Linear buckling and nonlinear analysis for hollow section beams

[Bopeco]

Hi to all, i'm modeling a beam with hollow rectangular section subjected to bending and once i have verified that the stresses in the structure are ok i want to be sure that the beam is verified to buckling.
The vertical sides are very slender so i'm expecting those to be the weakest point.


First i ran a linear buckling analysis and it gave me the first eigenvalue of 1.6 so i'm pretty confident to be in safe conditions.

Then i ran a nonlinear static analysis to see if some nonlinearities influenced the linear solution but the nonlinear analysis failed to converge at about half the total load.

Is this meaning that some nonlinear buckling occur at that level of load or may be something other that cause the non-convergence?

I know that linear buckling analysis is less conservative than real life but i don't know if the safety factor of 1.6 is a sufficient margin.

 

[nlgyro]

this is too scant an information to really suggest anything.

can you post your input file?

 

[Bopeco]

Yes, i'm using femap and my input is this:

INIT MASTER(S)
NASTRAN SYSTEM(442)=-1,SYSTEM(319)=1
ID Femap
SOL NLSTATIC
TIME 10000
GEOMCHECK, NONE
CEND
TITLE = nonlin
ECHO = NONE
DISPLACEMENT(PLOT) = ALL
SPCFORCE(PLOT) = ALL
FORCE(PLOT,CORNER) = ALL
NLSTRESS(PLOT) = ALL
STRESS(PLOT,CORNER) = ALL
SPC = 1
NLPARM = 1
LOAD = 1
BEGIN BULK
$ ***************************************************************************
$ Written by : Femap with NX Nastran
$ Version : 11.1.2
$ Translator : NX Nastran
$ From Model : E:\...
$ Date : ...
$ ***************************************************************************
$
NLPARM 1 5 5 25 PW NO+
+ .001 .001 1.-7 3 25 4 .2 .5+
+ 5 20.
PARAM,LGDISP,1
PARAM,POST,-1
PARAM,OGEOM,NO
PARAM,AUTOSPC,YES
PARAM,K6ROT,100.
PARAM,GRDPNT,0
CORD2C 1 0 0. 0. 0. 0. 0. 1.+FEMAPC1
+FEMAPC1 1. 0. 1.
CORD2S 2 0 0. 0. 0. 0. 0. 1.+FEMAPC2
+FEMAPC2 1. 0. 1.



I realized that i'm having very high stress concentrations because i applied the load on a small surface (to "simulate" a contact) but maybe the surface i trimmed is too small and so the stresses are too high to make the simulation converge.
Is this a possible explanation?

 

[Bopeco]

Any idea?

 

[ESPcomposites]

Did you run nonlinear geometry, nonlinear material properties, or both? Clearly one possibility is if the column is "short" (i.e. a Johnson column). In that case, the Euler solution would over predict the actual result and the nonlinear solution would be more representative of the actual response. Of course, you should probably also consider crippling.

Brian

http://www.espcomposites.com

 

[Bopeco]

I ran both nonlinear material and geometry. Well, the beam is not too long so maybe it can be considered as short column but the linear buckling analysis should take into account that. Or not?
My doubt is about the safety margin of the linear solution (1.6) and if it is a sufficient margin to consider. If the nonlinear solution failed to converge due to the loss of stability of the beam at about half the total load, it would mean a coefficient of 0.5 so very very different from the linear one.

 

[ESPcomposites]

Sorry, I read that wrong the first time and didn't see that is a was beam in bending (as opposed to a column with an axial load). If the walls are relatively thin (high b/t), then they will buckle elastically. In that case, the eigenvalue solution will be appropriate (though you may want a certain MS for imperfections). However, if the walls are relatively thick (low b/t), then the failure mode may be crippling In that case, the eigenvalue solution would over predict the actual capability.

And yes, failure to converge at a lower load than the applied load could indicate instability has occurred. Can you look at the deformation in the last step? That may give you an idea. Also, is the bending load the only applied load? If you have an axial load then you have a beam-column.

Brian

http://www.espcomposites.com

 

[Bopeco]

Thanks for the reply, i have no axial load because the beam is bent by a transversal force at the top of it.
I have a b/t of about 60 so i guess that the walls are pretty thin.
The deformation in the last step gives me a lateral displacement of about 2 mm in the position that should be the most critical for buckling.

I wonder why, if the walls are thin and they should buckle elastically, the difference between the linear buckling and the nonlinear static solutions is so big ( i didn't introduce any imperfection in the model)

 

[nlgyro]

Can you post your input file?? If it is possible

 

[Bopeco]

I've posted it in the third post of this thread

 

[ESPcomposites]

It sounds you need to determine why the solver is terminating earlier than you expect. Is the last step consistent with the buckled shape from the eigenvalue analysis? If not, something else is going that is causing it to terminate early. You will have to identify what that is and adjust it accordingly. Some pictures would help.

Brian

http://www.espcomposites.com

 

[nlgyro]

Thats just the control cards not the model