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]]. | |||
== 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]] | |||
Revision as of 15:22, 27 July 2013
The Kirsch equations describe the elastic stresses around the hole in an infinite plate in one directional tension. They are named after Ernst Gustav Kirsch.
Result
Loading an infinite plate with circular hole of radius a with stress σ, the resulting stress field is:
References
- Kirsch, 1898, Die Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre. Zeitschrift des Vereines deutscher Ingenieure, 42, 797–807.