"Why does a perfect FEM cylinder buckle with axial compression?" 1

[BuckTU]

Hi Fellow engineers,

my question is short, but not simple.

"Why does a numerical cylinder, without any imperfections, buckle in the FEM program MSC.Marc with axial compression?"

I've worked with axial buckling and FEM programs for a long time now, but didn't ask this question to myself, because I was only looking for approximations of physical buckling problems. I know how to use FEM and to calculate the buckling force, half-wavelengths and other problems, But this fundemental question has sneaked on me from behind and haunts me to this day.

Who will be the (or one of the) gostbuster(s)....

BuckTU

 

[feadude]

columns buckle when lateral stiffness goes to zero.

good57morning@netzero.com

 

[rb1957]

assuming you're meshing a cyclinder and running linear FEA.

like the response above, the column is not buckling in the euler sense, since linear FEA doesn't (cannot) include the effects of displacement. i expect the elements have a small up of plane stiffness due to the curvature of the elements (8 noded) or due to faceting of the surface (4 noded).

 

[BuckTU]

Hi Fellow engineers,

my question is short, but not simple.

"Why does a numerical cylinder, without any imperfections, buckle in the FEM program MSC.Marc with axial compression?"

I've worked with axial buckling and FEM programs for a long time now, but didn't ask this question to myself, because I was only looking for approximations of physical buckling problems. I know how to use FEM and to calculate the buckling force, half-wavelengths and other problems, But this fundemental question has sneaked on me from behind and haunts me to this day.

Who will be the (or one of the) gostbuster(s)....

BuckTU

Thanks for the quick reply,

but what I meant is, "What does the program do to simulate the initiation of the displacement", because if you would apply a displacement axially then the Cylinder will buckle in the Numerical program with a wave mode. But why doesn't the Cylinder compress it into a thick ring, without any waves. In the past people would give a cylinder or pipe a small imperfection to initiate the buckling mode, this would force the cylinder to follow the least resistant path. But if you use today's FEM programs, e.g. MSC.MARC, this is not the case, what does MSC.MARC do with a cylinder composed out of solid “20 hex nodes” elements.

Please reply also on this..Gostbusters

BuckTU

 

[gwolf]

I suspect because Marc is running nonlinearly without you knowing. In this case, any imperfections in your mesh will act as buckling seeds if the axial load is high enough.

I sometimes perform buckling analyses for complex shapes (for which there is no mathematical solution) by introducing a small imperfection in the mesh, applying a huge load, and running the analysis nonlinearly. The program will show asymptotically high deflections and terminate very close to the buckling load.

 

[SWComposites]

Assuming you are running a nonlinear analysis and not an eigenvalue analysis, numerical round-offs and/or small imperfections in the mesh are probably the cause. It also could be do to bending-extensional coupling in the material stiffness matrix - is this a composite or metal cylinder? Have you called Marc tech support? - I know some of the guys that do the support and they are quite knowledgable.

 

[rb1957]

buckTU,

a perfectly straight column buckles ... see euler.
a imperfect column buckles at a lower load.
imperfections would be added to tests (real and FE) to cover the range of real geometries.

as with other posters, i'm assuming you're using non-linear MARC. if MARC calculates the euler load for a perfectly straight column, i can only speculate that it is understanding the problem that euler posed (and solved).

i suspect that you'd need to talk to a MARC specialist to understand the actual mathematics it uses to come up with this answer.

 

[mtnengr]

Classical buckling of cylindrical shells is based upon determining the minimum eigenvalue problem for the load case being considered. Several papers are given in "Buckling of Shells. Proc. of a State-of-the-art Colloq., Univ. Stuttgart, Germ.", May 6-7, 1982, edited by E. Ramm. ISBN 3-540-1185-7.

An adjacent perturbed state is assumed. The large strain-displacement relations are derived along with the coupling of the rotations and stress resultants in the equations of equilibrium. From these sets of equations an eigenvalue is obtained. If only axisymmetric loads are considered, the buckling pattern will be axisymmetric. If non-axisymmetric responses are assumed, the response will be non-axisymmetric. Most of the time, the non-axisymmetric response will give lower eigenvalues. The computer program used for these cases must consider these loads a priori. Any FEM program must include these responses.

Koiter has demonstrated that considering imperfections of differing geometry, the minimum eigenvalue is lowered in a particular and predictable way. These values vary with imperfection amplitude and are well below the original classical eigenvalue.

If you go to my website

http://www.volcano.net~d.citerley,

you will find papers and programs that can solve this class of problems

 

[corus]

mtnengr, the web site doesn't exist when you click on it.

The answer to the question probably lies with the fact that quadrilateral elements are being used and there always seems to be a slight error in the nodal force calculation at the mid-side nodes. That's just a guess. Try running the problem with 8 noded bricks and see if it still buckles.

corus

 

[mtnengr]

My typing error. The site is http:/

http://www.volcano.net/~d.citerley

 

[crisb]

bucktu: my question is short and simple, was it a nonlinear or linear analysis?

 

[GregLocock]

My question is short: how does the computed buckling load comapre with the hand calculated Euler buckling load?

Or don't we do hand calculations any more?




Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[mtnengr]

GergLocock: Euler buckling load is when the centerline of a strut or cylinder buckles (bifurcates) into a sine wave. The sine wave can have multiple values, ie sin mL. For a simply supported shell at both ends, the cylinderical shell can bifurcate where the centerline remains the same but the surface of the shell can form a sine wave, ie cos(n theta) x sin(mL). The more general solution is
cos(n theta) x sin(mL) + sin (n theta) x cos (mL), where n =0,N and m = 1,M. Note, For the case of an Euler load, n=1.

Crisb: A linear analysis is when the geometry of the shell or strut does not change with load. Nonlinear analysis accounts for the change in geomerty prior to buckling.

 

[feadude]

I do not think mapped and symmetric hex elements will cause small imperfections to effect buckling load. However tet elements will create small imperfections that will effect buckling load.

good57morning@netzero.com

 

[GregLocock]

Thank you mtnengr, what I meant was for the OP to do some calculations himself.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[SWComposites]

Euler buckling is appropriate for long columns. For analytical solutions and emperical correlations for cylindrical shell buckling under various loads see NASA SP-8007.