Reaction forces for membrane wrong

Hi :slight_smile: I have modelled a membrane 3mx3m with prestress. Now I added a surface load of 1kN/m2 but my summed up reaction forces are super small: {-1.7001e-7,-1.6466e-7,0.324299} kN
In my opinion that makes no sense as I have 9kN vertical resultant in total but I cant find my mistake - maybe anyone can help me here ?

debugging.3dm (130.8 KB)
debugging.gh (57.6 KB)

Hi @Niclas_Brandt,
sorry, this seems to be a bug in Karamba3D. I will try to fix it a.s.a.p.
Thank you very much for the example!
– Clemens

Ok cool:)) And I have another question - maybe you can also help me here. If I load the membrane with only prestress and gravity the Prinicpal stress lines tend to change when I change the pre stress. But they dont really change when i change the gravity load. I thought PSL’s are independent from the magnitude of loads ? Can you maybe explain why the prestress change the rincipal stress lines ?
debugging_2.3dm (251.9 KB)
debugging_2.gh (197.1 KB)

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.

Hi @rudolf.neumerkel thanks a lot for the explanation:)) It makes sense with the planar stress that it is numerically tricky especially for a square flat sheet. The reason for that I did it was just because i wanted to tension a flat membrane to use it as formwork for concrete:) thats why I was interested in the stresses for that state. And The formfinding in kangaroo I had to do as karamba otherwise gave me errors. But yes I agree gravity loads help :))

Hi @Niclas_Brandt,
when using second order theory with small displacements assumption (like in the ThII-component of Karamba3D) the out of plane gravity load does not impact the in-plane normal forces. The reason is that the in-plane strains are proportional to the square of the transverse displacement differences and thus are neglected.
– Clemens