Effects of External Pressure on a Cone

AI Thread Summary
The discussion focuses on calculating hoop stress in a hollow conical structure subjected to external pressure. The user seeks established methods or analogous derivations for determining these stresses, similar to those used for uniformly-thick cylinders. They express dissatisfaction with generic search results and request more specific insights. The conversation highlights the need for specialized knowledge in stress analysis for tapered geometries. Overall, the inquiry emphasizes the complexity of applying known principles from cylindrical structures to conical forms under external pressure.
Shain3
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In my study I deal with tubulars frequently, and it is well known how to calculate stresses due to external pressure on a (hollow) uniformly-thick cylinder (i.e. a pipe).

Suppose now that I have a cone, tapering downward like a V, with a hollow cylindrical interior (like the inside of a pipe) to which I apply external pressure. Given that the pressure will act perpendicularly to the tapered exterior of the cone, is there a well-known way to compute stresses (specifically hoop stress) on the interior of this body? Or perhaps someone could point me in the direction of some analogous derivation that could get me started?
 
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To be honest I was hoping for something more insightful than a non-specific google search I'd already done.
 
The search results include the derivation you were asking about.
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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