Buckling Near A Hole in an Infinite Plate Under Tension.
Costello, Robert Graham
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If an infinite flat elastic plate containing a circular hole is subjected to a loading which amounts to simple uniaxial tension at distances remote from the hole, the classical solution by Kirsch provides an evaluation of the stress components throughout the plate, provided the loading is sufficiently small. However, if the tensile loading is progressively increased, there comes a point when Kirsch's solution becomes invalid, either through inelastic action at the most highly stressed regions in the plate, or through buckling of the plate from its original plane. The question of buckling under these circumstances has previously been discussed only by Danis, who dealt experimentally with finite plates, and by Pellett who performed a theoretical study of an infinite plate. The present thesis pinpoints and corrects some errors in Pellett's analysis, and leads to the result that buckling impends when the tensile stress reaches the value Scr = 1.720 E (t/a)sq. where E denotes Young's modulus and t/a denotes the ratio of plate thickness to hole radius. This evaluation is for Poisson's ratio v = 0.3, a commonly used value, but evaluations are also made for other values of v, indicating that the variation with respect to v is quite small.
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