Optimization – Science or Philosophy?

 Background

 

A previous article  I wrote introduced structural optimization concepts and methodology. In this article we look at some of the philosophical questions which arise when considering optimization; and which may indeed drive the approach taken and the tools used.

The first question to consider is the context in which we are planning structural optimization. This is more fundamental than the particular software or methodology and can embrace radical new designs or evolution of existing designs.

Radical New Designs

 

If we are looking for fresh new designs which break away from traditional configurations then a Topology Optimization approach can be used. It is important to understand from the outset that we need to maximize the potential solutions that are achievable in practice and are considered optimal in a broad enough context. Factors include:

• Uncertainty of operational environment
• Manufacturing Feasibility
• Incompatibility with packaging requirements
• Ignoring of thin wall solutions
• Too radical a change from traditional designs
• Vulnerability to other environmental factors
• Aesthetic incompatibility

 

We will look at all these points in the following discussion.

One of the biggest challenges to optimization is if the operational environment is uncertain. This can include external applied loads and boundary conditions. It may be that the overall design concept is not mature enough. For example an electronics chassis is to be mounted in a vehicle, but the location within the vehicle, attachment method, electronic component weight, maneuvering envelope, crash scenarios have not yet been developed. In traditional FE analysis we would take care to idealize and analyze the structure with a view to providing preliminary sizing confirmation, approximate local response levels etc. We would expect to refine the model as the overall design progressed to a frozen state. How can we adapt this approach in an optimization strategy?

One way would be to use a robust optimization approach where the spread of uncertainty is included. Traditionally this is done with material properties and dimensional tolerances, but here variation in loading and boundary stiffnesses are more important. Robust optimization strategy relies on a very large number of analysis variations being run, evolving towards the most stable across a variation in input parameters.

Another approach would be to include the uncertain external design parameters into a multi-objective analysis. With two objectives we can look at trade off studies where each of the objectives is dominating in turn. In the electronics chassis example these could become trends for resisting inertia loading level and supplying varying attachment stiffness. Useful guidance could be fed back into the overall design for the implications of high or low g loading with flexible or stiff attachment fittings. Typically hundreds if not thousands of design configurations would be evaluated. Each successful candidate design would be an optimum in its own right, so only best in class results are used for trade off studies. More than two objectives can be considered, but there is then a danger of not being able to visualize the tradeoffs in an intuitive manner.

It is interesting to note the traditional limitations to manufacturing are being overcome in some areas by 3D printing methods. We have all seen examples where an integral chain or gear train is produced which is impossible to manufacture and assemble using traditional methods. With the advent of structural materials into this arena, which allow further levels of optimization if they are orthotropic or anisotropic, wider possibilities emerge. I recently saw a 3D printed UAV wing and blended body where the internal structure was more reminiscent of a bird’s skeletal structure than a traditional spar and rib layout. Many radically new designs follow a similar relationship to natural structures, such as leaves, trees, root systems etc.

The UAV wing prompted an interesting discussion on where to store the fuel – or in general, packaging design. We often see topology optimization whittling away design space, but working around fixed ‘no go’ volumes which are to contain fuel, electronics, motors etc. One of the challenges here is to avoid making up front decisions about packaging volumes, which dictate the evolution of an ‘optimum’ design, but in themselves are not optimal. I have not seen an integrated approach to this (in fact I would welcome any examples of this). Conversely if the fuel volume is squeezed into available voids in the UAV optimum organic structure then again we may be missing an overall optimum design, perhaps of a radically different configuration. In a similar way support and loading positions are often ‘frozen’ topology mesh zones, which remain intact. To be truly optimum the location of these zones should also be adaptable.

If we use 3D topology optimization to explore design space, then the resultant design will be biased towards organic 3D ‘solid’ type structures. If the mesh fidelity in design space is high enough, then we can approach thin wall thickness. However there is no natural reason why the optimizer would recognize that a region of planar thin wall may be an ideal design trend. Again, I am not aware of any topology optimization tools that can recognize the emergence of a thin wall bias. The closest to this I have seen is when we have a 2D topology optimization space beginning to ‘checker board’ over a region of the structure. Checker boarding occurs when an optimizer can’t find a strong direct load path, so tries to spread the load through a physically unrealizable element based pattern of weak and strong material – rather like a sponge or honeycomb. It is useful to view this as an attempt to introduce an intermediate thickness of material. I have successfully taken a region like this, defined it to be a thin shell idealization and turned the problem into a sizing optimization of the shell thickness.

