Closed-form solution of the equations of caustics about cracks in fracture mechanics |
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| Authors: | NI Ioakimidis |
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| Institution: | Chair of Mathematics B'', School of Engineering, University of Patras, P.O. Box 1120, GR-261.10 Patras, Greece |
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| Abstract: | The shape of a caustic and its initial curve about a crack in fracture mechanics for plane elastic media is defined by a pair of equations, the first of which does not in general possess a closed-form solution, being of fifth or higher degree and, frequently, transcendental. A closed-form solution of this equation is obtained on this basis and after an appropriate modification of the method of Burniston and Siewert. An application to the problem of a straight crack under tensile loading at infinity is made and the diameters of the caustic and its initial curve are evaluated analytically and numerically with excellent accuracy after the solution of an equation of fifth degree in closed-form. |
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