M. A. Journal of Applied Physics. 26:1955;182.
9. Biot M. A. Journal of Applied Mechanics, Transactions of ASME. 78:1956;91.
10. Bonnet, M. (1995) Equations Integrales et Elements de Frontière. Eyrolles, Paris.
11. Brebbia C. A., Butterfield R. Appl. Math. Modelling. 2:1978;132.
12. Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C. (1984) Boundary Element Techniques - Theory and Applications in Engineering. Springer-Verlag.
13. Carvalho, J. L. (1990) Poroelastic effects and influence of material interfaces on hydraulic fracture behaviour. Ph.D. dissertation, University of Toronto, 1990.
14. Carvalho, J. L. and Curran, J. H. (1998) Three-dimensional displacement discontinuity solutions for fluid-saturated porous media. International Journal of Solids and Structures, this issue, 1998.
15. Cheng A. H.-D. Int. J. Rock Mech. Mining Sci. Geomech. Abstr. 34:1997;199.
16. Cheng A. H.-D., Detournay E. Int. J. Numer. Anal. Meth. Geomech. 12:1988;551.
17. Cheng A. H.-D., Liggett J. A. International Journal of Numerical Methods in Engineering. 20:1984;255.
18. Cheng A. H.-D., Liggett J. A. International Journal of Numerical Methods in Engineering. 20:1984;279.
19. Cheng A. H.-D., Liu P. L-F. Appl. Ocean Res. 8:1986;22.
20. Cheng A. H.-D., Predeleanu M. Appl. Math. Modelling. 11:1987;285.
21. Cheng, A. H.-D., Badmus, T. and Detournay, E. (1988) Singular integral equation method for cracks embedded in poroelastic space. In Boundary Elements X, Vol. 3 Stress Analysis, Southampton, U.K., ed. C. A. Brebbia, pp. 265-278, Springer-Verlag.
22. Cheng, A. H.-D., Carvalho, J. and Detournay, E. (1990) Equivalence between direct and indirect boundary integral equations for linear poroelasticity. Computational Engineering with Boundary Elements, Vol. 2 : Solid and Computational Problems, University of Delaware, eds. A. H.-D. Cheng, C. A. Brebbia and S. Grilli, Comp. Mech. Publ, pp. 199-209, BETECH 90.
23. Cleary M. P. International Journal of Solids and Structures. 13:1977;785.
24. Coussy, O. (1995) Mechanics of Porous Continua. Wiley.
25. Crouch, S. L. and Starfield, A. M. (1983) Boundary Element Methods in Solid Mechanics. Allen and Unwin.
26. Curran, J. H. and Carvalho, J. L. (1987) A displacement discontinuity model for fluid-saturated porous media. Proc. 6th Cong. Int. Soc. Rock Mech., Vol. 1, pp. 73-78, Montreal.
27. Dargush G. F., Banerjee P. K. Int. J. Numer. Anal. Meth. Eng. 28:1989;2423.
28. Dargush G. F., Banerjee P. K. Journal of Applied Mechanics. 58:1991;28.
29. Detournay E., Cheng A. H.-D. Journal of Applied Mechanics. 54:1987;783.
30. Detournay E., Cheng A. H.-D. International Journal of Solids and Structures. 37:1991;1645.
31. Detournay, E. and Cheng, A. H.-D. (1993) Fundamentals of poroelasticity. Chap. 5. In Comprehensive Rock Engineering : Principles, Practice and Projects, Vol. II, Analysis and Design Method, ed. C. Fairhurst, pp. 113-171. Pergamon Press.
32. Gringarten, A. C., Ramey, H. J. Jr and Raghavan, R. (1974) Unsteady-state pressure distributions created by a well with a single infinite-conductivity vertical fracture. Soc. Pet. Eng. J. 347-360.
33. Hong H. K., Chen J. T. Journal of Engineering Mechanics. 114:1988;1028.
34. Jaswon, M. A. and Symm, G. T. (1977) Integral Equation Methods in Potential Theory and Elastostatics. Academic Press.
35. Kane, J. H. (1994) Boundary Element Analysis in Engineering Continuum Mechanics. Prentice-Hall.
36. Krishnasamy, G., Rizzo, F. J. and Rudolphi, T. J. (1992) Hypersingular boundary integral equations : their occurrence, interpretation, regularization, and computation. Chap. 7. In Developments in Boundary Element Methods, eds. P. K. Banerjee and S. Kobayashi, 7. Elsevier.
37. Love, A. E. H. (1944) A Treatise on the Mathematical Theory of Elasticity, 4th edn. Dover.
38. Morse, P. M. and Feshbach, H. (1953) Methods of Theoretical Physics, Part I and II. McGraw-Hill.
39. Mura, T. (1982) Micromechanics of Defects in Solids. Martinus Ni jhoff, Hague.
40. 3. In Boundary Elements, ed. Du Qinghua, pp. 439-448. Pergamon.
41. Nishimura N., Kobayashi S. International Journal of Solids and Structures. 25:1989;1.
42. Pan E. Acta Mechanica. 87:1991;105.
43. Pan E., Maier G. Computational Mechanics. 19:1997;169.
44. Predeleanu M. Anal. Univ. Bucuresti, Seria Stiintele Naturii, Matematica, Mecanica. 17:1968;75.
45. Renshaw C. E., Harvey C. F. J. Geophys. Res. 99:1994;21.
46. Rice J. R., Cleary M. P. Rev. Geophys. Space Phys. 14:1976;227.
47. Rudnicki J. W. International Journal of Solids and Structures. 17:1981;855.
48. Rudnicki J. W. Mech. Mat. 5:1987;383.
49. Sharp S. Int. J. Numer. Anal. Meth. Geomech. 7:1983;269.
50. Vandamme L., Detournay E., Cheng A. H.-D. Int. J. Numer. Anal. Meth. Geomech. 13:1989;215.