Efficient Computation Techniques for a Standard Topology Optimisation Routine

Topology Optimisation (TO) is a powerful optimisation technique that is used mainly in research and engineering areas to derive optimal and sometimes innovative material layouts, the main objective of TO usually concerns the reduction of material volume (weight) while trying to improve mechanical performance without compromising its structural resistance to imposed loads. This can be achieved by systematically re-distributing material contained in a specific design space, this technique often results in intricate and complex geometries that may be two-dimensional or three-dimensional depending on the specific application. Such a technique requires a way to link a physical model with a computational representation, in this sense, the always popular, Finite Element Method (FEM) provides the necessary computational framework to evaluate the mechanical properties of optimised designs, in further detail, FEM is utilised to model the behaviour of structures (any structure is valid) subjected to external forces (which can be of very different nature), enabling practitioners to simulate and analyse complex systems. FEM works on meshes of simple discrete elements and their corresponding nodes, while elasticity theory and mathematical modelling allow the obtention of the structural response to mechanical loads. Such response is then used as the basis over which TO routines work. Many TO methods can be used to obtain optimal designs, however, direct programming of them often requires elaborated codes that are not always accessible or even easy to understand. Some authors leave cumbersome FEM codes to third-party software, others, offer practical simpler codes to allow beginners to understand the basic TO method. In this second approach we revise one code implementation, that, despite solving the TO problem using a discrete TO approach, it leaves the practitioner with an antiquated, slow, resource consuming and often non-scalable implementation. The main objective of this work is to recommend some simple changes addressing many of these problems while offering tests showing the pros and cons of each technique.