Re: Thick walled spherical pressure vessel

In article <1159023876.831097.278350@xxxxxxxxxxxxxxxxxxxxxxxxxxx>, "Edward Green" <spamspamspam3@xxxxxxxxxxx> writes:
I'm trying to develop a description of a thick walled spherical
pressure vessel constructred of homogeneous and isotropic material,
subject to finite linear elastic deformation (stress and strain assumed
to be linearly related, but the deformations not necessarily small).

Thoughts so far:

We want to work with spherical shells of thickness dr.

We want to keep track of droh ("d roh"), the increment in the original,
undeformed, thickness of the material contained within dr, at least in
intermediate steps.

It will be sufficient to consider stress in the radial and tangential
directions, the latter isotropic in the tangential plane.

It will be sufficient to consider the material properties bulk modulus
and Poisson's ratio.

Each spherical shell will contribute an increment in radial stress by
the usual bubble condition.

We want to develop a continuity equation in r enforcing both mechanical
stability and the condition that the material started as an initially
unstrained elastic continuum.

I'm lazy. Have I left out anything? Any hints on how to set this up?

This probelm appears, fully solved, in Landau's "Theory of
Elasticity". Think you could find a copy?

Mati Meron | "When you argue with a fool,
meron@xxxxxxxxxxxxxxxxx | chances are he is doing just the same"
.

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