Dear Johanna,
What you describe here makes sense. Such a transformation is described
at this link
<https://www.brown.edu/Departments/Engineering/Courses/En221/Notes/Polar_Coords/Polar_Coords.htm>
(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
On 2022/10/01 11:07, Johanna Meier wrote:
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
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