在解決無窮域和半無窮域的問題時，邊界元素法是一種較為有效率的數值模擬方法。有眾多學者，如Pan、Chen and Amadei [1]、Wei and Ting [2]和Hwu [3]都有提出半無窮域基本解，本論文此次研究目的是運用前人所設定的基本解進行延伸整理出異向性熱彈問題無窮域及半無窮域基本解推導[20]，並運用Fortran熱傳分析程式的溫度以及溫度梯度結果帶入到本論文的熱彈分析中。
此次研究計算時不需要建立無窮遠處之邊界以維持邊界元素法的特性，更重要的是，本篇論文驗證了經由傅立葉轉換後可以消除原本熱彈邊界方程式在面對多域問題時所產生的額外線積分，在分析無窮域和半無窮域熱彈問題時，我們會分別運用有限域和無窮域之邊界積分式設置大板挖孔的建模，以模擬出無窮域和半無窮域之情境與本篇論文推導之邊界積分式分析結果進行比較。

When tackling the challenges posed by infinite and semi-infinite domains, the boundary element method stands out as a more efficient numerical simulation technique. Numerous scholars, including Pan, Chen, and Amadei [1], Wei and Ting [2], and Hwu [3], have proposed fundamental solutions for semi-infinite domains. Ke[21] is to extend and organize the derivation of fundamental solutions for anisotropic thermoelastic problems in infinite and semi-infinite domains, building upon the groundwork laid by previous researchers. Additionally, the temperatures and temperature gradients obtained from Fortran thermal analysis programs are integrated into the thermoelastic analysis presented in this paper.

In this study, there is no need to establish boundaries at infinity to maintain the characteristics of the boundary element method. More importantly, this paper validates that Fourier transformation can eliminate the additional line integrals generated by the original thermoelastic boundary equations when facing multi-domain problems. When analyzing thermoelastic problems in infinite and semi-infinite domains, finite domain and infinite domain boundary integral formulations are respectively used to model large plate perforations, simulating scenarios of infinite and semi-infinite domains. The results obtained from the boundary integral analysis are then compared with those derived from the developed boundary integral formulations in this paper.

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