Numerical solution of 3D Green's function for the dynamic system of anisotropic elasticity

2009 ◽  
Vol 373 (35) ◽  
pp. 3145-3150 ◽  
Author(s):  
Hüseyin Koçak ◽  
Ahmet Yıldırım
Keyword(s):  
Dynamic System ◽  
Green’S Function ◽  
Numerical Solution ◽  
Green's Function ◽  
Anisotropic Elasticity

Defect Green’s Function of Multiple Point-Like Inhomogeneities in a Multilayered Anisotropic Elastic Solid

2004 ◽  
Vol 71 (5) ◽  
pp. 672-676
Author(s):  
B. Yang
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Elastic Solid ◽  
Anisotropic Elasticity ◽  
Matrix Inversion ◽  
Numerical Results ◽  
Multiple Point ◽  
Present Formulation ◽  
Anisotropic Elastic ◽  
The Continuum

Defect Green’s function (GF) of multiple point-like inhomogeneities in a multilayered solid has been derived within the theory of linear anisotropic elasticity. It is related to the (reference) GF of the multilayered matrix excluding the inhomogeneities through the continuum Dyson’s equation. While the reference GF is available, the defect GF can be solved. The expressions are first analytically reduced by realizing the point-likeness of the inhomogeneities. The subsequent procedure involves the solution of the response of each individual inhomogeneity to a far-field straining in the multilayered matrix and a matrix inversion on the order of the number of inhomogeneities. Furthermore, the defect GF is applied to derive the field induced by inhomogeneous substitutions in a multilayered solid. Numerical results are reported for arrays of cubic and semispherical Ge inclusions in a Si/Ge superlattice. The numerical results have demonstrated the validity and efficiency of the present formulation.

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

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Wave Speed ◽  
Integral Transform ◽  
Anisotropic Elasticity ◽  
Alternative Form ◽  
Wave Speeds ◽  
Speed Dependence ◽  
Anisotropic Solid ◽  
The Subject

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.

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