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The hypersingular Somigliana identity for the stress tensor is used as the basis for a traction boundary integral equation (BIE) suitable for numerical application to nonplanar cracks and to multiple cracks. The variety of derivations of hypersingular traction BIE formulations is reviewed and extended for this problem class. Numerical implementation is accomplished for piecewise-flat models of curved cracks, using local coordinate system integrations. A nonconforming, triangular boundary element implementation of the integral equations is given. Demonstration problems include several three-dimensional approximations to planestrain fracture mechanics problems, for which exact or highly accurate numerical solutions exist. In all cases, the use of a piecewise-flat traction BIE implementation is shown to give excellent results.
analytical methods, stress intensity factors, three dimensions, linear elastic fracture mechanics, boundary integral equations, boundary element methods, fracture mechanics, fatigue (materials)
H. Fort Flowers Professor, Vanderbilt University, Nashville, TN
Assistant professor, Politecnico di Milano, Milan,