Membranes are endlessly fascinating, so I have to share some thoughts.
In your script, you are using Kangaroo to define an orthotropic mesh. This mesh however stays planar when I run the script, so I am not sure why you are formfinding it. Furthermore, you are fixing all naked mesh vertices which would lead to a dome-like shape, not sure how you want to achieve this shape in a membrane that will be pestressed (other than a snow load).
The flat membrane is then input into the Karamba sim. Generally a flat membrane is sth very numerically tricky. For example in 2D linear theory, the horizontal force of an arch / cable is H = (q * l^2) / (8 * f). When f → 0, H goes to ∞, which is impossible. You are using ThII, but I am not sure it will deliver accurate results, you would probably have to use ThIII. But that probably isnt what you are after.
Regarding the stress lines, you are in principle right, that the principal stress directions should not change when only magnitudes are changed and proportions stay the same. In your script this is however not the case, here is my logic (I might be wrong):
With the prestress state you are creating a hydrostatic stress state, which means that stresses are the same in all directions. It does not matter how the principal stress vectors are oriented - as long as they are perpendicular to each other - they will always be the same. Thats why you get such a strange stress line field with the Karamba component, as the script cant decide how to orient the principal stress vectors.
Here I would suggest not to use the stress lines, but the visualization of the principal stress vectors per element, they are a much better description of the stress state in 2D stress states. Furthermore, you can see that all principal stresses are the same, when using the Quick Graph
and it is also visible that all principle stress vectors are the same vector length, the corresponding Karamba component is ShellVecResults
. You can see, how the native Karamba principal stress lines are trying to create curves from given seeds in the given arbritrary stress state (I guess that must mean, that a hydrostatic stress is not properly orientable).
Now when the Gravity
is applied, you get a more meaningful stress line field, as there isnt a hydrostatic stress state anymore.