Arc length factors in Riks method

[Staszkinson]

Hello,

It would be grateful if someone could explain me how to calibrate arc length increment factors in Static, Riks method in Abaqus.

For a default input in Static, Riks step I get max LPF factor equal 147(this value is probably correct, expected 147.8). Unfortunately, I'm not satisfied in number of increments(the result of 12 increments). The question is: how to calibrate arc length increment factors(initial, minimum, maxium arc length increment and estimated total arc length) to get more accurate results.

I found something about it, quote:

In cases of severe nonlinearity, the Riks method may not converge or may converge to previously obtainted equilibrium configurations. Often such problems are caused by the arc length being to large. If you suspect that this is the problem, look in the message file to find the typical arc lengths used and return the analysis with a smaller maxium arc length.

What are typical arc lengths?

 

[hd1989]

Hi Lukasinski,

I think you probably might have figured by now, still I would like to share what I know. I'm also working on the Riks procedure.

I usually use 0.05 or 0.1 as initial arc length which means 5% or 10% of the load is applied in the first increment and I keep 0.1 or sometimes 1 as the maximum arc length increment(Abaqus decides how much load to apply in each increments based on the number of iterations in the previous increments and it doesn't exceed the specified maximum limit). I keep the maximum number of increments as 200 or 300. You'll know how to decide these values by hit and trial.

The thumb rule is to "allow" abaqus to apply a smaller portion of the load in each of the increments to get proper results.

Good luck,

 

[Staszkinson]

Hi!

Thank You for a message!

I have found my own way to find the correct LPF in Riks method and it's very similar to yours. Your post is very helpful.
I'm wondering if the initial arc length = 1 is correct. It seems not to be a big value(initial loading is 2 x 1kN force).
The maximum arc length = 10.
Estimated total arc length = 1.

In this case my beam behaviour is correct - first the lateral torsional buckling occur and then, after LPF reach the maximum value, the beam deformations are continious, I mean that in the other cases(for example The maximum arc length = 15) my beam deflect in the oposite direction to the loading(typical unloading case in the elastic range), so I guess in that(second) case analysis goes wrong.

What do You think about it?

 

[hd1989]

Hi,

I have done cylinder buckling analysis and in that I have observed when I give a higher value for the maximum arc length, sometimes after buckling the LPF goes below zero and instead of inward buckle I see an outward buckle(which is not expected).

In your case, I believe the beam buckles at 147 LPF then initial arc length = 1 seems ok to me. Why don't you try reducing the maximum arc length to 4 or 5, this of course takes more increments but gives more data points on the curve.

Regards,

 

[Staszkinson]

Hi,
Yeah, LPF below zero, that's what I'm talking about

If I reduce maximum arc length to 4 or 5 the results are very similar to the maxium arc length 15 case(incorrect - LPF < 0).

I see that the correct analysis require tests,
Thanks to you I know something more about arc length method now.

Regards,