應力強度因子是探討裂縫問題之重要參數，其定義式與裂縫尖端周圍的應力息息相關，不過不幸的是在裂縫尖端的附近會有奇異性，因此往往都需要將裂縫表面切割成相當細、相當多的元素才能夠準確的求出應力強度因子，再加上當裂縫延展後有所轉折時，想要求出正確的應力強度因子又更為困難了，因此本研究為了能夠計算像是轉折裂縫這種複雜的問題，將採取與路徑無關的H積分來做應力強度因子的計算，使計算應力強度因子中所需要使用到的高斯點物理量遠離裂縫尖端，避免奇異性問題的產生。
由實驗可以得知，當H積分的路徑越遠離裂縫尖端，則裂縫表面所需要切割的元素數將會減少，因為越不會受到裂縫影響，因此為了兼顧效率與速率，本研究除了原本舊有的任意圓形積分路徑，還推導出任意多線段的H積分路徑之輔助解，並且與內插法做結合，更利用已知的邊界解內插計算應力強度因子當中所需要的高斯點位移與應力，如此不但能夠遠離裂縫尖端避免奇異性，更是能夠利用邊界解沿著邊界做H積分的計算來求出應力強度因子。

The stress intensity factor is an important parameter to discuss the crack problem, and its definition is depended on the stress around the crack tip. Unfortunately, there will be singularity near the crack tip, so it is often necessary to build many elements on the crack surface. Thus, in order to calculate the stress intensity factors of turning cracks. The path independent H-integral will be used to calculate the stress intensity factor. Therefore, the integral path can be far away from the crack tip to avoid the problem of singularity.
Depend on the experiment result, when the path of H-integration crosses the crack tip, the requirement of element number on the crack surface will be reduced. Thus, in order to balance efficiency and accuracy, this research expect to derived the traction auxiliary solution of the arbitrary piecewise line H-integral path. Simultaneously, combined with the interpolation method, and calculate the displacement and stress on the Gaussian point which required to calculate the stress intensity factor. In this way, not only can avoid the singularity on the crack tip, but also the stress intensity factor can be calculated by the H integral around the boundary.

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