以下为句子列表：
英文: By virtue of the stochastic bifurcation theory,the transition of the atom movement at a crack tip in fatigue damage system is investigated.Using the singular point theory of one-dimensional diffusion process and the stochastic averaging approach of energy
中文: 采用随机分叉理论，探讨疲劳损伤系统裂尖粒子运动性质突变.利用一维扩散过程的奇点理论，并结合能量包络的随机平均法，建立了随机扰动的疲劳损伤同宿分叉系统裂尖粒子运动模型,通过研究奇异边界的扩散指数、漂移指数以及特征指数特性，考查疲劳损伤裂尖粒子运动的同宿分叉系统受参激白噪声影响的分叉行为.
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英文: Furthermore, the effects of the stress intensity factors on all strain components at crack tip are investigated.
中文: 进而探讨了应力强度因子对于非局部各个应变分量的影响。
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英文: It is shown that the singularity of the strain field at the crack tip is smoothed in non-local theory.
中文: 根据基于不同形式权函数的非局部理论，分析了Ⅰ-Ⅱ型复合裂纹尖端的应变场。
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英文: Positive electrode and negative electrode that execute spanning crack prevention are simulated as the source point and merged point, so the temperature field owing to the concentration of current around the crack tip is educed at the moment when the curre
中文: 将实施跨越止裂时的正、负电极比拟为电流场中的源和汇，从而导出了在瞬间电流作用下，裂纹尖端附近区域因绕流而形成的温度场。
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英文: Stress analysis in variation states at crack tip and notch crown tip is presented.
中文: 摘要分析了椭圆孔口端点和裂纹端点处的变动态应力。
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