Summary
The semi-infinite plate which is rigidly stiffened at a part on the boundary and with a crack originating from an end of the stiffened edge is analyzed as a mixed boundary value problem in a plane elastic problem. A complex variable method and a rational mapping function are used for the analysis. A closed solution is obtained. The rational mapping function is formed as a sum of fractional expressions. Distributions of stress and displacement in the neighbourhood of the crack and the stiffened edge are investigated for the state before and after occuring of a crack. Stress intensity factors which are important in linear fracture mechanics are obtained for various crack lengths.
Übersicht
Eine Halbscheibe, die an einem Teil ihrer Berandung verstärkt ist und einen Haarriß hat, der von dem einen Ende des verstärkten Randes ausgeht, wird als ein gemischtes Randwertproblem innerhalb eines Scheibenproblems analysiert. Eine Methode komplexer Veränderlicher und eine Abbildungsfunktion werden zur Analyse verwendet. Eine geschlossene Lösung läßt sich angeben. Die Abbildungsfunktion wird als Summe von Partialbruchzerlegungen dargestellt. Spannungs- und Verschiebungs verteilung in der Umgebung des Risses werden berechnet. Der verstärkte Rand wird auf den Zustand vor und nach dem Entstehen eines Risses untersucht. Spannungsintensitätsfaktoren, die in der linear-elastischen Bruchmechanik von Bedeutung sind, werden für verschiedene Rißlängen ausgerechnet.
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Hasebe, N. Uniform tension of a semi-infinite plate with a crack at an end of a stiffened edge. Ing. arch 48, 129–141 (1979). https://doi.org/10.1007/BF00536837
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DOI: https://doi.org/10.1007/BF00536837