本論文中探討功能梯度條板中存在絕熱裂紋的問題，條板的兩邊界有兩種不同的邊界條件型式，第一種型式為條板的兩邊界有固定溫度，第二種型式為兩邊界有穩態熱通量通過。條板中的材料性質假設為指數函數型式，變化的方向和裂紋面垂直，且根據疊加原理(superposition principle)，上述兩種邊界條件型式的問題均可各自分為條板中無裂紋的子問題，和條板中有裂紋存在的子問題進行討論。利用傅立葉轉換，可先將兩個子問題的溫度場求出，再將其代入混合邊界條件中得到一系列的奇異積分方程組，最後再以高斯-切比雪夫積分公式(Gauss-Chebyshev integration formula)和高斯-拉讓德求積法(Gauss-Legendre quadrature)進行運算，可求得裂紋周圍溫度場和熱通量強度因子的數值解。藉由探討條板邊界和材料非均質參數的變化對數值結果所造成的影響，可發現在固定溫度邊界條件下，裂紋周圍的溫度場分佈和熱通量強度因子的大小主要和條板中材料的熱阻有關；而在固定熱通量邊界條件下，裂紋周圍的溫度場和熱通量強度因子的大小明顯受到邊界效應的影響。本文中的研究結果，對於分析含裂紋的功能梯度條板，在高溫或需承受熱負載的環境中所產生的破壞問題有很大的助益。

In this paper, the problem of an insulated crack in a functionally graded strip with the prescribed temperature or steady-state heat flux at boundaries is considered. The material properties is in exponential form and vary in the direction perpendicular to the crack surfaces. According to the superposition principle, the problem with each boundary condition can be separated into two sub-problems, and then be reduced into a system of singular integral equations by using Fourier transformation. In order to solve the problem numerically, the Gauss-Chebyshev integration formula and the method of Gauss-Legendre quadrature are used. Numerical results are presented graphically to illustrate the influence of strip boundaries and material inhomogeneity on the temperature distribution around the crack and the heat flux intensity factors at crack tips. With prescribed temperature at boundaries, the variation of temperature distribution and heat flux intensity factors are related to different thermal resistances of the strip. With steady-state heat flux at boundaries, the variation of temperature distribution and heat flux intensity factors are obviously affected by edge effect. Consequently, the results of this study may be helpful in understanding the phenomenon of fracture in FGM strip subjected to thermal boundary conditions.

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