Hello everyone,
I would like to compare two shells with each other.
One is a parabolic hyperboloid and the other is a slightly modified form of the first.
I am surprised that I have a huge displacment, which cant beand that the two shells are so similar. Also I would have expected a bigger difference between those forms, since one has more curvature than the other.
They are about 100x100m. in planview and have two supports:
Assuming that it’s in compression in both directions, amount of ability to resist gravity is proportional to the curvature. The ‘mathematical’ surface has +1 curvature in one direction and -1 curvature in the other direction, meaning one produces an +1 upward force and the other produces a -1 downward force, canceling out each other. So, you need to make the curvauture in one direction (the direction that draws an arch between the supports) larger than the other. Even if you did so, you need to reinforce the boundary edges all the way around and that reinforcement might be far bulkier than you think,
If you stick to a ‘mathematical’ hyperbolic surface with two directions give the same amount of curvatures except that the signs are flipped, perhaps simply adding edge beams may work. In that case, you should see tension forces flow in one direction and compression forces flow in the other directtion. (even if curavture is +1 vs -1, when stresses are +1 vs -1, the reaction force is +1+1=+2, which is different from pure-compression cases.)
Yes. I put a reference in the original post.
Thanks for your extensive answer and detailled explication! I guess I will have to put somethin below the high points, as in the pictures, probably.Not sure
sorry for bumping this. I am still not sure if I set up the Model right, and it would be great to get a quick feedback from an expert, if any possible:)
Hi @Baris,
thanks for this very interesting example!
Please find attached an improved version of your definition: 240314_ShellKaramba_Internalized_cp.gh (52.5 KB) where I did the following:
scale down the geometry by a factor of 0.01 since K3D by default assumes geometry input to be given in meters.
move the structures closer to the origin of the coordinate system. Sometimes GH has problems when geometry lieas far off from zero.
The structures are still nearly kinematic because they are each supported in two nodes only. This is visualized in the definition above using the Eigenmodes-component.
An node has no spacial extension and is infinitely small. Also, shells in K3D have no drilling stiffness - that is stiffness against rotation about an axis perpendicular to the shell element’s middle plane. One solution would be to support a larger number of nodes at the edges. This would however cause a fixed support there. Alternatively you could add beams at the naked shell edges near the supports - or also embedded in the shell. These beams distribute the support reactions into the shell avoiding stress singularities and can be properly supported at single node supports.
thank you so much for your detailed answer! It is really nice to see the difference for me
1)I did suspected, that there is something wrong with the scale
2)vertex precision and float numbers- I should have been aware of
