This might be a very easy question but I am new to karamba so I don’t really know. I have found the buckled shape of a shell structure using second order deformations. However, I now need the exact load (in kN) under which it buckles to produce the first buckling mode. I am sure there is an easy solution to this but I cannot seem to find it.

My problem is that for an applied load of 2.5kN, the structure does not buckle and gives an buckling load factor of 1.551069. but when I multiply the 2.5kN by 1.5 (instead of 1.551069 for a load which almost reaches buckling) and get roughly 3.75 kN, the structure buckles and gives me 0.769919. I have attached screen shots below to illustrate my problem.

I do not know why the structure is not making sense.

Thanks for your reply.
I do not think I understand what you mean exactly. There was no form of buckling with the 2.5kN/m2 loading as the program showed no buckling modes but a buckling load factor of 1.55.
However, when the 3.75kN/m2 were applied, the program showed four buckling modes, even though the 3.75 values is less than the 2.5 multiplied by the actual buckling load factor of 1.55.

I agree with you, normally if the distribution of your internal forces in the structure is exactly the same, between a 2.5 kN model and another at 3.75 kN, the buckling factor should indicate the factor you need to apply on your loads to achieve stability

But in your model is not.
On your 2.5kN model, your first buckling mode, look like a global buckling mode, with 6 “waves”
On your 3.5kN model, your first buckling mode is a local buckling of your grid.

This is why you cannot find the right relationship between the buckling factor and your load values.

But on your 3.5 kN model, if you are looking for more buckling mode, you can find the 2nd buckling which has approximately the same deformation as your first buckling mode on the 2.5 kN model.

I don’t really explain why it’s not the same thing, but it means that you don’t have the same distribution of effort (equivalent) on each bars.
Maybe we can explain this by the overall stiffness of the grid, which is affected by your load, and therefore can change the distribution of your forces.

If you try a test on a single span beam, the relationship between the buckling factor and the value loads will be checked.

Hello @michela_m,
thank you for your example and for providing the definition. It looks like there is a bug which causes the problem. I will try to locate it.
Best,
Clemens

sorry that it took me so long to come back to you.

The source of the problem in your definition is, that the calculation of the NII values in the ‘AnalyzeThII’-component do not converge because the system of equations is not postive definite any more due to buckling. Thus the NII values which control buckling are not correct.

What’s more the NII values change from calculation run to calculation run because the solver in Karamba 1.3.2. does not return numerically reproducible results in that situation. This has to do with how the solver uses parallel processes. This problem will be solved in the next release of Karamba3D.

As a workaround try to reduce the external loads so that the initial load-level is closer to the theoretical buckling limit.