中文摘要：

结合Ⅱ型断裂问题，研究建立了裂尖区应力强度因子计算的Williams广义参数单元和过渡单元。结合Williams级数解和广义参数有限元法，研究建立了弹性断裂问题的Williams广义参数单元计算格式；同时为了方便连接奇异区的Williams单元和常规区域的普通等参单元，建立了过渡单元模型。结合算例详细分析了计算模型中径向离散因子、离散数以及Williams级数项对计算结果的影响，并给出了建议值，同时研究了矩形板尺寸对Ⅱ型应力强度因子的影响，证实了解析解的局限性。计算结果表明．由于Williams单元位移模型中含有与应力强度因子直接相关的参数，所以可以避免传统有限元法需通过其他物理量间接计算应力强度因子的缺陷．且Williams单元具有较高的精度，构造使用方便。

英文摘要：

The Williams generalized parametric element and the transition element are developed for mode Ⅱ crack problems. The relationship between the leading coefficients of the Williams series and the stress intensity factor is obtained. The finite self-similar elements are generated in the singular domain around the crack tip. Based on the Williams series and the method of finite element with generalized degrees of freedom, the global and local displacement fields near the tip are described by Williams expansion series and the conventional shape function of the FEM, respectively. The Williams element and the transition element are proposed, respectively. The influence of the radial discretizing ratio, radial partition number in singular domain and the number of the terms of the Williams expansions on computing precision are illustrated, their design values are presented. The influence of the plate＇s dimensions on the stress intensity factor is analyzed. Several examples are used to demonstrate the accurate and convenient determination of the stress intensity factor by the proposed element.