Summary
The problem of a V-notched isotropic elastic half-plane under generalized plane stress or plane strain conditions can be reduced, by using the complex variable technique, to a complex Cauchy type singular integral equation along one of the V-notch edges. This equation can be numerically solved by use of the Gauss-Jacobi method and reduction to a system of linear equations. The values of the stress intensity factorK I at the V-notch tip were evaluated for some notch angles in the case of pure tension and the results obtained are in accordance with the available results in the case of a V-notched finite isotropic plane elastic medium. The difficulties faced in evaluatingK I are investigated and a discussion on them is made. The method is also applicable even when the V-notch edges are curvilinear and their loading arbitrary.
Zusammenfassung
Das Problem der V-förmig gekerbten, isotropen, elastischen Halbebene unter generalisierten ebenen Spannungs-, oder ebenen Verzerrungsbedingungen kann, mittels der Methode der komplexen Variablen, zu einer komplexen singulären Cauchy-Integralgleichung entlang einer der Kerbkanten reduziert werden. Diese Gleichung läßt sich mittels der Gauß-Jacobi-Methode und Reduktion zu einem System linearer Gleichungen numerisch lösen. Die Werte des spannungsintensitätsfaktorsK I am Kerbgrund werden für einige Kerbwinkel für reinen Zug ermittelt. Die Ergebnisse stimmen mit den verfügbaren Resultaten für den Fall eines V-förmig gekerbten, finiten, isotropen, ebenen, elastischen Mediums überein. Die Schwierigkeiten für die Ermittlung vonK I werden betrachtet und diskutiert. Die Methode ist ebenso anwendbar, wenn die Kerbkanten gekrümmt und die Belastung beliebig ist.
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Theocaris, P.S., Ioakimidis, N.I. The V-notched elastic half-plane problem. Acta Mechanica 32, 125–140 (1979). https://doi.org/10.1007/BF01176138
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DOI: https://doi.org/10.1007/BF01176138