本研究旨在探討二維異向性彈性材料於自重作用下之半無窮域應力場分布，採用邊界元素法（Boundary Element Method, BEM）為數值分析基礎，結合前人發展之體積力轉換公式與程式，建立具體可行之有限域建模策略。研究重點為評估有限域模型模擬半無窮域問題的可行性與準確性，並透過逐步放大模型尺寸與捨去部分區域，成功建立一套兼具效率與穩定性的簡化模型架構。
在數值模擬方面，為驗證本簡化方法之可行性，設計多項範例進行驗證與探討，包含均布與非均勻平面載重、地基上建築物作用、多孔洞排列效應與孔洞襯砌材料設計等。模擬結果皆展現良好的穩定性與物理一致性，能準確反映幾何、材料與施力條件變化對孔洞周圍應力場之影響。綜合分析結果顯示，本研究所建構之有限域邊界元素模型不僅可有效模擬二維異向性材料在自重下之行為，亦具備作為模擬半無窮域分析之簡化模型。

This study aims to investigate the stress field distribution in a two-dimensional anisotropic elastic half-infinite domain under self-weight. The Boundary Element Method (BEM) serves as the core numerical approach, combined with previously developed formulations and codes for body force conversion to establish a feasible finite-domain modeling strategy. The primary objective is to evaluate the feasibility and accuracy of using a finite-domain model to simulate half-infinite domain behavior. By gradually enlarging the model size and eliminating unnecessary regions, a simplified model framework with both computational efficiency and stability is successfully developed.
To validate the proposed simplification method, several numerical examples are designed and analyzed, including uniform and non-uniform surface loading, structural loading on the ground surface, interactions between multiple circular holes, and lining material configurations. The simulation results exhibit good stability and physical consistency, accurately capturing the effects of geometry, material properties, and loading conditions on the circumferential stress distribution around holes. Overall, the proposed finite-domain BEM model demonstrates its effectiveness in simulating the behavior of anisotropic materials under self-weight and serves as a simplified and efficient alternative for half-infinite domain analysis.

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