Overhang Constraint in Frequency Optimization, density of elements too small

Clement Cavadini

Hello everyone,

I'm doing a topology-frequency optimization with Optistruct on a simple simple beam as an exercise to learn how to use the Overhang constraint.

The objective function is to increase the first three natural frequencies, and at the same time I want to keep the volume of the beam under 30% of the original volume. 

Without any other constraints, the software simply reduces the volume of the structure to the minimal volume I've allowed him to use with the frozen elements I put at the base of the beam, which makes sense. 

However, when I put other frozen Elements at the top of the beam and used the OHA constraint, here are the results I've had: (The elements with a density under 0,014 are not displayed)

 I was expecting a design with some kind of lattice structure that would support the top of the beam. 

Here is what I've done to parametrize my optimization: 
I've included the two small areas at the top and the bottom   in the design space and have set their densities equal to 1 as a Volfrac constraint. But as you can see on this graph, this design constraint is only respected on the green area at the base of the beam, while it isn't respected at the top of the beam, and the optimization stopped even though I had put the maximum number of iterations at 100.

Volfrac at the top of the beam, red area	Volfrac at the base of the beam, green area

I've used the BIGOPT Optimization algorithm and set the minimal dimension equal to 3.1 times the size of an element in the parameters of my design variable.

I've also tried an other method, which is to not include the two areas at the top and the bottom in the design space, and to parametrize the Overhang so that the Non-design spaces and the holes are not self-supporting,  so that the area at the top should be supported by material, but it doesn't work neither.

Would someone have an Idea as to why there isn't some kind of support structure for the top of the beam, and why the optimization process stops even though my VolFrac constraint isn't satisfied?

regards,
Clement

Robert Hoglund

Hi Clement,

I have a couple of suggestions that you can try with this model.

First the way you have optimization set up in the deck is to maximize WFREQ.  The WFREQ response is actually the weighted inverse eigenvalue, so to maximize the frequencies, you want to minimize WFREQ.

The overhang constraint method with the CONSTR parameter you are using is generally a strict constraint.  That in combination with the other constraints you have are leading to an infeasible design.  You can try using the PENALTY parameter to penalize the overhanging regions instead.

Equality constraints are difficult to satisfy, you can just set a lower bound of 100% volume on those regions (instead of both lower and upper bound) or consider whether it should be a design space, if you are required to have 100% of the material.

The SUPP/UNSUPP parameter dictates whether the non-design space can have material grow out from it in the direction of the build volume.  So for instance, if you made the bottom green part non-design space, you would need the SUPP parameter to be able to "grow" material out of the base.  Hopefully some of these suggestions are helpful.

Thanks,

Rob H.

Robert Hoglund

Hi Clement,

I have a couple of suggestions that you can try with this model.

First the way you have optimization set up in the deck is to maximize WFREQ.  The WFREQ response is actually the weighted inverse eigenvalue, so to maximize the frequencies, you want to minimize WFREQ.

The overhang constraint method with the CONSTR parameter you are using is generally a strict constraint.  That in combination with the other constraints you have are leading to an infeasible design.  You can try using the PENALTY parameter to penalize the overhanging regions instead.

Equality constraints are difficult to satisfy, you can just set a lower bound of 100% volume on those regions (instead of both lower and upper bound) or consider whether it should be a design space, if you are required to have 100% of the material.

The SUPP/UNSUPP parameter dictates whether the non-design space can have material grow out from it in the direction of the build volume.  So for instance, if you made the bottom green part non-design space, you would need the SUPP parameter to be able to "grow" material out of the base.  Hopefully some of these suggestions are helpful.

Thanks,

Rob H.