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This paper applies topology optimisation to the design of structures withperiodic microstructural details without length scale separation, i.e.considering the complete macroscopic structure and its response, whileresolving all microstructural details, as compared to the often usedhomogenisation approach. The approach takes boundary conditions into accountand ensures connected and macroscopically optimised microstructures regardlessof the difference in micro- and macroscopic length scales. This results inmicrostructures tailored for specific applications rather than specificproperties.  Dealing with the complete macroscopic structure and its response iscomputationally challenging as very fine discretisations are needed in order toresolve all microstructural details. Therefore, this article shows the benefitsof applying a contrast-independent spectral preconditioner based on themultiscale finite element method (MsFEM) to large structures withfully-resolved microstructural details.  The density-based topology optimisation approach combined with a Heavisideprojection filter and a stochastic robust formulation is used on variousproblems, with both periodic and layered microstructures. The presentedapproach is shown to allow for the topology optimisation of very large problemsin \textsc{Matlab}, specifically a problem with 26 million displacement degreesof freedom in 26 hours using a single computational thread.

Robust topology optimisation of microstructural details without length scale separation - using a spectral coarse basis preconditioner