A singular planar element with rotational degree of freedom for fracture analysis

A triangle singular planar element with corner node rotational degree of freedom (DOF) is developed for crack tip field analysis. On this element's two sides adjacent to crack tip, quarter point nodes with only tangent DOF are employed to generate tangential r1/2 displacement. Meanwhile, interpolated by both corner nodal translational and rotational DOFs, a normal displacement with r1/2 term is constructed on these two sides. On the non-singular side of this element a displacement function equivalent to that of Allman element is also proposed. Singularities predicted by this singular element have been proven obviously more accurate than those predicted by 5-node quarter-point element (QPE). For planar problem, though accuracy of this singular element is slightly inferior to that of 6-node QPE under coarse mesh, it rapidly approaches the latter with mesh refining. When applied in shell structure, models employing the proposed element can achieve more accurate results than those using 6-node QPE even with less total DOFs.