本文以無網格法計算裂縫之應力強度因子，並考慮材料韌度之隨機性進行裂縫成長之隨機性分析。在應力強度因子計算上考量裂縫尖端處之應力奇異性，在裂縫尖端附近區域於位移函數中加入應力奇異性項次，於裂縫尖端處外則僅使用一般再生核形狀函數，利用微分再生核近似法(Differential Reproducing Kernel Approximation Method, DRKM)配合置點法建立聯立方程組以最小平方法解得節點變位及應力強度因子。在數值算例中，則分析求解不同型式裂縫問題，包括邊緣水平裂縫、邊緣傾斜裂縫、中央水平裂縫、中央傾斜裂縫以及邊緣雙裂縫等問題，並討論其分析精度。
在裂縫成長的隨機性分析上，則考量材料韌度受製造過程及其他因素影響下，假設材料韌度為一隨機性分布，並以數值方式模擬材料韌度之隨機性，再依應力強度因子及材料韌度決定裂縫成長方向，以統計方法分析於該隨機性影響下裂縫成長方向之隨機變異性；最後以隨機方式模擬裂縫成長軌跡並對照最大環向應力準則之軌跡，以探討材料韌度之變異性等因素對裂縫成長之隨機性的影響。

In this thesis we use a meshless method to compute the stress intensity factor of crack and develop a stochastic model for predicting of crack propagation which is based on material toughness uncertainty. The meshless method is adapting point collocation with differential reproducing kernel approximation method (DRKM) to capture the stress singularity near the crack tip, the singular term will be added to the crack tip to model the high gradient of the stress.
In the stochastic modeling of crack propagation, we consider the uncertainty of material toughness by supposing the material toughness near the crack tip have random properties along the circumferential direction, thus the direction and length of crack propagation will be determined by the stress intensity factor and the material toughness along the circumferential direction.
The trajectory of crack propagation of the stochastic model will be compared with maximum circumferential stress criterion to illustrate the effect of stochastic properties of material toughness.

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