For this year's COMSOL Conference I presented how Shape and Topology Optimization can be used in a product design process. I use loudspeakers as an example the product, but the techniques can be applied across many types of products. I look at many combinations of physics and optimization, and I have shown a few of them below. The presentation and the paper will soon be available at COMSOL's homepage.
Topology Optimization of Woofer Basket
The first example is a topology optimization of a woofer basket, which I seek to make as stiff as possible for the given loads and boundary conditions. You typically want the woofer to be stiff as to not having to include it in your design DOFs. Starting out with the design of the left and limiting the design domain, so that only 50 % of it can be assigned a value indicative of structure, the optimized design is shown of the right.
As with many topology optimized design, there is a kind of 'organic' feel to it. While designing a stiff basket using more traditional method may not be that challenging, it is still interesting to see the result from a formal optimization procedure. Also, for more complex structures it will be much more relevant to use mathematical techniques in the design process.
Topology Optimization of Tweeter
The second example is a topology optimized tweeter, which is actually from last year's conference. A phase plug has grown out of an assigned design domain, and an improvement in the on-axis sound pressure level was found. The phase plug shown in grey could not have found via other methods unless some a priori knowledge is available, such as where approximately to place it, and which approximate shape it should have. With topology optimization, the design appears without this a priori information, and afterwards shape optimization can be applied, if necessary.
Shape Optimization of Woofer Cone
One of the shape optimization examples was a woofer cone whose shape was controlled by simple polynomials. While not necessarily indicative of how you would use shape optimization in your design process, it still illustrates how the shape optimization setup can help in determining which steps to take towards improving problematic designs, compared to more combinatorics/trial-and-error methods. To make the optimization more efficient, I used the Rayleigh integral for the acoustics, which makes it possible to have more DOFs in the structural design, so that the shape optimization can be run on the actual geometry without simplifications.
Topology Optimization of Woofer Heat Sink
The final example looks at the physics of heat conduction in solids combined with topology optimization to design a heat sink for a woofer. For a given design domain an optimal heat conduction via a heat sink geometry if found, leading to a quite interesting design.
More examples are available in the paper and presentation, and there are many more that could be done. While it should not be your first tool to grab for in the toolbox, formal mathematical optimization has great potential, and when used with proper care, you can come up with favorable and non-intuitive designs that more traditional methods cannot reach.
I hope you enjoy the examples, and let me know if you would like to see more of this.