# Compliance Response

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When I set my objective in a topology optimization to minimum compliance, what does that mean?  I assume it means to maximize stiffness, but where at on the object?  Is it the overall structure or just points where forces are applied?  If you know mathimatically what its calculating, that would help.

Thanks

-Dave

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Hi Dave,

you are right, miminum compliance means maximizing the stiffness of the structure.

It could be for the entire structure of individual components, depending on how you define while creating responses.

Compliance can be defined as C= 1/2*(F^2T)/K^T where C is compliance, F is applied force and K is the stiffness of the component or structure.

Since the applied forces are constant your FE model, now you can say that F is constant throughout.

This means C is inversely proportional to Stiffness of the component or structure. So, in order to increase the stiffness C has to be decreased.

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Keep in mind that this is only valid for "force controlled" loadcases. If you have a SPC defining an enforced displacement, then you want to maximize the compliance for maximizing the stiffness.

Seen here:

http://www.trinity-eng.co.kr/ez/pdf/OptiStruct01.pdf

Regards,

Merula

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I do not grasp why the formula reads C = (1/2) F2 (1/K).

Why is the force squared?

Also in the document of the last post, it says C = FT U, which makes more sense to me.

Can anyone help on deriving the above-mentioned equation for C, C = (1/2) F2 (1/K)?

Kind regards,

Robbin

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Hi Robbin,

That was a typo error. It should be C= 1/2*(F^2T)/K^T

Compliance is equal to 1/2*(U^T)*F and F= K*U. If you replace U with F/K in the compliance equation, you will end up with F sqaured and powered with T

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Thanks Prakash. I also found it in the Optistruct User's Guide, it makes sense now

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On 26/09/2014 at 2:47 PM, Merula said:

Keep in mind that this is only valid for "force controlled" loadcases. If you have a SPC defining an enforced displacement, then you want to maximize the compliance for maximizing the stiffness.

Seen here:

Regards,

Merula

Hello Merula,

I know it has been two years you posted this message, but by any chance would you (or anyone else reading this) still have that file (http://www.trinity-eng.co.kr/ez/pdf/OptiStruct01.pdf) ? It seems the link doesn't work anymore.

Also I am really interested in learning more in depth about the difference between "force controlled"  or "enforced displacement controlled" load case and how the solver considers both cases. I tried to search a bit in Optistruct documentation but haven't found anything that talks about it.

Thank you!

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