This presentation was made at the NAFEMS European Conference on Simulation-Based Optimisation held on the 15th of October in London.

Optimisation has become a key ingredient in many engineering disciplines and has experienced rapid growth in recent years due to innovations in optimisation algorithms and techniques, coupled with developments in computer hardware and software capabilities. The growing popularity of optimisation in engineering applications is driven by ever-increasing competition pressure, where optimised products and processes can offer improved performance and cost-effectiveness which would not be possible using traditional design approaches. However, there are still many hurdles to be overcome before optimisation is used routinely for engineering applications.

The NAFEMS European Conference on Simulation-Based Optimisation brings together practitioners and academics from all relevant disciplines to share their knowledge and experience, and discuss problems and challenges, in order to facilitate further improvements in optimisation techniques.

Resource Abstract

Topology optimisation (TO) is an increasingly popular generative design method that forms an established part of the design process in various branches of industry. The density-based approach, introduced by Bendsøe (1989), is dominant and available in several commercial software packages. TO is most often used to generate design concepts in an early stage of the design process, and optimises a material distribution defined in terms of local density variables. Designs generated by density-based TO exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. How to bridge the gap between TO and CAD is a longstanding challenge. Addressing this problem by manual design adjustments or smoothing is time-consuming and affects the optimality of TO designs.



This research proposes a fully automated procedure to obtain unambiguous, accurate and optimised geometries from arbitrary 3D TO density fields. The procedure starts with a geometry extraction stage using a parametric level-set-based design description involving radial basis functions, similar to Luo et al. (2008). The geometry extraction is followed by a shape optimisation stage involving local analysis refinements near the structural boundary using the Finite Cell Method (FCM) introduced by Parvizian et al. (2007). Elements located outside the structural domain are discarded to improve the computational efficiency of the shape optimisation, see Figure 1.



Well-defined bounds on basis function weights ensure that sufficient sensitivity information is available throughout the shape optimisation process. The sensitivity analysis for the shape optimisation is very similar to that of TO. Therefore the proposed method can easily be used for post-processing all kinds of TO optimisation problems with limited implementation effort. Our approach results in highly smooth and accurate optimized geometries, and its visual effectiveness is illustrated in Figure 2.