Unique, explicit, and exact expressions for the first- and second-order derivatives of the three-dimensional Green's function for general anisotropic materials are presented in this paper. The derived expressions are based on a mixed complex-variable method and are obtained from the solution proposed by Ting and Lee (Ting and Lee, 1997,“The Three-Dimensional Elastostatic Green's Function for General Anisotropic Linear Elastic Solids,” Q. J. Mech. Appl. Math. 50, pp. 407–426) which has three valuable features. First, it is explicit in terms of Stroh's eigenvalues () on the oblique plane with normal coincident with the position vector; second, it remains well-defined when some Stroh's eigenvalues are equal (mathematical degeneracy) or nearly equal (quasi-mathematical degeneracy); and third, they are exact. Therefore, both new proposed solutions inherit these appealing features, being explicit in terms of Stroh's eigenvalues, simpler, unique, exact and valid independently of the kind of degeneracy involved, as opposed to previous approaches. A study of all possible degenerate cases validate the proposed scheme.
Unique and Explicit Formulas for Green's Function in Three-Dimensional Anisotropic Linear Elasticity
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Manuscript received July 31, 2012; final manuscript received November 27, 2012; accepted manuscript posted February 11, 2013; published online July 12, 2013. Assoc. Editor: Marc Geers.
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Buroni, F. C., and Sáez, A. (July 12, 2013). "Unique and Explicit Formulas for Green's Function in Three-Dimensional Anisotropic Linear Elasticity." ASME. J. Appl. Mech. September 2013; 80(5): 051018. https://doi.org/10.1115/1.4023627
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