Optimising Continuous Microstructures: A Comparison Of Gradient-Based and Stochastic Methods

Optimisation techniques are used by engineers to design structures to satisfy many criteria, such as high strength or low weight. Recent advances in computer controlled manufacturing technology have also allowed the construction of such structures to be automated, so that the machine plays a significant role in both design and building processes. The work in this paper investigates optimisation of a microstructure suited to a rapid prototyping technology known as stereo lithography that is capable of construction at a high resolution, currently around 0.05mm. Our technique is based on the seamless repetition of a tiny structural module over a large volume such that the overall object behaves as a continuous material. It is, in effect, operating at a scale between traditional large-scale manufacturing and nanotechnology.

The optimisation method is analysed with the specific requirements of this technique in mind, but involves generic structural principles that are shared with many other optimisation problems. As such the methods investigated in this paper can be applicable to other types of structures. The types of structures investigated are known as space frames. Space frames are made of linear members that can be oriented in any direction in 3 dimensional space, and connected at node points either by rigid or flexible connections. To define a particular space frame one must specify both the members themselves, and the locations and orientations of the nodes in 3-dimensional space. We refer to these as the topology and geometry of the structure respectively, and it is these two properties that are considered by a structural optimisation algorithm.

We compared a deterministic gradient-based method with a stochastic genetic algorithm in optimising the geometry of a given topology. Each method yields a fitness in terms of the total member stresses under load, and the variance in these fitnesses over a number of runs has been taken as a measure of confidence in that fitness. The results have shown that a topology can be judged by the fitness of a geometry that might not be the global optimum.