It may be that the resultant design is too radical for the application. For example if the UAV wing concept described is to achieve certification in a manned aircraft then it would require an enormous amount of testing and analysis to validate the structure. No design guides for this type of configuration exist to help in the certification process and there is no operational experience. It is probably the way of the future, but it takes some time to establish the level of confidence required. However many applications will not be so restrictive and in any event selecting from a wide candidate configuration basis will always drive innovation. The level of radicalness needs to be tailored to the application.

When evolving a radical new design using topology optimization, the influence of loading and environmental issues beyond the basic design definition may have to be considered. For example a structure may be robust enough to survive all the defined load cases, but is too fragile to be handled or assembled. A ‘chunky’ structure that is traditionally only considered for strength requirements may now be a much more distributed slender structure, vulnerable to buckling or low resonant frequencies. A classic example of structural optimization saw the development of geodesic type aircraft structures, somewhat like a basket weave. These were lightweight, strong and stiff, but unfortunately had very poor fatigue characteristics.

Finally, the optimal solution may be aesthetically unacceptable. For consumer products this may be a driving factor, but even cars, planes and ships are assessed this way. An organic, fibrous looking vehicle body may be ideal for stiffness, crash, crash worthiness etc., but may not have much curb appeal! An aircraft which is not contemporary in appearance may not inspire passenger confidence…

Evolution of Existing Designs

 

If a design is considered mature in terms of layout and configuration then ether Sizing Optimization can be used for fabricated structures idealized as thin shells and beams, or Shape Optimization can be used for thin shell or solid type structures.

Sizing Optimization is based on changing the physical properties of the elements in the FEA mesh. This means the method is limited to idealizations using 1D or 2d elements. The method has a very long and successful history in traditional industries such as automotive, maritime and aerospace with thin shell fabrications. The structural layout has been determined by other considerations, often using high level parametric optimization studies. The sizing optimization is then a search for an optimum within that pre-defined configuration.

However I have started to see companies using this approach to evaluate stiffnesses of different load paths within a solid type component. A joint fitting for example can be broken down into bending and axial load paths with a high level of idealization using 1D elements. The motivation for such a drastic approach is to allow rapid sizing optimization of the simplified structure. This gives useful information about the importance of each load path and provides a direction for useful design evolution. The simplified structure also tells a clearer story as to ‘why’ the structure is successful. Many thousands of configurations can be studied very quickly.

 

Shape optimization traditionally used a fixed FEA mesh which was then distorted in some way, but kept the same topology. It was perhaps the most unusable type of optimization solution as methods to achieve candidate mesh distortions were tedious to set up and not very general. However modern methods have broken away from the traditional paradigm based on design variables (geometric features), objective function (mass) and constraints (stresses and deflections).  Instead the methods revert back to the very early Optimality Criteria approaches. An Optimality Criteria such as Fully Stressed Design simply stated that a promising design evolution would follow a predefined criterion, such as trying to maximize stresses in all parts of a structural component to ensure it was working most efficiently. The modern shape optimization tools use more sophisticated criteria, such as stress homogeneousness (the stresses should flow smoothly throughout a structure) and control the mesh perturbations in a more sophisticated way, including re-meshing if required.

Shape optimization seems to work best when honing a mature design. For example quite subtle changes in hole or fillet profiles can make significant changes to local stress concentrations and hence fatigue life.

Overall, some caveats apply equally to refining mature designs as when evolving radical new designs

• Uncertainty of operational environment
• Manufacturing Feasibility
• Incompatibility with packaging requirements

General Observations

 

Whichever stage of optimization is being considered, some basic recommendations are common.

• The physics of the engineering structure must be fully understood before any meaningful optimization can be attempted.
• The FEA implementation of the structure must be sound, modeling errors will usually invalidate an ‘optimum’ solution.
• The scope of the optimization study must be clearly defined – conceptual or derivative.
• The breadth of the study must be realistic – will we be able to make sensible engineering judgments based on the answers we get back?
• Will the volume of output data swamp our decision making process?

There are many more practical or philosophical questions that could be asked to make sure that the ‘optimum’ that is delivered is valid and meaningful to us in design.