Summary
A solution is derived appropriate to the application of pressure to the faces of a plane crack covering the outside of a circle in an infinite elastic thick plate. It is assumed that the conditions on the upper surface of the crack are identical with those on the lower surface and the free boundary is stress free. By using the theory of dual integral equations, the problem is reduced to that of solving a Fredholm integral equation of second kind. Expressions for various quantities of physical interest are derived for large values of the thickness of the plate by finding iterative solutions of the equation. For values of the thickness of the plate near unity, Fredholm integral equation has been solved numerically.
Zusammenfassung
Eine Lösung des Problems einer an den beiden Flächen eines über die Außenfläche eines Kreises sich erstreckenden ebenen Risses durch Druck beanspruchten dicken, elastischen, unendlichen Platte wird angegeben. Dabei wird vorausgesetzt, daß die Bedingungen an beiden Flächen des Risses dieselben sind und daß die beiden Plattenoberflächen spannungsfrei sind. Unter Verwendung der Theorie der dualen Integralgleichungen wird das Problem auf das der Lösung einer Fredholmschen Integralgleichung 2. Art zurückgeführt. Ausdrücke für verschiedene interessierende Größen werden für den Fall großer Plattendicke durch Iteration hergeleitet und für Werte der Plattendicke ungefähr gleich Eins durch numerische Lösung der Integralgleichung.
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Dhawan, G.K. The distribution of stress in the vicinity of an external crack in an infinite elastic thick plate. Acta Mechanica 16, 255–270 (1973). https://doi.org/10.1007/BF01179994
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DOI: https://doi.org/10.1007/BF01179994