Static Green's functions in multilayered half spaces

Applied Mathematical Modelling

Volumn 21, Issue 8, 1997, Pages 509-521

  Pan, Ernian ^a  

^a UCB 450   (United States)

Author keywords

Green's function; Multilayered half space; Transverse isotropy

Indexed keywords

ANISOTROPY; MATRIX ALGEBRA; MULTILAYERS; VECTORS;

GAUSS QUADRATURE POINTS; MULTILAYERED HALF SPACE; TRANSVERSE ANISOTROPY;

GREEN'S FUNCTION;

EID: 0031207919     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(97)00053-X     Document Type: Article

References (76)

1. Crampin, S. A review of wave motion in anisotropic and cracked elastic-media. Wave Motion 1981, 3, 343-391
2. Pan, E. Thermoelastic deformation of a transversely isotropic and layered half-space by surface loads and internal sources. Phys. Earth Planet. Inter. 1990, 60, 254-264
3. Yin, W. L. Thermal stresses in anisotropic multilayered structures. Thermal Stress and Strain in Microelectronics Packaging, ed. J. Lau, Van Nostrand-Reinhold, New York, 1993, pp. 95-138
4. Zouari, K, and Lee, Y. C. Stress analysis of the vertical interconnect for three-dimensional packaging. J. Electronic Packaging 1991, 113, 233-239
5. Daniel, I. M., Wang, T. M. and Gotro, J. T. Thermomechanical behavior of multilayer structures in microelectronics. J. Electronic Packaging 1990, 112, 11-15
6. Wait, J. R. Electromagnetic Waves in Stratified Media. Pergamon Press, New York, 1970
7. Selvadurai, A. P. S. and Yue, Z. Q. On the indentation of a poroelastic layer. Int. J. Numer. Anal. Methods Geomech. 1994, 18, 161-175
8. Senjuntichai, T. and Rajapakse, R. K. N. D. Exact stiffness method for quasi-statics of a multi-layered poroelastic medium. Int. J. Solids Struct. 1995, 32, 1535-1553
9. Cathles, L. M. The Viscosity of the Earth's Mantle. Princeton University Press, Princeton, NJ, 1975
10. Booker, J. R. and Small, J. C. Finite layer analysis of viscoelastic layered materials. Int. J. Numer. Anal. Methods Geomech. 1986, 10, 415-430
11. Seale, S. H. and Kausel, E. Point loads in cross-anisotropic, layered halfspaces. J. Eng. Mech. 1989, 115, 509-524
12. Pan, E. Static response of a transversely isotropic and layered half-space to general surface loads. Phys. Earth Planet. Inter. 1989, 54, 353-363
13. Pan, E. Static response of a transversely isotropic and layered half-space to general dislocation sources. Phys. Earth Planet. Inter. 1989, 58, 103-117
14. Kennett, B. L. N. Elastic wave propagation in stratified media. Advances in Applied Mechanics, Volume 21, ed. C. S. Yih, Academic Press, New York, 1981, pp. 79-167
15. Kennett, B. L. N. Seismic Wave Propagation in Stratified Media, Cambridge University Press, New York, 1983
16. Ju, T. H. Analysis of fracture in composite laminated plates. Ph.D. Thesis, University of Colorado at Boulder, 1991
17. Bahar, L. Y. A state space approach to elasticity. J. Franklin Institute 1975, 299, 33-41
18. Rao, N. S. V. K. and Das, Y. C. A mixed method in elasticity. J. Appl. Mech. 1977, 44, 51-56
19. Abhyankar, N. S. and Chandrashekara, S. Concise expressions for the dispersion relations for waves in an infinite isotropic plate. Mech. Res. Commun. 1990, 17, 409-414
20. Chandrashekara, S. and Santhosh, U. An efficient solution to the free vibration of thick angle-ply laminae. Int. J. Solids Struct. 1991, 27, 999-1010
21. Waas, G. Linear two-dimensional analysis of soil dynamics problems in semi-infinite layer media. Ph.D. Thesis, University of California, Berkeley, 1972
22. Kausel, E. and Roesset, J. M. Stiffness matrices for layered soils. Bull. Seism. Soc. Am. 1981, 71, 1743-1761
23. Kausel, E. and Seale, S. H. Static loads in layered halfspaces. J. Appl. Mech. 1987, 54, 403-408
