On singular, nine-noded, distorted, isoparametric elements in linear elastic fracture mechanics

Abstract Distorted, nine-noded, Lagrangian, isoparametric elements are studied to determine if stress intensity factors can be calculated more accurately with these elements than with eight-noded quarter-point elements. To achieve square-root singular stress behavior in the nine-noded element, the mid-side nodes adjacent to the crack tip are moved to the quarter-point and the nodal point within the element is positioned along the element diagonal, at least at the quarter-point. Several optimal positions for this node are determined. Through two numerical examples, it is seen that the eight-noded element performs nearly as well, and sometimes better than the nine-noded element.