Multiscale structural, thermal and thermo-structural optimization towards three-dimensional printable structures

This thesis develops a robust framework for the multiscale design of three-dimensional lattices with macroscopically tailored structural and thermal characteristics. The work exploits the high process flexibility and precision of additive manufacturing to the physical realization of complex microstructure of metamaterials by developing and implementing a multiscale approach. Structures derived from such metamaterials exhibit properties which differ from that of the constituent base material. Inspired by the concept of Free Material Optimization (FMO), a periodic microscale model is developed whose geometric parameterization enables smoothly changing properties and for which the connectivity of neighbouring microstructures in the large-scale domain is guaranteed by slowly changing large-scale descriptions of the lattice parameters. The microscale model is evaluated at full factorial design points to discretely populate material property spaces. A property point is fully defined for a micro-architecture when its elasticity matrix, thermal conductivity matrix and volume fraction is determined. The process of property-space population is facilitated by leveraging the existence of micro-architecture symmetries so that there exists a 95% reduction in the simulations required despite a full-factorial design of experiments. The discrete property evaluations are converted to continuous functions by response surface modelling so that the properties exist as continuous functions of the micro-architecture geometry parameters. A lattice-based functional grading of material is derived using the finite element method. The optimization is driven by a chain-rule combination of sensitivities derived by the adjoint method and sensitivities derived from explicit material property expressions. The novelty of the work lies in the use of multiple geometry-based small-scale design parameters for optimization problems in three-dimensional real space. The approach is demonstrated by solving structural, thermal and thermo-structural optimization problems. The results show designs with improved optimality compared to commonly implemented optimization methodologies. The optimal designs obtained are physically realizable by additive manufacturing techniques.Open Acces