Negative buckling factor 1

[ThisIsMe86]

Hi all,

Please can anyone help me interpret negative buckling factor? Also, how can I change my deck to show me positive buckling factor?


Thanks,

Arun

 

[ThisIsMe86]

I have found the solution and I am writing it here for helping others.

Negative buckling factor is a NON_PHYSICAL thing which indicates that buckling occurs when the loadcases are reversed.

They way I tweaked my input deck to show me only positive buckling factors is by asking the solver to start looking for buckling factors above a very low positive value (0.001). Earlier, I asked the solver to report only positive buckling modes by setting the value mentioned to ZERO. But apparently, the solver doesn't do it.


- This is me

 

[jhardy1]

Sometimes, negative buckling factors are very real, physical considerations - when the load can be reversed (even if only partially).

Consider a thin-walled tank or silo, which is normally filled with fluid or powder which exerts an outward pressure loading. Your FEA package should predict a very small negative buckling factor for this load case - which indicates the tank wall would buckle under a small external pressure (or a very small partial internal vacuum). This is a very real phenomenon, which can arise when the tank or silo is emptied rapidly, but the air inlet is constrained so that air can't flow in as fast as the tank contents are emptied, causing a catastrophic failure of the tank.

You can test this yourself - take a large PET milk bottle or soft drink bottle (1.5 or 2 litre size is good), fill it with water, and invert it over the sink with the cap off. The water escapes faster than air gets back in, the pressure inside the bottle drops below ambient, and the bottle wall "implodes". Now assume this was a railway oil tanker, and someone steam cleaned the inside but forgot to ensure the pressure relief valve was open ...

http://www.youtube.com/watch?v=2WJVHtF8GwI&feature=related

Don't always be too quick to disregard negative buckling factors!

http://julianh72.blogspot.com

 

[crisb]

This is a topic which has been raised before a number of times on here.

I am not convinced that the negative load factors relate either to real life situations, or that they represent buckling modes with the direction of load reversed.

Negative load factors do not occur routinely in eigenvalue buckling analyses, and are the exception rather than the norm. I would expect them to occur routinely if the above comments were true.

My experience is that they are more prevalent in certain software, with certain elements, and with badly conditioned mesh.

Incidentally, sometimes I alter the value of applied loads so that the load factor is above 1, and error messages are not displayed and the run terminated.

 

[ESPcomposites]

Crisb,

Perhaps you could have a look at how numerical methods are used to solve an eigenvalue problem. A basic iterative solver method can be used to clearly show why a negative eigen value occurs, and how it relates to a structure.

Negative eigen values are not a function of "certain software, certain elements, or a poor mesh". They are simply found during the iterative eigen value iterative solution.

Sometimes they are meaningful and sometimes not. It is up to the user to decide what they mean and how to interpret them. Have a look at a numerical solution algorithm, it will probably change your opinion of what it means.

Brian

http://www.espcomposites.com

 

[jhardy1]

@crisb,

Did you actually read my post?!

There are certainly classes of problems which should not yield negative bucking factors - e.g. a classical Euler Column will not buckle under axial tension load. But suppose you set up the analysis with a positive axial load (i.e. axial tension) instead of a negative (compression) load? What do you think would be the appropriate Buckling Factor for this problem?

Sure, if your structure cannot undergo partial load reversal of any of the components, you may be able to ignore any negative buckling factors - but if any of the load components can be partially reversible, be careful!

http://julianh72.blogspot.com

 

[crisb]

Yes, a very simple model such as a strut in tension will give a negative load factor, if it fails to find the requested number of positive modes first. Some software will however create an error message if the load factor is below 1 and/or will not run.
I regularly do and review complex buckling analyses, and sadly the few times I have seen negative load factors have nearly all been on the same software (and with certain elements types and poor mesh), and have not usually been repeatable on other software. So yes I agree be careful, and sometimes they are meaningful and sometimes not.

