在分析無窮域和半無窮域問題時，邊界元素法被認為是一個較為有效率之數值模擬法。對此有許多學者，如Pan, Chen and Amadei [9]、Wei and Ting [15]和Hwu [2]皆有提出半無窮域之基本解，本論文旨在重新探討如何設定無窮域及半無窮域異向靜彈之基本解，並將其應用於邊界元素法之程式中，來探討在全無窮域及半無窮域內挖孔洞之工程分析。此外，文中亦有研究如何有效的模擬在半無窮域表面施加任意負載函數時，分析域內挖孔表面之應力。
二維基本解中包含指數函數會造成在無窮遠處響應無法收斂，此處利用剛體運動的計算來達到無窮域響應的收斂，最終不需要對建立無窮遠處邊界以達到邊界元素法的特性，並由無窮域及半無窮域內部挖孔洞驗證公式和程式編寫的正確性，以及半無窮域多層材料、平面旋轉、平面加載的問題是對於工程應用上提供可使用的模擬範例。

Boundary element method (BEM) is considered to be an efficient numerical simulation method for analyzing engineering problems with infinite and half-infinite plane. In this regard, many scholars, such as Pan et al. [9], Wei and Ting [15] and Hwu [2], have proposed the fundamental solutions of half-infinite plane. The purpose of this thesis is to revisit this problem as to properly formulate their corresponding fundamental solutions and implement them in an existing BEM code. For verifying the successful implementation, a few numerical examples of underground tunnels are effectively investigated to simulate the hoop stress on the tunnel surfaces. Moreover, for further demonstrating the capability of the implemented code in simulating practical problems, an arbitrarily designed functional loading is partially applied on the half-infinite plane of some cases.
Since the conventional logarithmic Green's function of 2D elastostatics is not convergent at infinity, the corresponding fundamental solution is modified by rigid-body-motion relation so as to acquire the convergence. By applying this modified Green's function, no meshes are required to model the infinite/half-infinite places. The validity of all formulations and the implementation in program are verified by comparing the results with the analyses of those examples being applied meshes at a far distance to model infinity. For marking the applicability of the implement program to practical engineering cases, some examples are also designed to involve multi-layer materials, planar rotation and arbitrary loading on the plane surface.

[1] Cruse, T. A., Boundary element analysis in computational fracture mechanics, Kluwer Academic Publishers, 1988.
[2] Hwu, C., Anisotropic elastic plates, Springer-Verlag US, 2010.
[3] Hwu, C., Anisotropic elasticity with Matlab, Springer International Publishing, 2021.
[4] Lekhnitskii, S. G., Anisotropic plates, Gordon and Breach, 1968.
[5] Lekhnitskii, S. G., Theory of elasticity of an anisotropic body, Mir Publishers, 1981.
[6] Muskhelishvili, N.I., Some Basic Problem of the mathematical Theory of Elasticity, Noordhoff Publisher, Groningen, 1954.
[7] Pan, E., & Amadei, B., Stress concentration at irregular surfaces of anisotropic half-spaces, Acta Mechanica, 113(1-4), 119-135, 1995.
[8] Pan, E., & Amadei, B., Fracture mechanics analysis of cracked 2-D anisotropic media with a new formulation of the boundary element method, International Journal of Fracture, 77(2), 161-174, 1996.
[9] Pan, E., Chen, C. S., & Amadei, B., A BEM formulation for anisotropic half-plane problems, Engineering Analysis with Boundary Elements, 20(3), 185-195, 1997.
[10] Shiah, Y. C., & Tan, C. L., Calculation of Interior Point Stresses in Two-Dimensional Boundary Element Analysis of Anisotropic Bodies with Body Forces, Journal of Strain Analysis for Engineering Design (Professional Engineering Publishing), 34(2), 117-128, 1999.
[11] Stroh, A. N., Dislocations and cracks in anisotropic elasticity, Philosophical Magazine, 3(30), 625-646, 1958.
[12] Suo, Z., Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 427(1873), 331-358, 1990.
[13] Swedlow, J. L., & Cruse, T. A., Interactive program for analysis and design problems in advanced composites technology, In. United States: NASA Center for Aerospace Information (CASI), 1971.
[14] Telles, J.C.F., Mansur, W.J. and Wrobel, L.C., On boundary elements for external potential problems, Mechanics Research Communications, 11, 373-77, 1886.
[15] Wei, L., & Ting, T. C. T., Explicit expressions of the Barnett-Lothe tensors for anisotropic materials, Journal of Elasticity, 36(1), 67-83, 1994.
[16] Wrobel, L. C., & Kassab, A. J., Boundary Element Method, Volume 1: Applications in Thermo-Fluids and Acoustics, Applied Mechanics Reviews, 56(2), B17-B17, 2003.
[17] 夏育群、陳春來，「邊界元素法之入門介紹」，高立圖書有限公司，中華民國93年12月15日。