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中文摘要：
基于反平面断裂是工程结构的一类重要断裂类型,利用常规单元或奇异单元分析Ⅲ型裂尖应力强度因子（简记为SIF）时存在诸多困难,首先建立Ⅲ型裂纹裂尖奇异区单元总体位移场的Williams级数表达式,利用普通有限元形函数建立奇异域子单元的局部位移场,然后根据总体场控制局部场的原则,建立裂尖奇异域分析的Williams单元,以直接确定Ⅲ型裂纹裂尖的SIF。在此基础上,研究Williams单元的径向离散因子、离散数和级数项这3个重要参数以及裂纹长度对裂尖SIF的影响,并给出这3个重要参数的建议值。研究结果表明：对于Ⅲ型裂纹应力强度因子,Williams单元具有很高的计算精度和效率。
英文摘要：
Based on the fact that the anti-plane crack is one of the basic and crucial fracture type for engineering structures, and there are some limitations for traditional finite element in determination of mode-Ill stress intensity factor （SIF）. Williams series for global displacement fields in singular region near the tip ofmode-III crack were presented. The local displacement field of subelement were approximated by means of the shaped function of conventional finite element method.According to the principle that the global field determines the local one, the Williams element was presented for singular region near the crack tip, so that the mode-III SIF could be directly determined by the coefficients of the Williams element. Three important parameters, i.e the radial scale factor, the number of subelement and the series term, were discussed for Williams element. The influence of the relative length of crack on the SIF was investigated. The results show that the Williams element can achieve high accuracy and efficiency in evaluation of SIF.
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