用拉格朗日等参数单元计算应力强度因子

 本文证明了在二次或三次拉格朗日等参数单元中,假使边上点和内节点移动适当的位置即可产生奇异性。在标准的拉格朗日等参单元中,使一边缩并成一点,成为三角形单元,再适当的选择边上点和内节点的位置,可以在单元的角点产生奇异性,因而,可以计算应力强度因子。在奇异元外面,适当移动边上点和内节点可以形成过渡元,可得到较精确的结果。通过几个例子表明,用这种奇异元,只要较少的单元数和节点数就能得到较精确的结果。

CALCULATION OF STRESS INTENSITY FACTORS USING LAGRANGIAN ISOPARAMETRIC FINITE ELEMENTS

Tt is proved in this paper that a singularity occurs in quadratic or cubic Lagrangian isoparametric Unite elements when the side-nodes and internal nodes are displaced properly from their normal position. As the quadrilateral elements are collapsed into triangular elements around the crack tip and the side-node and internal node positions on standard la-grangian isoparametric elements are so chosen that the singularity occurs exactly at the corner of an element, it is possible to obtain inverse square root singularity of the strain field at the crack tip. In addition, a transition element can be easily constructed by shifting side-nodes and internal nodes to some properly calculated points. Stress intensity factors may be computed with considerably high accuracy by using transition element between crack-tip singular elements and remaining non-singular elements. Several numerical examples show collapsed Lagrangian isoparametric singular element gives excellent results even when a comparatively few elements and nodes are used.