There is a bit of history in the name. At first, people started optimizing things like truss member sizes. This is called Size Optimization. Then came Shape Optimization to answer questions like what is the optimal shape for the openings in the web of an I-beam. Shape optimization is a bit more sophisticated than size optimization. But people realized that both size and shape optimization cannot alter the topology of the structures. That’s when Topology Optimization started to take shape. At first truss topology optimization was studied and the so-called “ground structure” approach was developed but this essentially still size optimization. The Topology Optimization as it is known today has really been started when computers became more powerful and pioneers like Sigmund, Kikuchi and others were able to run large continuum models and optimized the “density” of each finite element to generated structures in a fashion just like pixels formed raster images.



Topology Optimization is more computationally “expensive”, but it has the most freedom and hence is capable of generating the most optimal designs. Topology optimization, in theory, contains both size and shape optimization. However, current computers are still not powerful enough for representing all details of structures in the pixelated fashion. More over, the true optimal structures may not be suitable for manufacturing (except for the fast growing 3D printing technology). Thus shape and size optimization are still useful in practice.

I think that the future of Topology Optimization can be in the micro-engineering space. True optimal structures are often in the form of microstructures. This was regarded as the “gray area” problem that needs to be avoided in the past because it was thought to be not feasible to manufacture. When I defended my Ph.D. degree at UIUC, professor Phillip Geubelle asked me how would the microstructures that the optimization code generates be manufactured. I answered I had no idea. But just a few years later, with the advent of 3D printing technology, the answer became obvious. The main idea is to design a material microstructure field which is different at every point in the structure. This is applicable to all types of microstructures, including composites with fiber orientation and reinforcement amount for composites etc.


More examples of microstructure optimization for dynamics responses:
https://www.youtube.com/watch?v=zhPGv8N0dKc
https://www.youtube.com/watch?v=3qlS849lsTw
https://www.youtube.com/watch?v=Vj2307sl5LU