探討三維無窮域異向性材料受一集中力作用之格林函數是基本且重要的研究課題，文獻中藉由Stroh公式，可將格林函數之位移場與應力場用Stroh特徵值問題之特徵值表示，而此特徵值與異向性材料常數有關，一般而言特徵值需透過數值計算，本文建立數值分析程序考慮特徵值不重根之情況，以數值探討等向性材料與異向性材料之三維無限域受一集中力作用之位移場與應力場，並就數值結果做了討論。

The Green’s function for a point force in three dimensional infinitely extended anisotropic materials is a basic and important research topic. In the literature, by means of the Stroh formalism the displacement and stress fields of the Green’s function are represented by Stroh eigenvalues. These Stroh eigenvalues are related to anisotropic material constants. In general, the eigenvalues are needed to be calculated numerically. In this thesis, numerical procedures are set up to compute the eigenvalues. With the assumption that the eigenvalues are distinct, the displacement and stress fields of the Green’s function of isotropic and anisotropic materials are numerically investigated, and the numerical results are discussed.

Fredholm I. Sur les equation de l’equilibre d’um corps solide elastique.
Acta Math. Vol.23,1-42.1900.

Federico C., Buroni & Andres S. Three dimensional Green’s function and its derivative for materials with general anisotropic magneto electro elastic coupling. Proc.R.Soc. Vol.466,515-537.2010.

Lifshitz, I. M. & Rozentsveig, L. N. Construction of the Green tensor
for the fundamental equation of elasticity theory in the case of
unbounded elastically anisotropic medium. Zh. eksper. i teoreticheskoi
fiziki Vol.17,783-791.1947.

Lee, V.-G. Explicit expressions of derivatives of elastic Green’s functions for general anisotropic materials. Mech. Res. Comm. Vol.30, 241-249.2003.

Lee, V.-G. Derivatives of the three dimensional Green’s functions for anisotropic materials. Int. J. Solids Struct. Vol.46, 3471-3479.2009.

Pan, E. & Chon, T. W. Point force solution for an infinite transversely isotropic solid. J.Appl. Mech. Vol.43,608-612.1976.

Phan, A.V.,Gray L.J & Kaplan, T. Residue approach for evaluating the
three dimensional anisotropic elastic Green’s function:multiple roots.
Eng.Analysis with Boundary Element. Vol . 29,570-576.2005.

Sales, M. A. & Gray L. J. Evaluation of the anisotropic Green’s function and its derivatives. Comput. Struct. Vol.69,247-254.1998.

Ting, T. C. T. & Lee, V. G. The three dimensional elastostatic Green’s function for general anisotropic linear elastic solids. Q. J. Mech. Appl. Math. Vol.50,407-426.1996.

Tonon, F.Pan, E. & Amadei, B. Green’s functions BEM formulation
for 3D anisotropic media.Comput.Struct. Vol.79,469-482.2001.

Tavara, L., Ortiz, J. E., Mantic, V. & Paris, F. Unique real variable
expression of displacement and traction fundamental solutions covering
all transversely isotropic elastic materials for 3D BEM.Int. J.Numer.
Meth.Eng. Vol.74,776-798.2008.

Wilson, R. B. & Cruse, T. A. Efficient implementation of anisotropic
three dimensional boundary integral equation stress analysis. Int. J.
Numer. Meth. Eng. Vol.12,1383-1397.1978.

Wang, C.-Y. Elastic fields produced by a point source of general anisotropy. J. Eng. Math. Vol.32,41-52.1997,