Stress in cylindrical coordinate system

[Johanna Meier]

Hi all,

I am having a conceptual issue and hope someone might be able to help me out on it.

My question is, if there is a way to transform stresses from cartesian to cylindrical coordinates so that I can examine, for example, the circumferential stress in a tube? A setup I had in mind is similar to step 18 in geometry, but instead of applying a load on top of the cylinder I would pressurize the inside. Or step 44 but replacing the geometry by a cylinder.

My initial idea was to somehow rotate the stress at a quadrature point during postprocessing from the global cartesian coordinate system to a local cartesian system of which one axis is aligned with the radial direction and another one with the z-direction. The remaining axis would be tangential to the "theta" axis (circumferential direction). Does something like that make sense at all?

How are situations like this handled in practice? Any hints would be welcome!

Best,

Johanna

[Jean-Paul Pelteret]

Dear Johanna,

What you describe here makes sense. Such a transformation is described at this link (see section 2.7 "Converting tensors between Cartesian and Spherical-Polar bases". I think that the circumferential stress would then be S_{\theta \theta}, according to their notation). Its just that (in general) your rotation matrix would have to change for each evaluation point, as the radius and angle with respect to the axis would change.

We have a couple of functions already implemented that might help you to achieve this:

• Rotation matrices (2d,3d): https://dealii.org/current/doxygen/deal.II/namespacePhysics_1_1Transformations_1_1Rotations.html#a68bba56f6c1ebfbb52f871996df965ae
• Basis transformation: https://dealii.org/current/doxygen/deal.II/namespacePhysics_1_1Transformations.html#a626b00a6e08a79449cbf120cb3e81fdb

I hope that this helps you.

Best,

Jean-Paul

--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups "deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to dealii+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/57d95553-e531-4030-b9b8-266fc394da96n%40googlegroups.com.

[Johanna Meier]

Dear Jean-Paul,

Thank you so much for your response and the provided links! That definitely helped a lot. 

Best,

Johanna