 

[jhardy1]

A "strut in tension" [sic] should typically have NO positive buckling factors, only negative buckling factors!

There should be no reason to generate an "error message" for a computed buckling factor of less than 1.0, other than by way of warning the user that the magnitude of the computed buckling load is less than the magnitude of the applied load - but this would be a "design warning" rather than any sort of "computational error message". (Many analysts will set up arbitrary "Unit Load Cases", such as an axial load of 1 newton or 1 kilonewton, which can be multiplied by arbitrary load factors of any appropriate magnitude, so the software has no way of knowing whether a computed buckling factor of 0.5 times Load Case 3 is "safe" or "unsafe".)

The same applies for negative buckling factors - they are a natural consequence of the numerical methods being used to extract the Eigen Values of the stiffness matrix, and should not be seen as an "error". Whether they have "physical meaning" only an intelligent human being can determine; if the loads are reversible, they may have physical meaning; if the loads are not reversible, they are still computationally valid for the numerical model, but may not have physical meaning for your actual structural system. (Always remember that FEA only creates a numerical model; it does not purport to be "the real thing", but it is sometimes easy to forget this when you look at those lovely Technicolour stress plots!)

Your FEA software may allow an option to only search for and display the positive Eigen Factors, but this does not mean that the negative factors don't exist; only you, the intelligent human designer, can make the judgement about whether to ignore any negative Eigen Factors the software is able to find.

If your preferred FEA software is not capable of generating negative Eigen Factors (where they exist for the stiffness matrix in question), I would see this is a limitation of the FEA code which can't find them, rather than being an "error" in the FEA code which can find the negative Eigen Values!

http://julianh72.blogspot.com

 

[crisb]

In my code buckling load factor = 1/(1-eigenvalue), and eigenvalues are extracted in ascending order. Therefore if a load factor is negative it will only have been extracted after failure to obtain the requested number of positive load factors. In my experience in many cases this will indicate either a very simple model, one that has been modelled badly with far too course a mesh, or a very large number of modes have been requested.

 

[ThisIsMe86]

The code did display negative buckling factors and, because in my particular case, negative buckling factors doesn't mean anything I had to tweak my input deck to ignore all the negative buckling factors.

Thank you everyone for sharing your experiences/knowledge regarding buckling. I see I still have a long way to go to understand some of the things being discussed.


-This is me

 

[jhardy1]

My final word on this thread (I promise!):

Do a Google search for "negative buckling factor". Don't you find it a little bit odd that the home websites and official support forums for Catia, MSC, SolidWorks, ProEngineer, Strand7, etc all pop up prominently in the search results? And they are all saying the same thing (paraphrased): Negative buckling factors mean the structure will buckle under loading applied in the opposite direction to what has been modelled.

(It hardly seems like a problem with "certain codes" or "a very large number of modes have been requested"!)

If your code identifies negative buckling factors, you may be able to determine they have no physical meaning for your problem (e.g. if reverse loading is physically impossible) and exclude them from your study, but I would prefer to know that my structure could be prone to buckling for small load reversals (as in the case of a thin-walled tank subject to partial internal vacuum), because then I can design accordingly.

If your code can't (or won't) find the negative buckling factors, you should see this as a limitation of your code, not as an error in all the others!

http://julianh72.blogspot.com

 

[ESPcomposites]

jhardy is correct (so that you know you are not alone in the discussion).

Though it has been many years now, I have coded an iterative eigen value solution. Negative eigen values are not "abnormal behavior", but rather are fully expected for some problems. In fact, their absence would indicate a problem. I would not want to use a code that would yield an error if a negative eigen value was found, nor am I familiar with one. Having a look at the numerical methods often gives a greater appreciation, though I realize that is not always practical for end users.

Another example would be buckling of a shear loaded plate. The applied shear (and the opposite direction) would yield pairs of (+) and (-) eigen values.

Brian

http://www.espcomposites.com