Progressively measurable process: Difference between revisions

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The '''Kirsch equations''' describe the [[Elasticity (physics)|elastic]] [[stress (physics)|stresses]] around the hole in an infinite plate in one directional tension. They are named after [[Ernst Gustav Kirsch]].
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== Result ==
 
Loading an infinite plate with circular hole of radius ''a'' with stress ''σ'', the resulting stress field is:
 
<math>
\sigma_{rr} = \frac{\sigma}{2}\left(1 - \frac{a^2}{r^2}\right) + \frac{\sigma}{2}\left(1 + 3\frac{a^4}{r^4} - 4\frac{a^2}{r^2}\right)\cos 2\theta
</math>
 
<math>
\sigma_{\theta\theta} = \frac{\sigma}{2}\left(1 + \frac{a^2}{r^2}\right) - \frac{\sigma}{2}\left(1 + 3\frac{a^4}{r^4}\right)\cos 2\theta
</math>
 
<math>
\sigma_{r\theta} = - \frac{\sigma}{2}\left(1 - 3\frac{a^4}{r^4} + 2\frac{a^2}{r^2}\right)\sin 2\theta
</math>
 
==References==
 
*Kirsch, 1898, ''Die Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre.'' Zeitschrift des Vereines deutscher Ingenieure, '''42''', 797–807.
[[Category:Solid mechanics]]

Latest revision as of 12:36, 30 November 2014

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