Topology and Idealised Form / Performance

At the beginning of my career as a manual Draughtsman, it was a reality that the geometry we were able to define, the ‘form’, ‘shape’ or indeed ‘topology’ of the intended 3D product, was restricted to a major extent by the limitation imposed from the mechanics of the manual draughting process. We defined out planar views with: straight lines, circles and parts of circles, conic curves and the occasional ‘free form’ curve. The very process of manual draughting dictated to a great extent the 3D form we could define with reasonable unambiguity. The ‘shapes’ defined would be subject to some basic stress calculations, mostly manually calculated and very occasionally a design would be subject to detail stress calculations, or indeed some early Finite Element Modelling (FEM) and solving (Analysis FEA) with, by today’s standards, an incredibly coarse mesh. Larger than desired safety factors were implemented to provide some allowance for the fact the calculations were not ‘accurate’. This process ‘locked-in’ most of the design freedom at the draughting stage. The Topology of the part already highly restricted any further modification or correction.  

As 3D CAD with its complex 3D surface definition capability coupled with solid modelling methods developed, we were able to define a closer approximation of the 3D part we had intended. However once again the process of modelling and the functional limitation of the specific CAD system limited our ability to define a more optimal ‘form’. This was also coupled, as had always been the case, with the limitations of the proposed manufacturing method and material choice. We were however then able to better inform the structural validation with FEM methods becoming more refined and available. However Stressing, was move a validation process, post geometry (topology) definition with most focus on adding material where a risk of failure existed. Still, a more resolved solution was possible than was the case previously. This process also ‘locked-in’ the topology, and limited the subsequent freedom to modify the ‘shape’.

We then moved into the era of ‘Parameterization’ initiated by PTC, but followed by all the major CAD vendors, this gave us, we were told, freedom to modify the design downstream, including post analysis. If we consider this proposition, it is not the whole story, we were still constrained by the way the model was built (its tree structure that defined dependencies) and the fundamental ‘topology’. So, for example we could drive changes to a cylinder, but we could not easily replace this with a tapered elliptical form that may have been a better solution for the situation. It was also difficult to ‘optimise’ from say, three radial triangular webs to seven arbitrarily placed buttresses. The result is once again that the ability to ‘optimise’ and refine the design is still constrained by the topology (and parameterisation) that has been defined and the geometry (topology) stage. Even if we couple the geometry to an FEA tool and drive our model parameters from this, we are far away from an idealised solution as both the topology and parameterisation regime has already ‘locked-in’ and limited the freedom to optimise.   

Today we see the rise and adoption of what are described as “Topology Optimizers”, where we can define the structural environment the part(s) are to perform within (the boundary conditions) the material characteristics (properties) and some limited manufacturing consideration. The “Optimizer” then uses these inputs to evolves us an ‘ideal’ form, or set of ‘idealised’ forms, that meets the defined conditions. At last the opportunity to truly optimise the part topology in line with required performance? Well partly is the answer, it’s not the full story for as long as every possible set of

conditions was informed on the model we are getting closer. Do we know all the conditions, and even if we do, can we inform them all on the model at the same time? We could have natural frequency objectives, many loading situations, many more abuse cases and certification cases to consider, fatigue requirements and many more. Even if we have covered all the external influences on the model that play a part in defining the optimal solution, is the resulting geometric form useful to us? The answer is that it probably only has limited use. It will likely be a faceted model (following the FE mesh boundaries created in the optimization code) not smooth forms that can easily be made. It may also contain zero radius internal corners that are in real life a likely initiator of cracks and failure. Also, the solution(s) the optimizer produced for us were defined, limited by the algorithms and technology applied. As an example, it may have generated a skeletal solid form that could be manufactured by rapid manufacturing methods but not mass produced in a traditional factory environment. Worse, it may for example, have given us a monolithic solid solution when in fact a lattice or cell interior, with a solid shell may well have been a better solution.

In conclusion, as with all tools and technologies, we need to understand the limitations of optimization in all its guises, just as we need to trade off; material choices, manufacturing methods, modelling method and design tools. As long as we as engineers use our knowledge, experience and most importantly judgment, and take the useful benefits of topology optimisation as helping us achieve a more optimal product design, we will take significant benefit from the technology. But never forget that every tool we use to define the geometry and performance of our products, limits our freedom the optimize it, including the tools currently being presented as ‘optimizers’. This is not to say ‘Topology Optimizers’ are not an extremely useful addition to the engineer armoury, they are. just understand that they don’t give us a final design solution, but they can be exploited to help us get to a final solution, faster.

It is a fundamental truth that topology and performance are coupled, but they are bound by the limitations of the tools we have available to design, analyse, optimise and manufacture real parts and products.

Post Script.

‘Rapid manufacturing’ methods along with close to ‘net metal’ manufacturing and ‘additive manufacturing’ are being coupled with optimization tools and promoted as future product development and manufacturing approaches. This will be the subject of a later article.