Stress matrix components in cylindrical coordinates for solids.

disla

Hi Everyone,

I’m working to derive the Stress Matrix in Cylindrical coordinates.
Attached is the preliminary result ( file ) in case you want to use the formulas.
Those who have the _OK have pass some basic tests I have been doing. Would be nice if some of you can test it with models in which you know the expected result.


It is valid for objects centered and aligned with the Z-Axis .
For a more generalized case with an arbitrary orientation and position it is needed to provide the axis of the object and a point on it which I have no idea how to derive it from data provided in the geometry ( maybe searching for flat curvatures or similar). I have seen a video of much more expensive software than Mecway in which the origin and axis input needs to be introduced by the user, so I do not think it is an easy problem to solve automatically.
The easy solution is to move the model and align it to match the default Z axis.

Can be useful for solid models such as Pressure Vessels, Storage Tanks, Nozzles or revolution objects.
It works also for shell models (only ccx) but I think it is not needed. Use “Stress in element coordinates” which is mostly the same than using cylindrical if you align properly the elements.

This is v.1.0. Just in case.

Victor

Thank for working out those shear components. I checked all 6 of them on an arbitrary shaped model with an arbitrary stress state by:

• comparing to stress in global coordinates in the XZ plane, and they're all the same as that on at least a couple of nodes and to at least the first 4 digits.
  
• comparing to the cylindrical stress values on an identical model rotated by various angles about the Z axis. They're all independent of rotation angle for the nodes and angles I checked.