Nonlinear Buckling

What are the weird oscillations in your upper graph? And isn't the load vertical rather than horizontal? (Unless you rotate the drawing by 90°) Sorry if I'm confused.

Hi Tornado, thanks for reply

The above graph is show the convergence process, Not relative with load ( vetical or horizontal), but It unconverge, you can see from this graph. I don't know why it unconverge..

I'm confused. Is it an axial force? putting compression into the cantilever?

I am not conversant with Ansys and I can't read the text on your diagrams, so I won't attempt to interpret them.

With L = 5m and a cross section 0.4m x 0.4m, why would you expect large deformations? Why would you expect nonlinear buckling? What is your material...concrete? Perhaps you are getting material failure without buckling, i.e. crushing.

I am sorry I am missing something here, first can you consider your beam as a post? and then using simple manual calculation to work out buckling. why do you need to go to use software for simple beam ie cross section is not changed from end to end and simple applied force

Manual calculation is sufficient, but perhaps the OP is testing his software to ensure that it works correctly on a simple problem before applying it to more complex situations which are not so easily checked by hand methods...just a guess on my part, but something I have done myself from time to time.

Rhabe,

Interesting, but since we are dealing with a cantilever, shouldn't you be taking the effective length as 2*5 = 10m? The radius of gyration is 0.4/√12 = 0.1155m so the L/r value is 10/0.1155 = 86.6. Since we do not know the material in question or any of its properties, do we know that we are dealing with a short column?

Ba/el,

to my knowledge the ratio from 1:10 ... 1:17 is the transition region from pure plastic buckling to mostly elastic buckling for vertically oriented steel cantilevers without the influence of the weight.

This is equivalent to Euler-buckling mode 1 (the lowest buckling load).

I did never recalculate the buckling forces in units of length to gyration radius - would be interesting.

Not knowing the material: you are right, this beam may behave elastically.

Rubber: no doubt.

Steel and other metals ?: up to 1% elastic limit, but how much allowed or necessary deformation ? So here once more there is the necessity to apply the load with a reasonable eccentricity and calculate as a longitudinally loaded elastic beam and look how much deformation is allowed within elastic behaviour.

RHABE

Another GA for RHABE! I agree 110%.....brillant deduction.....he nailed this one squarely on the head!!!

I shouldn't get into this! Sounds like you have a horizontal column--primarily axial load. Isn't the failure of columns rather sudden and total? Thus the load where it "un-converges" would be the failure load, and loads more than this become meaningless? With a safety factor to an allowable load, your program analysis may be working just fine.

- is your beam one single element or is it subdivided into several elements ? it should be subdivided so that you can get the buckling mode shape

- your element is probably concrete (400mmx400mmand 5m long). am I right?

- if this is a structural element, the codes generally ask that you apply a nominal out of plane force (between 1% to 5% of the applied load depending if you are doing a simple buckling analysis or if it is a disproportionate collapse condition). this will generate an initial eccentricity to the deformed shape that will enable the software to not oscillate about the answer.

- there are several solvers in this software. try using another one of them. sometimes they even recommend a solver for a particular calcualtion such as buckling or non linear buckling.

- you may also need to introduce an end bearing eccentricity to the model as the codes also ask for that

I fyou can come back to us on these points, I think we will be clearer on what to do.

I suspect that the oscillations are from iterated Pdelta calculations. I loosely deduce that there is a load on the cantilever and the OP is trying to find the failure axial capacity in combination with that load. Divergence is because delta gets bigger each time instead of smaller.

Not enough information to give more than an educated guess.