Nonlinear analysis convergence failure

[mon1299]

HI Everyone,
I am trying to find the ultimate load capacity of a steel beam.I am doing the nonlinar large displacement analysis with stress stiffness on,applying load as displacement, using perfectly elastic plastic material properties and von Misses yield criteria. I am applying unknown displacement and trying to draw the load deflection curve.For some dimesion I was able to determine the ultmate load from the curve as I am getting the curve after the ultimate load also. But for some beam dimension, When the solution reaches near ultimate it can not converge any more even for very very small load increment. So I am not getting the curve after that part.I tried both arc length method and newton raphson method. Is there anyone wo can felp me in this regards? I want to get the curve after ultimate load because only then I am sure that this is the ultimate load.By the way my beam is subjected to local buckling as steel thickness is very small and I am using Shell181 element.

 

[Stringmaker]

Why don't you perform a nonlinear buckling analysis instead? Perhaps you've reached the bifurication point hence you're solution cannot converge. If your analysis is still running I would stop the analysis and review the last converged substep. Perhaps the entire section has already gone plastic?

 

[mon1299]

Dear Stringmaker,
Thanks for your reply. I couldnt understand what do you mean by Nonlinear buckling analysis? I think what I am doing is nonlinear buckling analysis. For nonlinear buckling analysis the buckling load should be determined from the load deflection curve as far as I know. After that buckling load the deflection will increase and load will decrease.I am not getting this phenomena. For me load capacity increases with the increase deflection, after a point it canot converge more. I checked the last converged solution and found that some part of the beam is in plastic. I think this situation is like the structure is unstable now. Any idea how to simulate this?
regards
Mon

 

[cbrn]

Hi,
it seems that you are effectively reaching the buckling instability. The behaviour you are getting is nothing strange, both from a physical and from a numerical point of view. Buckling is not necessarily a decrease in load, it is foundamentally an un-stability, i.e. at a certain point the increase of the deflection, for a small increase in applied load, tends to become infinite (loss of stability = absence of equilibrium).
When the beam has buckled it can no longer find any equilibrium, so the solution can NOT converge any more.
In that case, you could say, in a slightly conservative way, that the load carried at the last converged "timestep" is the ultimate load.
For example, if you ramp a load from 0 to 1000 kN in 500 substeps, and the solution diverges in the 480th step, then the ultimate load is "near" 479*(1000/500)=958 kN, higher than this value and lower than the next timestep's load value.
At this point, either you take this result (a bit conservative, since it is an estimatiion by defect), or you launch a second analysis ramping from 958 to 480*(1000/500)=960 kN in, say, 100 substeps (so you get an "accuracy" of 0.02 kN), and so on till you get satisfied (consider that this kind of analysis has an inherent error band of something like +/- 5%).

Regards