0
Research Papers

Transient Green's Function for the General Anisotropic Solid: An Alternative Form

[+] Author and Article Information
L. M. Brock

Fellow ASME
Mechanical Engineering,
University of Kentucky,
265 RGAN,
Lexington, KY 40506-0503
e-mail: brock@engr.uky.edu

Contributed by the Applied Mechanics of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 27, 2012; final manuscript received January 8, 2013; accepted manuscript posted February 12, 2013; published online July 12, 2013. Assoc. Editor: John Lambros.

J. Appl. Mech 80(5), 051019 (Jul 12, 2013) (5 pages) Paper No: JAM-12-1422; doi: 10.1115/1.4023635 History: Received August 27, 2012; Revised January 08, 2013; Accepted February 12, 2013

The Green's function for the general anisotropic solid has been the subject of several studies. Here a variation of a standard integral transform approach allows the transient Green's function to be expressed in a somewhat different form. This alternative form is less compact, but features explicit integrals of functions in terms of polar and azimuthal angles defined with respect to the principal basis coordinates. Dimensionless expressions for the three anisotropic wave speeds are also given in terms of these angles, and sample calculations presented that show wave speed dependence on propagation direction. Some standard formalisms of anisotropic elasticity are not invoked, but similar terms are identified in the course of the analysis, and help define the solution expressions.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kelvin, L., 1848, “Note on the Integration of the Equations of Equilibrium of an Elastic Solid,” Cambridge and Dublin Mathematical Journal, 3, pp. 87–89.
Ting, T. C. T., 1996, Anisotropic Elasticity, Oxford University, New York.
Sneddon, I. N., 1972, The Use of Integral Transforms, McGraw-Hill, New York.
Synge, J. L., 1957, The Hypercircle in Mathematical Physics, Cambridge University, Cambridge, UK.
Stroh, A. N., 1958, “Dislocations and Cracks in Anisotropic Elasticity,” Philos. Mag., 3, pp. 625–646. [CrossRef]
Stroh, A. N., 1962, “Steady State Problems in Anisotropic Elasticity,” J. Math. Phys., 41, pp. 77–103.
Barnett, D. M., and Lothe, J., 1973, “Synthesis of the Sextic and the Integral Formalism for Dislocations, Green's Function and Surface Waves in Anisotropic Elastic Solids,” Phys. Norv., 7, pp. 13–19.
Ting, T. C. T., and Lee, V., 1997, “The Three-Dimensional Elastostatic Green's Function for General Anisotropic Linear Elastic Solids,” Q.J. Mech. Appl. Mathematics, 50, pp. 407–426. [CrossRef]
Wang, C.-Y., and Achenbach, J.D., 1994, “Elastodynamic Fundamental Solutions for Anisotropic Solids,” Geophys. J. Int., 118, pp. 384–392. [CrossRef]
Willis, J. R., 1973, “Self-Similar Problems in Elastodynamics,” Philos. Trans. R. Soc. London, Ser. A, 274, pp. 435–491. [CrossRef]
Payton, R. G., 1983, Elastic Wave Propagation in Transversely Isotropic Media Martinus Nijhoff, The Hague.
Wang, C.-Y., and Achenbach, J. D., 1995, “Three-Dimensional Time-Harmonic Elastodynamic Green's Functions for Anisotropic Solids,” Proc. R. Soc. London, Ser. A, 449, pp. 441–458. [CrossRef]
Willis, J. R., 1980, “Polarization Approach to the Scattering of Elastic Waves –I. Scattering by a Single Inclusion,” J. Mech. Physics Solids, 28, pp. 287–305. [CrossRef]
Van der Pol, B., and Bremmer, H., 1950, Operations Based on the Two-Sided Laplace Integral, Cambridge University, Cambridge, UK.
Barber, J. R., and Ting, T. C. T., 2007, “Three-Dimensional Solutions for General Anisotropy,” J. Mech. Phys. Solids, 55, pp. 1993–2006. [CrossRef]
Hohn, F. E., 1965, Elementary Matrix Algebra, MacMillan, New York.
Abramowitz, A., and Stegun, I. A., eds., 1972, Handbook of Mathematical Functions, Dover, New York.
Jones, R. M., 1999, Mechanics of Composite Materials, 2nd ed., Brunner-Routledge, New York.
Crandall, S. H., and Dahl, N. C., eds., 1959, An Introduction to the Mechanics of Solids, McGraw-Hill, New York.

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In