24. Datta, S. K., Shah, A. H. and Karunasena, W. Wave propagation in composite media and material characterization. Elastic Waves and Ultrasonic Nondestructive Evaluation, ed. S. K. Datta, J. D. Achenbach and Y. S. Rajapaske, Elsevier Science Publishers B. V., North-Holland, 1990, pp. 159-169
25. Mal, A. K. Guided waves in layered solids with interface zones. Int. J. Eng. Sci. 1988, 26, 873-881
26. Mal, A. K. Wave propagation in layered composite laminates under periodic surface loads. Wave Motion 1988, 10, 257-266
27. Biot, M. A. A new approach to the mechanics of orthotropic multilayered plates. Int. J. Solids Struct. 1972, 8, 475-490
28. Biot, M. A. Simplified dynamics of multilayered orthotropic viscoelastic plates. Int. J. Solids Struct. 1972, 8, 491-509
29. Biot, M. A. Buckling and dynamics of multilayered and laminated plates under initial stress. Int. J. Solids Struct. 1974, 10, 419-451
30. Biot, M. A. Fundamentals of generalized rigidity matrices for multi-layered media. Bull. Seismol. Soc. Am. 1983, 73, 749-763
31. Small, J. C. and Booker, J. R. Finite layer analysis of layered elastic materials using a flexibility approach. Part 1 - Strip loadings. Int. J. Numer. Methods Eng. 1984, 20, 1025-1037
32. Small, J. C. and Booker, J. R. Finite layer analysis of layered elastic materials using a flexibility approach. Part 2 - Circular and rectangular loadings. Int. J. Numer. Methods Eng. 1986, 23, 959-978
33. Choi, H. J. and Thangjitham, S. Stress analysis of multilayered anisotropic elastic media. J. Appl. Mech. 1991, 58, 382-387
34. Thangjitham, S. and Choi, H. J. Thermal stresses in a multilayered anisotropic medium. J. Appl. Mech. 1991, 58, 1021-1027
35. Pindera, M. J. and Lane, M. S. Frictionless contact of layered half-planes. Part I: Analysis. J. Appl. Mech. 1993, 60, 633-639
36. Pindera, M. J. and Lane, M. S. Frictionless contact of layered half-planes. Part II: Numerical results. J. Appl. Mech. 1993, 60, 640-645
37. Wang, Y. and Rajapakse, R. K. N. D. An exact stiffness method for elastodynamics of a layered orthotropic half-plane. J. Appl. Mech. 1994, 61, 339-348
38. Kuo, C. H. and Keer, L. M. Three-dimensional analysis of cracking in a multilayered composite. J. Appl. Mech. 1995, 62, 273-278
39. Lin, W. and Keer, L. M. Analysis of a vertical crack in a multilayered medium. J. Appl. Mech. 1989, 56, 63-69
40. Lin, W. and Keer, L. M. Three-dimensional analysis of cracks in layered transversely isotropic media. Proc. R. Soc. Lond. A 1989, 424, 307-322
41. Thomson, W. T. Transmission of elastic waves through a stratified medium. J. Appl. Phys. 1950, 21, 89-93
42. Haskell, A. The dispersion of surface waves on a multilayered media. Bull. Seism. Soc. Am. 1953, 43, 17-34
43. Gilbert, F. and Backus, G. Propagator matrices in elastic wave and vibration problems. Geophys. 1966, 31, 326-332
44. Dunkin, J. W. Computation of modal solutions in layered elastic media at high frequencies. Bull. Seism. Soc. Am. 1965, 55, 335-358
45. Schwab, F. and Knopoff, L. Surface wave dispersion computations. Bull. Seism. Soc. Am. 1970, 60, 321-344
46. Apsel, R. J. Dynamic Green's functions for layered media and applications to boundary value problem. Ph.D. Thesis, University of California at San Diego, 1979
47. Luco, J. E. and Apsel, R. J. On the Green's function for a layered half-space, Part I. Bull. Seism. Soc. Am. 1983, 73, 909-929
48. Chen, X. A systematic and efficient method of computing normal modes for multilayered half-space. Geophys. J. Int. 1993, 115, 391-409
49. Singh, S. J. Static deformation of a multilayered half-space by internal sources. J. Geophys. Res. 1970, 75, 3257-3263
50. Jovanovich, D. B., Husseini, M. I. and Chinnery, M. A. Elastic dislocations in a layered half-space - I. Basic theory and numerical methods. Geophys. J. R. Astro. Soc. 1974, 39, 205-217
