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what is the meaning of "the 1st(2nd) satisfied convergence ratio=xxx"?

Hello. I am doing a topology optimization. The goal is maximum stiffness. Two responses are volfrac and compliance. Optimization constraint is 0.3 of total volume. 'Draw' manufacturing constraint with stamp options are applied.

On completion of optimization run, OptiStruct tells me small design change, iteration stopped. Then I check compliance values over iterations and find that in iteration 20 compliance value has increased dramatically, like 656%. Previous two iterations 18 and 19 has a massage saying 'the 1st satisfied convergence ratio = xxx(some numeric value)' and 'the 2nd satisfied convergence ratio = yyy (some numeric values)' respectively.

Can anyone help me identify the problem and tell me what is the meaning of the massage? Thanks!

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Altair Forum User

For the compliance minimization with volume constraint I have the made the same observation. As I understand it, 1st and 2nd convergence are just verifying that the convergence criterion (by default the change in % of the objective) is really fulfilled, for two subsequent iterations.

But for the case of compliance minimization it seems that the optimization has to converge (including 1st and 2nd) three times.

- After the first convergence something is changed that causes a steep increase in compliance.

- After the second convergence something is changed that causes a steep decrease in compliance.

- Finally the optimization ends after the third convergence.

At least this is what happends in my optimization (see attached plot). However its just a slight increase in compliance compared to your 656%. Does your optimization continue after this?

My guess would be that this is related to a temporary increase of the penalization of the intermediate densities to achieve a more uniform design, but I would be really interested what's going on in detail.

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Altair Forum User

For the compliance minimization with volume constraint I have the made the same observation. As I understand it, 1st and 2nd convergence are just verifying that the convergence criterion (by default the change in % of the objective) is really fulfilled, for two subsequent iterations.

But for the case of compliance minimization it seems that the optimization has to converge (including 1st and 2nd) three times.

- After the first convergence something is changed that causes a steep increase in compliance.

- After the second convergence something is changed that causes a steep decrease in compliance.

- Finally the optimization ends after the third convergence.

At least this is what happends in my optimization (see attached plot). However its just a slight increase in compliance compared to your 656%. Does your optimization continue after this?

My guess would be that this is related to a temporary increase of the penalization of the intermediate densities to achieve a more uniform design, but I would be really interested what's going on in detail.

Thanks your comment.

In my case, optimization has run a few iteration after the sharp increase in compliance. However, compliance value is not changing anymore, and that is why OptiStruct tells me 'small design change', I guess.