Karamba, buckling problem about intermediate configurations

Replies to This Discussion

Permalink Reply by Romain Mesnil on June 16, 2017 at 5:50am

Hi Davide,

the linear buckling analysis gives a critical load where 2nd order effects take over and when linear analysis (first order) ceases to be relevant. Therefore you need to perform a 2nd order analysis to get the intermediate steps between the linear calculation and the buckled configuration.

It is recommended to add a geometrical imperfection of small amplitude, usually you can take the shape of the first buckling mode or a combination of several buckling modes. If you look at a column with a vertical load, the 2nd order calculation with no imperfection will not predict buckling (because everything is perfectly balanced, so to say). If you add a tiny geometrical imperfection, the coupling between bending and axial force will be initiated and you will observe the transition from a linear behaviour to a nonlinear one.

If you want to have a further look at this issue, you can read a paper that I co-authored, for which we used Karamba. It's applied to the design of gridshell structures, Figures 5,6 and 7 are kind of related to your question.

 https://www.researchgate.net/publication/310347393_Linear_buckling_...

Cheers,

Romain 

Permalink Reply by Davide Girardi on June 16, 2017 at 8:08am

Hi Romain,

first of all I congratulate for the brilliant publication you linked me; moreover I want to thank you for the advise of adding the geometrical imperfection, it worked perfectly on the beam case study.

Now I am working on a similar case, but instead of a beam the case study is a rectangular shell; the target is the same, that is to obtain al the intermediate configuration of the shell between the non stressed situation to the buckled one; I have already tried to add a geometrical imperfection to the shell but this doesn't seem to work (I attach the definition I have created). Do you or anyone else have some suggestion on what to do?

P.S.: the target is to create something that works like the lamellar facade in this video ("One ocean" by Soma's)

https://www.youtube.com/watch?v=52gHW65lIiA 

Attachments:

• Study on Shell buckling.gh, 25 KB

Permalink Reply by Romain Mesnil on June 21, 2017 at 2:23am

Hi Davide,

thank you, I'm glad you enjoy the paper!

In the example you mention, I would say that it's a large displacement problem for beams (the shape changes a lot, so that equilibrium cannot be written on the initial configuration): this makes the analysis a bit tricky. In Finite Element programs, this is usually solved by an iterative method (modified Riks method), which is unfortunately not implemented in Karamba. There are other form-finding techniques, used for gridshells:

• Dynamic relaxation with kinetic or viscous damping. I used viscous damping and an implicit integration scheme (Bathe's method) for the form-finding of gridshells in this paper. For kinetic damping, you can look here. It was first used for beams by Sigrid Adriaenssens
• You can also look at Sina Nabei's PhD on the form-finding of twisted beams, and also the thesis of Frederic Tayeb (in french) and some papers in the link far below.

The main question remains the mechanical you are using: beam model (with torsion and bending) or shell model? In terms of solver, Kangaroo2 is powerful (although you don't have access to real engineering values, like Young's modulus), but there is no beam element with 4 or 6 degrees of freedom/node... Likewise, I'm not sure that shell elements (with bending) are implemented within Kangaroo2.

If you look for references of research on deployable structures for shading, you can look at the research at ITKE, but also a joint research effort between Princeton and l'Ecole des Ponts ParisTech.

http://thinkshell.fr/deployable-structures/

http://thinkshell.fr/form-finding-of-twisted-beams/

I hope this helps you...

Romain

Permalink Reply by Davide Girardi on June 21, 2017 at 2:29am

Hi Romain,

the mechanical model I am using is a shell mode; I solved the problem by giving a very small initial curvature to the shell and now I reached what I wanted with Karamba 2nd order analysis.

Thak you for your reply :)