Hello Mengli,

As shown by Lucian Bredean, the Riks method works for both displacement loading and force loading in ABAQUS. In displacement controlled loading, the actual load = applied load * LPF, while in force controlled loading, actual force= applied force* LPF.

I've been working on the snap through behavior of hollow sphere foam material recently . And I'm happy to show my results here as a supplement to Lucian's result. The first example is attached figure 1, which shows a comparison of load-displacement curves calculated by the static method, load controlled Riks method, and displacement controlled Riks method. Highly consistent results are obtained by the three methods. The difference in predicted critical buckling load < 1%. Note that the *static method also works out in this example because the displacement increases monotonically.

The Riks method is superior when the load and/or the displacement decrease as the solution evolves (figure 2). In which case, the general static method fails to capture the equilibrium path accurately. One example is the snap back behavior, where the *static method cannot capture the snap back (both displacement and force decrease).

As for your second question, the maximum load proportionality factor (LPF) cannot stop at the exact load (displacement) that's defined. This is related to the realization of the modified Riks method, also known as the arc length method. In the Riks algorithm, both load and displacement are treated as unknowns—termination occurs at the first solution that satisfies the step termination criterion. In other words, the increment of LPF is calculated automatically (based on the min. and max. increment of LPF you've specified), giving no precise control over LPF. Since displacement is unknown, if enforced to stop at exact displacements, interaction and lots of extra computation would be required. On the other hand, the method do stop near the defined stopping criteria. As long as the equilibrium path and post-buckling behavior can be captured, this is not a big concern. If you do want to have control over the increment size, try the *STATIC, RIKS, DIRECT keyword.

By the way, the results shown here belongs to the "snap through" type buckling. For the "bifurcation" type buckling (like compression of a straight bar), you should first introduce imperfection, then apply Riks analysis.

Good luck!

Zian

Dear Dr.Mengli,

please note that you may find useful information at 6.2.4 " Unstable collapse and postbuckling analysis" of the User's manual. Moreover, you are right, you should prescribe  only concentrated loads, pressure, and body forces. For the next question I cannot well understand why the program is not able to terminate the analysis, but you may try to give a close look at the example at paragraph 1.2.3 "Buckling of a cylindrical shell under uniform axial pressure". You may also try to specify the "DIRECT" parameter and also check if everything is fine with *STEP and *STATIC commands specifications (it might be helpful to check this directly on the input file more than on CAE).

I know sometimes it might be quite frustrating but do not give up. I hope you could find these few lines of some help.

Best regards,

Alessandro

Hello,

I have just tested if the LPF limitation works for Displacement loading, when using Riks analysis in Abaqus.

In my case, it worked. The displacement given for a node set defined for a RC framed structure (using the `Displacement/Rotation` option available as boundary condition in Abaqus) was 2mm; the load proportionality factor was set to 1, as it can be seen in the first figure attached.

The analysis stopped for a LPF value of 1.143, as it can be seen in the second figure attached. The value of 1 initially set for the LPF was slightly exceeded because of the good level of convergence of the solution: the LPF increment just before the end of the analysis was 0.38 (it can also be observed in the second figure attached).

The maximum displacement for node set defined was 2.28mm which is, in fact, the maximum displacement defined (2mm) multiplied with the LPF value at the end of the analysis (1.143).

Regarding the high number of increments of the analysis, this indicates a low convergence level.

Consequently, the maximum value set for LPF should work for force loads as well as for displacement loads. I hope my answer will be useful for you. 

Good luck with your research.

Best regards,

Lucian

Dear Lucian:

Thanks very much for your patient reply, I feel so luck to get help from someone like you, a big thank for you!

Dear Mr. Mustaine3:

But, I still got another basic question, can I use Riks to analyse the non-linear bifurcation buckling ?

I have tried so many times, the results are always yield do nothing with critical buckling load, I feel so discouraged, I know it more focuses on post-buckling, and snap-through collapse, but for bifurcation type buckling analysis, does this still work? The best choice will be the "buckling" in linear perturbation, but it is only for linear analysis, I want to study both non-linear material and non-linear geometry behaviour. Can you also give me some clues about this?

And for your program, did you successfully capture the critical buckling load in Load-Displacement diagram?

Thank you very very much! Your response will be highly valuable and important for me!

Best Regards & Sincerity,

Kyle

Did you get answer how to use both non-linear material and non-linear geometry behavior for post bucking analysis after riks analysis.

Please help me regarding this

Please share me the best answer might you get...

Hello Mengli,

As shown by Lucian Bredean, the Riks method works for both displacement loading and force loading in ABAQUS. In displacement controlled loading, the actual load = applied load * LPF, while in force controlled loading, actual force= applied force* LPF.

I've been working on the snap through behavior of hollow sphere foam material recently . And I'm happy to show my results here as a supplement to Lucian's result. The first example is attached figure 1, which shows a comparison of load-displacement curves calculated by the static method, load controlled Riks method, and displacement controlled Riks method. Highly consistent results are obtained by the three methods. The difference in predicted critical buckling load < 1%. Note that the *static method also works out in this example because the displacement increases monotonically.

The Riks method is superior when the load and/or the displacement decrease as the solution evolves (figure 2). In which case, the general static method fails to capture the equilibrium path accurately. One example is the snap back behavior, where the *static method cannot capture the snap back (both displacement and force decrease).

As for your second question, the maximum load proportionality factor (LPF) cannot stop at the exact load (displacement) that's defined. This is related to the realization of the modified Riks method, also known as the arc length method. In the Riks algorithm, both load and displacement are treated as unknowns—termination occurs at the first solution that satisfies the step termination criterion. In other words, the increment of LPF is calculated automatically (based on the min. and max. increment of LPF you've specified), giving no precise control over LPF. Since displacement is unknown, if enforced to stop at exact displacements, interaction and lots of extra computation would be required. On the other hand, the method do stop near the defined stopping criteria. As long as the equilibrium path and post-buckling behavior can be captured, this is not a big concern. If you do want to have control over the increment size, try the *STATIC, RIKS, DIRECT keyword.

By the way, the results shown here belongs to the "snap through" type buckling. For the "bifurcation" type buckling (like compression of a straight bar), you should first introduce imperfection, then apply Riks analysis.

Good luck!

Zian

Hi Zian,

I am curious, how did you solve this using static displacement?

We are working on compression of foam cells, similar to your hollow spheres. Next step is Riks.

Thanks,

Rickard