A modified Lekhnitskii formalism àla Stroh for anisotropic elasticity and classifications of the 6 × 6 matrix N

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 455, Issue 1981, 1999, Pages 69-89

  Ting, T C T ^a  

^a 1120 Science and Engineering Offices   (United States)

Author keywords

Anisotropic elasticity; Classifications; Elasticity; Lekhnitskii formalism; Matrices; Stroh formalism

Indexed keywords

EID: 33746412917     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0303     Document Type: Article

References (27)

1. Barnett, D. M. & Chadwick, P. 1991 The existence of one-component surface waves and exceptional subsequent transonic states of types 2, 4, and El in anisotropic elastic media. In Modern theory of anisotropic elasticity and applications (cd. J. J. Wu, T. C. T. Ting & D. M. Barnett), SIAM Proc. Series, pp. 199-214, Philadelphia, PA: SIAM.
2. Barnett, D. M. & Kirchner, H. O. K. 1997 A proof of the equivalence of the Stroh and Lekhnitskii sextic equations for plane anisotropic elastostatics. Phil. Mag. A 76, 231-239.
3. Barnett, D. M. & Lothe, J. 1973 Synthesis of the sextic and the integral formalism for dislocations, Greens function and surface waves in anisotropic elastic solids. Phys. Norv. 7, 13-19.
4. Chadwick, P. & Smith, G. D. 1977 Foundations of the theory of surface waves in anisotropic elastic materials. Adv. Appl. Mech. 17, 303-376.
5. Dempsey J. P. & Sinclair, G. B. 1979 On the stress singularities in the plane elasticity of the composite wedge. J. Elast. 9, 373-391.
6. Eshelby, J. D., Read, W, T. & Shockley, W. 1953 Anisotropic elasticity with applications to dislocation theory. Acta Metall, l, 251-259.
7. Gundersen, S. A., Wang, L. & Lothe, J. 1991 Secluded supersonic elastic surface waves. In Modern theory of anisotropic elasticity and applications (cd. J. J. Wu, T. C. T. Ting & D. M. Barnett), SIAM Proc. Series, pp. 186-198. Philadelphia, PA: SIAM.
8. Ingebrigtsen, K. A. & Tonning, A. 1969 Elastic surface waves in crystal. Phys. Rev. 184, 942-951.
9. Kosevich, A. M., Kosevich, Yu. A. & Surkin, E. S. 1985 Generalized Raylcigh waves and the geometry of isofrequency surfaces of sound oscillation waves in crystals. Sov. Phys. JETP 61, 639-644.
10. Lekhnitskii, S. G. 1963 Theory of elasticity of an anisotropic elastic body. San Francisco, CA: Holden-Day.
11. Pease, M. C. Ill 1965 Methods of matrix algebra. New York: Academic.
12. Stroh, A. N. 1958 Dislocations and cracks in anisotropic elasticity Phil. Mag. 3, 625-646.
13. Tanuma, K. 1996 Surface impedance tensors of transversely isotropic elastic materials. Q. Jl Mech. Appl. Math. 49, 29-48.
14. Ting, T. C. T. 1988 Some identities and the structure of Ni in the Stroh formalism of anisotropic elasticity. Q. Appl. Math. 46, 109-120.
15. Ting, T. C. T. 1992 Barnett-Lothe tensors and their associated tensors for monoclinic materials with the symmetry plane at x$ -0. J. Elast. 27, 143-165.
16. Ting, T. C. T. 1994 On anisotropic elastic materials that possess three identical Stroh eigenvalues as do isotropic materials. Q. Appl. Math. 52, 363-375.
17. Ting. T. C. T. 1996a Anisotropic elasticity: theory and applications. Oxford University Press.
18. Ting, T. C. T. 1996 Existence of an extraordinary degenerate matrix N for anisotropic elastic materials. Q. Jl Mech. Appl. Math. 49, 405-417.
19. Ting, T. C. T. 1997a Surface waves in anisotropic elastic materials for which the matrix N(v) is extraordinary degenerate, degenerate, or semisimple. Proc. R. Soc. Land. A 453, 449-472.
20. Ting, T. C. T. 19976 New explicit expression of Barnett-Lothe tensors for anisotropic linear elastic materials. J. Elast. 47, 23-50.
21. Ting, T. C. T. 1997c On extraordinary semisimple matrix N(v) for anisotropic elastic materials. Q. Appl. Math. 55, 723-738.
22. Ting, T. C. T. 1998 Anisotropic elastic materials for which the sextic equation is a cubic equation in p2. Math. Mech. Solids 3, 3-16.
23. Ting, T. C. T. & Barnett, D. M. 1997 Classifications of surface waves in anisotropic elastic materials. Wave Motion 26, 207-218.
24. Ting, T. C. T. & Hwu, C. 1988 Sextic formalism in anisotropic elasticity for almost non-semisimple matrix N. Int. Jl Solids Struct. 24, 65-76.
25. Wang, L. & Gundersen, S. A. 1993 Existence of one component surface waves in anisotropic elastic media. Physica Scr. 47, 394-404.
26. Wang, Y. M. & Ting, T. C. T. 1997 The Stroh formalism for anisotropic materials that possess an almost extraordinary degenerate matrix N. Int. Jl Solids Struct. 34, 401-413.
27. Yin, W. L. 1997 A general analysis method for singularities in composite structures. Proc. 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., pp. 2239-2246.