裂纹群应力强度因子分析的广义参数有限元法
摘要
Stress intensity factors (SIFs) at crack tips of crack groups were solved by means of the finite element method with generalized DOFs. Firstly, based on the improved Williams series, the typical Williams elements in the singular region around the crack tip were set up. Then the global governing equations were formulated through intergration of the block matrices. Finally, with the undetermined parameters of the Williams series, SIFs at all the crack tips could be directly obtained. The influences of the parameters such as the distance between the centers of 2 adjacent cracks, and angle <em>γ</em> between the oblique crack and axis <em>X</em> on the calculation results were further analyzed through several examples. The results show that the proposed method can effectively overcome the defects of traditional finite element methods and it has higher accuracy and efficiency. Moreover, as for an infinite plate with multiple collinear horizontal cracks, when the ratio of the distance between the centers of 2 adjacent cracks to the half crack length is bigger than 9, the interaction among cracks can be ignored, so multiple cracks can be regarded as a single crack for calculation. For an infinite plate with an even number of axisymmetric oblique cracks, as angle<em> γ</em> increases, <em>K</em><sub>Ⅰ</sub> decreases, but <em>K</em><sub>Ⅱ</sub> first increases and then decreases.