橫觀等向性材料為一常見之地質結構。本論文之研究將使用邊界元素法求解三維橫觀等向性材料之無窮域與半無窮域靜彈力學問題，欲模擬大地工程可能遭遇之實際情況:在大地工程領域中，當地下孔洞或建物與周遭環境之規模差異懸殊時，可視情況近似於無窮域或半無窮域問題。
邊界元素法為一具效率之數值計算方法。相較於有限元素法，其優勢在於僅需對模型邊界進行網格劃分；而不需進行全域劃分。且可使用其相對應之基本解自動滿足邊界條件，適合求解無窮域或半無窮域問題。本文先採用Pan and Chou[1]針對橫觀等向性材料之無窮域基本解與Lee[2]針對橫觀等向性材料之擾動場基本解相加，以模擬橫觀等向性材料之無窮或半無窮問題，並使用本師門Fortran程式求解六個數值範例，並將其結果數值和Ansys做比對，以驗證數值之準確性和本研究理論之合理性。

Transversely isotropic materials are common geological structures. This paper uses the boundary element method to solve the static elastic problem of three-dimensional transversely isotropic materials in infinite and half-infinite space, aiming to simulate the actual situation that may be encountered in geotechnical engineering: in the field of geotechnical engineering, when the scale difference between underground cavities or buildings and their surrounding environment is significant, the problem can be approximated as an infinite or half-infinite space problem.
The boundary element method is a highly efficient numerical calculation method. Compared with the finite element method, its advantage is that it only requires meshing the model boundary, without needing to mesh the entire region. In addition, the corresponding fundamental solution can automatically satisfy the boundary conditions, making it suitable for solving infinite or half-infinite space problems. This paper first uses the fundamental solution of the infinite field of transversely isotropic materials proposed by Pan and Chou[1] and the fundamental solution of the perturbation field of transversely isotropic materials proposed by Lee[2] to simulate the infinite or half-infinite problem of transversely isotropic materials. Then, the Fortran program developed by our lab is used to solve six numerical examples, and the numerical results are compared with the calculation results of Ansys to verify the accuracy of the numerical results and the rationality of the theory.

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