Methods for improving the robustness of optimised multiscale structures

Abstract

This thesis presents methodologies for improving the real-world robustness of optimised multiscale structures, progressing their advancement towards industrial applications. At its core, a two-scale optimisation framework is utilised to demonstrate the efficacy of the proposed models. At the microscale, a parameterised unit microstructure composed of three axis-aligned trusses is utilised. The radius of each truss can be freely modified to derive a wide range of microstructure configurations, and by extension material properties. Utilising numerical homogenisation, these material properties are efficiently represented within a macroscale optimisation domain. Response surface models are successfully constructed to link the microscale design variables (i.e. truss radii) and the resulting microstructure material properties (homogenised stiffness, volume fraction and stress). Given a design objective and constraint(s) the optimiser manipulates the radius of every microstructure truss in the domain to tailor the local material properties to reach an optimal design with respect to the objective. To ensure optimised multiscale structures can be reliably utilised in industrial applications it is important to understand and consider their robustness. In particular, this work focuses on preventing structural failure and incorporating geometric uncertainties introduced during the additive manufacture of optimised multiscale structures. To prevent failure, stress constraints are introduced within the optimisation framework. Microscale stresses are parameterised by six unit strains, enabling accurate microscale stress recovery for any macroscale strain enabling reliable microstructure stress predictions without the need for prohibitively expensive single-scale finite element simulations and enabling its use within a multiscale optimisation framework. To introduce manufacturing uncertainty, two geometric uncertainty models are presented. One which linearly erodes and dilates trusses and another which introduces design-dependent non-linear defects. The models are integrated within a robust optimisation framework to design structures whose standard deviation of compliance is up to 95% lower compared to equivalent standard deterministic designs, making them more tolerant of manufacturing imperfections and giving confidence in their real-world performance.