Summary
The plane elastostatic problem of a symmetrically branched crack in an infinite isotropic body loaded by normal stresses perpendicular to the main crack axis at infinity was studied by using the method of complex potentials. The problem was reduced to a system of three singular integral equations. By means of an approximation of the integrals through the Gauss and Lobatto numerical quadrature procedures, these singular integral equations were transformed into a system of linear equations, which can be readily solved. The stress intensity factors at the tips of the branched crack were computed directly from the solution of the above system of linear equations and were compared with the already existing experimental solutions.
Zusammenfassung
Es wird das ebene elastostatische Problem eines symmetrischen gegabelten Risses für den unendlichen, isotropen und mit senkrecht zur Riss-Hauptachse belasteten Körpers untersucht, und zwar unter Anwendung der Methode der komplexen Potentiale.
Das Problem wird auf ein Systen von drei singulären Integralgleichungen reduziert und weiter auf ein System linearer Gleichungen transformiert, vermittelst einer Näherung der Integrale mit Hilfe des leicht lösbaren numerischen Quadraturverfahrens von Gauss und Lobatto. Die Spannungsintensitätsfaktoren in den Spitzen des gegabelten Risses werden rechnerisch ermittelt und mit experimentellen Ergebnissen verglichen.
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Theocaris, P.S., Ioakimidis, N. The symmetrically branched crack in an infinite elastic medium. Journal of Applied Mathematics and Physics (ZAMP) 27, 801–814 (1976). https://doi.org/10.1007/BF01595131
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DOI: https://doi.org/10.1007/BF01595131