中文摘要：

为了在大型结构分析中考虑小裂纹或以小的代价提高裂纹附近求解精度,该文建立了分析三维裂纹问题的自适应多尺度扩展有限元法。基于恢复法评估三维扩展有限元后验误差,大于给定误差值的单元进行细化。所有尺度单元采用八结点六面体单元,采用六面体任意结点单元连接不同尺度单元。采用互作用积分法计算三维应力强度因子。三维Ⅰ型裂纹和Ⅰ-Ⅱ复合型裂纹算例分析表明了该方法的正确性和有效性。

英文摘要：

To consider small cracks in the analysis of large structures or to improve the accuracy of modeling around the cracks at a low cost, an adaptive multiscale extended finite element method（XFEM） for modeling three-dimensional crack problems is proposed. The posteriori error estimation for three dimensional XFEM is evaluated using the recovery method, and the elements with relative errors greater than a specified value are refined accordingly. An eight-node hexahedron element is used for any scale element, and an arbitrary-node hexahedron element is used to link differently scaled elements. The three-dimensional stress intensity factors are evaluated using the interaction integral method. Numerical examples including a three-dimensional mode Ⅰ crack problem and a three-dimensional mixed mode Ⅰ-Ⅱ crack problem are given to illustrate the correctness and efficiency of the proposed method.