Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Note on Green's function in anisotropic elasticity


Author: Martin C. Gutzwiller
Journal: Quart. Appl. Math. 20 (1962), 249-256
MSC: Primary 73.53
DOI: https://doi.org/10.1090/qam/141283
MathSciNet review: 141283
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Abstract: Green's function for an elastic, anisotropic medium is constructed with the help of the method used by Courant and Hilbert in the study of light propagation through an anisotropic dielectric. The amplitudes of the arrivals corresponding to each wave surface are expressed as functions of the curvature of the normal surfaces. Multi-valued solutions are expressed as integrals over the dislocation lines, whose motion is assumed to be known, but otherwise arbitrary. The formulae are worked out in detail for the isotropic medium.


References [Enhancements On Off] (What's this?)

  • [1] R. Courant and D. Hilbert, Methoden der mathematischen Physik, Vol. 2, Springer, 1937.
  • [2] M. J. Lighthill, Introduction to Fourier analysis and generalised functions, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York, 1958. MR 0092119
  • [3] A. E. H. Love, A treatise on the mathematical theory of elasticity, Cambridge University Press, 1927.

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DOI: https://doi.org/10.1090/qam/141283
Article copyright: © Copyright 1962 American Mathematical Society


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