The collapsed cubic isoparametric element as a ingular element for crack probblems

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Abstract
For the 12−node quadrilateral isoparametric elements, it is shown that the inverse square root singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing the quadrilateral elements into triangular elements around the crack tip and placing the two side nodes of each side of the triangles at 1/9 and 4/9 of the length of the side from the tip. This is analogous to placing the mid−side nodes at quarter points in the vicinity of the crack tip for the quadratic isoparametric elements. The advantages of this method are that the displacement compatibility is satisfied throughout the region and that there is no need of special crack tip elements. The stress intensity factors can be accurately obtained by using general purpose programs having isoparametric elements such as NASTRAN.

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