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Negative eigenvalues
2

Negative eigenvalues

Negative eigenvalues

(OP)
Hey,

I'm doing buckling analysis with 5 eigenvalues. One of the is negative, but my analysis still completes with out errors or warnings. Does anybody know how I can avoid the negative eigenvalues?

Senad

RE: Negative eigenvalues

Never heard of negative oens before. Are you they're just not almost zero, but a little negative? - just to be tehcnical.
Zero values will indicate the body is free to translate in a  particular direction.

corus

RE: Negative eigenvalues

(OP)
No, they are negative. I know of some reasons with rigid body motion, but the suprising thing is that the analysis completes.

Senad

RE: Negative eigenvalues

Buckling analysis can and will produce both positive and negative eigenvalues. They are both vaild "mathematical" solutions for the problem, just that the negative ones have no real relevance to the physical world.

RE: Negative eigenvalues

Negative eigenvalue just means that the load to cause the buckle is of the opposite sign to the applied load.  So if I applied a reference load of 1 MPa and the first eigenvalue was -0.5, then the load required to trigger the buckling mode is (1 x -0.5) = -0.5 MPa.

You may well get spurious buckling modes with eigenvalue extraction, I know I've seen them.  After all, the eigenvalues are just the mathematical solution to the problem, they may not necessarily be physically possible.  It's up to you, the analyst, to determine what is significant and what isn't.

Having said that, it's probably worth double-checking your constraints and loads anyway.

Regards

Martin Stokes CEng MIMechE

RE: Negative eigenvalues

You all type wwaayyyyy faster than me ...winky smile

Martin Stokes CEng MIMechE

RE: Negative eigenvalues

Bassmanjax,

Sorry for typing faster !

It's possible to set up a buckling analysis without an applied load, I've done this when writing beam analysis software using a "geometric stiffness" matrix (in place of the mass matrix for a natural freqency analysis) in conjunction with the standard stiffness matrix, and using the same eigen extraction routine as used in natural frequencies. This analysis produced probably as many negative eigenvalues as positive ones.

RE: Negative eigenvalues

(OP)
Thanks a lot.

RE: Negative eigenvalues

If you did the analysis correctly; to my understanding a negative eigenvalue means the structure buckles for that applied load.  If I am wrong someone please correct me.

RE: Negative eigenvalues

dkeatley - you are wrong.  See johnhors' comment above.

RE: Negative eigenvalues

What type of elements are using ? Thin Shell Elements?

Regards,
DLT

RE: Negative eigenvalues

(OP)
I'm using 8-noded shell elements.

RE: Negative eigenvalues

hi!

I'm doing a buckling for non linear analysis for two differents shell structures; I have obtained negative values for both cases, and for all the eigen values.

I know this is possible, but how can I to know which structure is stronger?

I mean, the first eige value for one is -1,54 and for the other -2,34.

Thank very much in advance,
cad1

RE: Negative eigenvalues

If your reference load is the same in each case, then the structure with an eigenvalue of -2.34 will buckle at a higher load.  The negative sign just means that the buckle load is in the opposite direction to the reference load.

Section 6.2.3 in the v6.7 Users Manual covers this quite comprehensively.

 

Martin Stokes CEng MIMechE

RE: Negative eigenvalues

What if you have negative eigenvalues in a static contact analysis problem? I get this as one of the few warnings in my impact model and the problem does not finish because of too many increment attempts. Would this be a major problem for the solver finding a solution? Is there no way of getting rid of these warnings?

RE: Negative eigenvalues

If you're modelling an impact problem, you would be better advised to look at using Explicit rather than Standard.

Regards

Martin Stokes CEng MIMechE

RE: Negative eigenvalues

hi bassmanjax,

I am interested in positive eigenvalues only in my analysis. However the analysis hasn't been able to give me the first positive eigenvalue after many negative values. I don't know how long it needs to run to find the positive value. Is there anyway to get positive eigenvalues only?

Thank you,

Arbor

RE: Negative eigenvalues

Arbor,

This doesn't sound right, I've never heard of this happening before! Could you attach a "small" input file that behaves this way?

RE: Negative eigenvalues

Is your applied load, putting the structure into tension rather than compression? If yes, try reversing it.

RE: Negative eigenvalues

johnhors,

I am trying to model the buckling of a pressure vessel head knuckle under internal pressure (there will be tangential compressive stress in the knuckle due to internal pressure). However, the model kept giving me negative values for the shell and head buckling which would be due to external pressure. I haven't been able to obtain the first positive number due to the real load yet. So it would be nice for me if there is a way that ABAQUS only finds the positive value for the real applied load.

Arbor

RE: Negative eigenvalues

Arbor,

Assuming you have modelled the whole pressure vessel then the vast majority of your structure will be in tension, hence the many negative eigenvalues found by Abaqus. There may be a considerable number of these encountered before Abaqus spits out the positive eigenvalue you seek. I am not aware of any means of suppressing negative eigenvalues. Have you considered running a static large deflection non-linear analysis using NLGEOM instead? This may be more appropriate than a buckling analysis for this type of problem.

RE: Negative eigenvalues

johnhors,

You are right about my model and the eigenvalues. I have several approaches to check different failure modes of a pressure vessel based on ASME code. The approaches include linear elastic and non-linear plastic analysis. The code also requires to check buckling when there is compressive stress. There is no very good analytical solution for head knuckle buckling load. So I am trying to see if ABAQUS can help for this case. Thanks

Arbor

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