A Primer for Design Engineers
Have you come across images of exotic, organic-looking part shapes in a CAD graphics window? Do they look like flights of fancy rather than disciplined work? These shapes may be the result of a topology optimization study — an application now readily available, so you can try your hand at it.
In a sense these shapes are indeed flights of fancy — but they originate not from a human mind, but from the determined logic of a computer algorithm.
Topology optimization takes a 3D design space and literally whittles away material within it to achieve the most efficient design. The method doesn't care about aesthetics, traditional approaches, or any other usual design constraint — if you define the loading and the constraint system, it will figure out the material needed to develop that load path.
Behind the scenes
The technology starts with a regular finite element analysis (FEA) mesh occupying the defined design space. An initial FEA shows the stress distribution throughout the space, and which regions are working efficiently. Each element reports back its stress level and strain energy — how hard it is working. Elements not picking up much stress, with little strain energy, are removed by the topology optimizer.
As it removes elements, it keeps an eye on whether the overall evolving structure is affected by their departure — in some cases, elements may be reprieved. The optimizer has a target number of elements to remove, based on the target volume fraction you set: aim for a fraction of 30%, and 70% of the elements in a regular mesh are sent to the chopping block. In practice, removal happens in steps, with the stress state stabilising at each iteration.
The kill zone
In many optimizers the action is subtler than outright deletion, which is technically complicated and computationally expensive. Instead, a "soft kill" approach drops the element stiffness and density down to a near-chewing-gum level — the element is still there, but marginalised. Many optimizers relax the strict segregation between parent materials (say, steel at relative density 1.0, and chewing gum near 0.0), letting an element adopt any stiffness and density across that range, while being "encouraged" to migrate to 1.0 or 0.0 — with a penalty for sitting in between.
Shades of grey
Optimizers won't always achieve the limiting values of 1.0 or 0.0 for every element — some end up somewhere in between. A grayscale representation shows regions of parent material in white, chewing gum in black, and shades in between. If the optimizer is struggling, large regions will show varying shades of grey; if it finds a well-defined load path, the distribution migrates clearly towards black or white.
The exotic shapes described earlier don't represent the element faces — they are surfaces fitted through the grey-scale contours. Surface smoothness is largely controlled by how fine the underlying FEA mesh is, and how well distributed the parent material is.
You are in control
Topology optimization is sometimes described as a wild ride — great at radical solutions, the flights of fancy described above. But engineers have many controls to steer toward more usable configurations: manufacturing constraints such as limiting member size within the design space, requiring symmetry about planes, extrudability, or mould-drawability, and more. Choosing the volume fraction controls how aggressive the optimizer will be.
