Non-linear buckling analysis

[neil.harrisCVPSJ]

Hello, I'm running a non-linear buckling analysis of a duo-pitch roof, with an uplift of 4kPa. The solution runs and I get a negative  "EIGV" value (-2.212). My understanding is that this means that the load that will cause buckling is acting in the opposite direction to what I applied. However, when I apply the same load in the opposite direction I get a completly different positive "EIGV" value (4.787). 

In order to  determine the buckling factor due to the uplift, if I run two analyses, one for uplift and one for downward force, can I restrict my anaysis runs to exclude the negative EIGV values? 

Many thanks for any advice. 

[John_Holtz · Accepted solution]

Hi @neil.harrisCVPSJ  Welcome to the Inventor Nastran forum.

The answer to your question is yes. Edit the analysis ("Analysis > Edit") and set the "Lower Bound" on the "Options" tab to a small positive value. Buckling loads less than the lower bound will be excluded.

Of course, you will need a much smaller mesh size before you get accurate results, but continue testing with your coarse mesh.

Also see this article from knowledge.autodesk.com: What is a nonlinear buckling analysis in Nastran

Let us know if you have any questions.

John

[neil.harrisCVPSJ]

Hi @John_Holtz, thank you for the reply.

If I run two load case (uplift and downforce), by excluding the negative eigenvalues would you say the results are valid or would I have excluded a response in the analysis, that needed to be considered?

With regards to the mesh size, what mesh size would you expect to give accurate results? I have been working on a mesh convergence study for this problem and although my results are now converging to a consistent eigenvalue  (~0.95) the number of modes I’m getting is also increasing (25mm mesh – 50 modes, 12mm mesh – 206modes & 6mm mesh 224modes, i've limited the number of modes between 0.001 and 5). Would you have expected the number of modes to also increase with the refinement in the mesh? 

I've reduced my mesh size in half each time and am down to a 6mm mesh (204,374 elements), which seems very fine for a shell element model.

[John_Holtz · Accepted solution]

Hi @neil.harrisCVPSJ 

I should have clarified this in regards to your original post. When you received the buckling multiplier of -2.2, that is only the lowest buckling shape. If you had requested more than 1, then the first positive multiplier would have been what you wanted. You are accomplishing the same thing by limiting the output to positive values only. (In other words, it is still calculating the result of -2.2 but it does not output that result.)

For a linear buckling analysis, I agree that a positive load that gives multipliers of -A < +B < +C and so on, would give  multipliers of -C < -B < +A and so on for a negative load. (It may be hard to get Nastran to output all those values because I think the tendency is to ignore the negative values. Whether the search algorithm is successful at rejecting the negative values is a different question.) However, you are performing a nonlinear analysis, so the displacement results due to the positive load do not need to equal the same displacement results (but in opposite direction) for a negative load. That's the definition of nonlinear: multiplying the load by X does not cause the displacements to be X times larger.

The next question is can the load be reversed in your situation? For example, if it were a snow load, snow can only push in one direction. There is no reason to worry about changing the direction of the load and calculate "matching" load multipliers. If your load can only act in one direction, you should try to set the Options as follows:

1. Number of modes: calculate N modes so that you can see what happens from one buckling shape to another.
2. Lowest value: 0.01
3. Highest value: blank.

This will tell the analysis to calculate the first N values that are larger than 0.01. There is no reason to calculate all values between the lowest and highest; that is what happens when you enter both the lower and upper limit.

Another example is wind. Wind only pushes in one direction, but the direction of the wind can be from any orientation. On a rectangular building, a positive load blowing north and a positive load blowing south should produce  produce similar results, equal and opposite. Likewise, a positive load blowing north and negative load blowing north should create the same result. (I am assuming that most buildings experience small displacements so a linear analysis would create "equal and opposite" results for + and - loads blowing north or south. Of course, I am ignoring local effects that occur on the windward side such as windows breaking!)

Hope I have not made things more confusing. (If so, just ask for clarification.)

John

[neil.harrisCVPSJ]

Thanks again @John_Holtz, 

Your reply made sences to me, I am considering two load cases for the wind loading, one which creates an uplift and another which creates a downward force on the roof. As there are not equal, I shall restrict each load case to only output the positive results. 

Thanks again for your help and clarifying.