Collapsed 12-Node Triangular Elements as Crack Tip Elements for Elastic Fracture
ARMY ARMAMENT RESEARCH AND DEVELOPMENT CENTER WATERVLIET NY LARGE CALIBER WEAPON SYSTEMS LAB
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For the 12-node bicubic, 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 element into triangular elements around the crack tip and placing the two mid- side nodes of each side of the triangles at 19 and 49 of the length of the side from the tip. This is analgous to placing the mid-side nodes at quarter points in the vicinity of the crack tip for the quadratic, isoparametric element. 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. The use of 12-node isoparametric element program APES may be simplified by eliminating the special crack tip elements.