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STRESS DISTRIBUTION DUE TO A LOGARITHMIC SPIRAL DISLOCATION
NEW MEXICO UNIV ALBUQUERQUE ENGINEERING EXPERIMENT STATION
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The problem of the logarithmic spiral dislocation cut is solved. A new theory and postulations for determining the complex potential functions are presented. The logarithmic form of the multiplevalued term is adopted for its ease of manipulation. The condition on the complex potential functions are such that they are no longer required to vanish at the terminus of the cut only the displacement is required to be finite there. This relaxation should enable the theory to cover a wider range of problems. In the specific problem of the logarithmic spiral dislocation cut, the stress pattern about the inner circumference, from the analytical solution, was observed to be symmetrical about a line which passes through the origin of the circular cutout and the terminus point of the dislocation cut. Since the geometry of the physical problem is anything but symmetrical, the symmetry of the stress pattern is unexpected. The maximum shearing stress is found to be finite at the terminus of the dislocation cut. This phenomenon again contradicts the concept of the wedge action in solids. Author
APPROVED FOR PUBLIC RELEASE