Efficient topology optimisation of multiscale and multiphysics problems

The aim of this Thesis is to present efficient methods for optimising high-resolution problems of a multiscale and multiphysics nature. The Thesis consists of two parts: one treating topology optimisation of microstructural details and the other treating topology optimisation of conjugate heat transfer problems.
Part I begins with an introduction to the concept of microstructural details in the context of topology optimisation. Relevant literature is briefly reviewed and problems with existing methodologies are identified. The proposed methodology and its strengths are summarised.
Details on the proposed methodology, for the design of structures with periodic and layered microstructural details, are given and the computational performance is investigated. It is shown that the used spectral coarse basis preconditioner, and its associated basis reutilisation scheme, significantly reduce the computational cost of treating structures with fully-resolved microstructural details.
The methodology is further applied to examples, where it is shown that it ensures connectivity of the microstructural details and that forced periodicity of the microstructural details can yield an implicit robustness to load position. An example of expansion control of a structure under compression is treated in detail, where it is shown that taking boundary effects into account is paramount.
Part II starts with an introduction to conjugate heat transfer and briefly reviews relevant literature. The governing equations used to describe heat transfer and fluid flow are outlined, describing both a commonly-used simplified convection model and the full natural convection model.
Topology optimisation using the simplified model is investigated as a means to reduce the computational time of optimising heat sinks. The model is shown to be useful in an industrial context to provide a first approximation in the design of heat sinks. However, serious flaws and drawbacks of combining the model with topology optimisation are identified.
In order to take full advantage of topology optimisation for providing insight into optimal design of heat sinks, a full conjugate heat transfer model is introduced. Optimised heat sinks are presented for both two- and three-dimensional natural convection problems, where similarities and differences are discussed. Generally, the observations are in line with classical heat sink design, but topology optimisation spawns designs exhibiting optimal characteristics without any prerequisite knowledge. Furthermore, it is shown that when using the full model, the local convection coefficients and surface fluxes are in direct disagreement with the assumptions of the simplified model.
The computational performance and scalability of the developed framework is presented and it is shown that it allows for efficient optimisation of problems with more than 300 million degrees of freedom and almost 30 million design variables. Finally, the framework is used to generate novel passive coolers for light-emitting diode (LED) lamps, where a 20 − 25% lower temperature of the LED package is achieved as compared to reference designs, using around 16% less material.