51. Sato, R. and Matsu'ura, M. Static deformations due to the fault spreading over several layers in a multi-layered medium, Part I: Displacement. J. Phys. Earth 1973, 21, 227-249
52. Singh, S. J. Static deformation of a transversely isotropic multilayered half-space by surface loads. Phys. Earth Planet. Inter. 1986, 42, 263-273
53. Yue, Z. Q. and Wang, R. Static solution for transversely isotropic elastic n-layered systems. Acta Scientiarum Naturalium, Universitatis Pekinensis 1988, 24, 202-211
54. Bouchon, M. and Aki, K. Discrete wavenumber representation of seismic source wave fields. Bull. Seism. Soc. Am. 1977, 67, 259-277
55. Bouchon, M. Discrete wave number representation of elastic wave fields in three-space dimensions. J. Geophys. Res. 1979, 84, 3609-3614
56. Bouchon, M. A simple method to calculate Green's functions for elastic layered media. Bull. Seism. Soc. Am. 1981, 71, 959-971
57. Zhu, J., Shah, A. H. and Datta, S. K. Modal representation of two-dimensional elastodynamic Green's functions. J. Eng. Mech. 1995, 121, 26-36
58. Zhu, J., Shah, A. H. and Datta, S. K. The evaluation of Cauchy principal value integrals and weakly singular integrals in BEM and their applications. Int. J. Numer. Meth. Eng. 1996, 39, 1017-1028
59. Dravinski, M. and Mossessian, T. K. On evaluation of the Green's functions for harmonic line loads in a viscoelastic half space. Int. J. Numer. Meth. Eng. 1988, 26, 823-841
60. Chan, K. S., Karasudhi, P. and Lee, S. L. Force at a point in the interior of a layered elastic half space. Int. J. Solids Struct. 1974, 10, 1179-1199
61. Pan, E. The static response of multilayered foundations to general surface loading and body force. Acta Mechanica Sinica 1989, 21, 344-353
62. Ding, Z. Y. and Shen, Y. Q. Quasi-static response of a layered viscoelastic half-space to general surface loading. Phys. Earth Planet. Inter. 1991, 66, 278-289
63. Huang, J. The general model of static responses in multilayered elastic media. Crust. Deform. Earthquake 1991, 11, 1-6
64. Pan, E. An exact solution for transversely isotropic, simply supported and layered rectangular plates. J. Elasticity 1991, 25, 101-116
65. Pan, E. Vibration of a transversely isotropic, simply supported and layered rectangular plate. J. Elasticity 1992, 27, 167-181
66. Patterson, T. N. L. The optimum addition of points to quadrature formulae. Math. Comp. 1968, 22, 847-856
67. Patterson, T. N. L. Algorithm for automatic numerical integration over a finite interval [D1]. Commun. ACM 1973, 16, 694-699
68. Hanggi, P., Roesel, F. and Trautmann, P. Evaluation of infinite series by use of continued fraction expansions: A numerical study. J. Comp. Phys. 1980, 37, 252-258
69. Chave, A. D. Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophys. 1983, 48, 1671-1686
70. Sato, R. Crustal deformation due to dislocation in a multi-layered medium. J. Phys. Earth 1971, 19, 31-46
71. Davis, P. J. and Rabinowitz, P. Methods of Numerical Integration, Academic Press, New York, 1975
72. Kundu, T. Computation of surface motion in a stratified half space. Ph.D. Thesis, University of California at Los Angeles, 1983
73. Mindlin, R. D. Force at a point in the interior of a semi-infinite solid. Physics 1936, 7, 195-202
74. Pan, Y. C. and Chou, T. W. Green's function solutions for semi-infinite transversely isotropic materials. Int. J. Eng. Sci. 1979, 17, 545-551
75. Wideberg, J. and Benitez, F. G. Elastic stress and displacement distribution in an orthotropic multilayered system due to a concentrated load. Eng. Anal. Boundary Elements 1995, 16, 19-27
76. Pan, E. and Amadei, B. 3-D boundary element formulation of an isotropic elasticity with gravity. Appl. Math. Modelling 1996, 20, 114-120