中文摘要：

通过改变三维8结点六面体等参单元的结点位置、结点数目和形函数，构造了一种12结点三维等参奇异单元，该单元的应力场具有1/√r奇异性，可以模拟裂缝前沿的奇异应力场；该单元的位移模式在其中两个坐标方向是线性变化的，因此．该单元与线性单元连接时不需要过渡单元，仍能保证交界面位移协调，克服了20结点三维等参奇异单元不能与线性单元协调连接的缺陷；文章最后将该奇异单元布置在裂缝前沿，应用有限元法计算了三点弯曲梁预制裂缝前沿的应力强度因子，该结果与规范公式计算值基本一致。

英文摘要：

A new type of three-dimensional isoparametric singular element was created by altering the node amount, node position and the shape function of the three-dimensional 8-node isoparametric ele ment. This new type of element has the stress field of 1/√r singularity, with which the element of this type can be applied to simulate the singular stress field near the crack. With the linear displacement pattern along two coordinate directions, the element can link with the linear elements without using the transition elements, the common boundary of which is harmonious in displacement. Finally, the stress intensity factor of the crack of the three-point ement laid along the crack front, the result of bending beam was calculated by FEM with this type of el which basically accords with the data computed by the formula.