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Two types of finite elements which can adequately represent the singular stress state at the tips of cracks in plane elastic structures are presented. By combining these special crack tip elements with more conventional finite elements, a more efficient analysis of crack structures is possible. One element is circular in shape and its imposed displacement pattern is that of the four leading symmetric terms of the Williams stress function. The other element is triangular in shape and its imposed displacement pattern is that associated with the crack tip singularity. The convergence and efficiency of these elements is studied.
fractures (materials), stresses, strains, loads (forces), cracks, elastic properties, plane geometry, matrix methods, elastic analysis, analytic geometry, displacement, stress analysis
Westinghouse Research Laboratories, Pittsburgh, Pa.