Linear Buckling - Spurious Modes 5

[Ingenium22]

Hello all,

this is my first post, so I hope this is the correct sub-forum for my thread. (By searching the forum, I did not find an answer to my problem).

I'm trying to create a very simple model for linear buckling analysis... at least I thought it was simple.

I want to create a model of a simply supported plate with three stiffeners under uni-axial compression in x-direction for Nastran SOL105 (once the model is running, I'll use more complex loadings and run Nastran SOL200). The plate is about 500x500mm and the three stiffeners are distributed evenly and showing in x-direction. I use CQUAD4 elements for the plate and CBAR elements for the stiffeners (no offsets). For the simply supported boundary conditions, I constrain the z-movement on all edges and I fix the center node in x- and y-translation and z-rotation. Nodal forces are applied on the +x and -x edge. PARAM K6ROT 100. is applied

The model is running and static subcase looks good, but I get spurious modes at the CQUAD elements which are next to the CBARs... without the CBARs, the modes look good. A colleague of mine said he once had such an issue ten years ago and he thinks it is related to the combination of 1D and 2D elements and hourglassing. But he can't remember any details. A refined mesh did not help.

Is this a general issue with 2D and 1D elements in linear buckling? I did not find anything on google about it. Do you know this problem?

Best regards,
Florian

 

[ShellsPlatesMeshes]

There is a website devoted specifically to shell buckling problems:

http://shellbuckling.com/

In particular, there is a whole list of professionals working in that area; you may consider contacting them to obtain assistance.

 

[ukbridge]

I wouldn't use bar elements personally, as they have zero bending stiffness and thus won't contribute to the buckling strength of the plate. Why not use beam elements instead? Plate buckling is a function of flexural/bending stiffness, bar elements won't do anything (as far as I'm aware). In practice if using them I'd only give them one division as they can do some funny things to your model.

Also why have you not assigned an eccentricity to the stiffeners? As the centroid of the bar elements in collinear with the NA of the plate I don't think it will increase the stiffness of the plate at.

I'm not too sure of axis convention in Nastran but I think you've made what is a symmetrical half model of your problem i.e. you've fixed rotation about the major axis in midspan. I think for a static analysis this would be fine but I don't think this is quite right for a buckling analysis; in the event why not just model the whole plate anyway for what takes less than 1minute for a solver to number crunch through?

An additional thought these "unexpected modes" may be local buckling of the stiffeners. As a rule of thumb the aspect ratio of the stiffeners should not be any more than about 10.5 otherwise you need to satisfy yourself that local torsional buckling of a stiffener will not be the critical buckling mode. I dont think this will occur in your model though as bar elements cant buckle!

Not sure of any aerospace standards, but BS EN 1993-1-5 (A COP in Structural/Bridge Engineering) has an Annex in which a longitudinally stiffened plate can be idealised as an equivelant plate by "smearing" the stiffeners. I think Koppel charts might also be useful for your case.

Good luck! Sorry if I've sounded like I've had a bit of a moan above, hope some of this helps though!

 

[Ingenium22]

Hello to both of you,

And thank you for your answer. I think that I finally found the problem (see below)

@ShellsPlatesMeshes: That’s an interesting website with nice case studies. Unfortunately my problem seems to be a pure numerical issue and has nothing to do with real buckling physics.

@ukbridge: Concerning your first point, I guess that we only use a different nomenclature. NASTRAN has basically three standard 1D elements:
- CROD can only take axial forces and torsional moments --> this matches your description
- CBAR are able to take bending moments. They represent the Euler-Bernoulli beam theory.
- CBEAM have all the features of the CBAR, but they are more suited to problems with asymmetrical profiles and in cases where the shear centre is not in the centre of gravity. It corresponds to the Timoshenko beam theory.

I avoided eccentricity as Offset were not functional for buckling analyses in previous NASTRAN versions. In the latest version it is functional, but I wanted to exclude possible errors until the model is debugged.

Yes, you are right, I will check the local buckling of the stiffeners later on separately. First I’m running an optimization to minimize the weight, and then I’ll check the weight optimal stiffener. And in fact, the numerical issue was connected to the torsional stiffness!

We also work often with a smeared stiffness, but in this case, the aim is to optimize the plate and a corresponding stiffener profile. So I cannot simplify the problem with a smeared stiffness.


So here is the solution I’ve found (in case anybody has the same problem in the future):
I rechecked all the inputs and read in the reference guide of NASTRAN. When I read the chapter about the PBAR (bar properties), I noticed that the default value of the torsional constant is 0.0, but for SOL 600 (non-linear buckling), the default is 0.5*(Ixx + Iyy)  Therefore I tried to add a torsional constant and it worked!
Even if you don’t need the torsional constant to describe your buckling problem in an analytical way, you need it to avoid numerical problems in the FEM. If the CBAR has no torsional constant, it can twist without any energy and this created spurious spikey modes in the skin (the integration points of the elements remained in their position, only the GRIDs (nodes) moved out of plane!) which have lower eigenvalues than the real physical modes. To verify, I changed the torsional constant to very high and very low values. High values do not change the result significantly, but at very low values, the spikey modes appear again. Now I’m using the PBEAML property and the torsional constant will be calculated automatically.

Today I’m a very happy engineer. :-D

 

[ukbridge]

Glad you fixed the problem! Thanks for the response : )

 

[aerostress82]

Just one question:
Since when are the BAR/BEAM offsets functional in Nastran - if you know when this exactly happened?...
Because this really changes everything!!! Finally!!!!!
^,^

Spaceship!!
Aerospace Engineer, M.Sc. / Aircraft Stress Engineer

 

[Ingenium22]

It should be available from v2012 on, but I'll check it.
Anyhow, you need to use the MDLPRM,OFFDEF,LROFF card to enable advanced offset calculations. (LR seems to be an acronym for large rotations)