Multiscale thermal and thermo-structural optimization of three-dimensional lattice structures

This paper develops a robust framework forthe multiscale design of three-dimensional lattices with macroscopically tailored thermal and thermo-structural characteristics. A multiscale approach is implemented where the discrete evaluations of small-scale lattice unitcell characteristics are converted to response surfacemodels so that the properties exist as continuous functions of the lattice micro-parameters. The derived frame-work constitutes free material optimization in the space of manufacturable lattice micro-architecture. The optimization of individual lattice member dimensions is enabled by the adjoint method and the explicit expressions of the response surface material property sensitivities. The approach is demonstrated by solving thermaland thermo-structural optimization problems, significantly extending previous work which focused on linear structural response. The thermal optimization solu-tion shows a design with improved optimality compared to the SIMP methodology. The thermo-structural optimization solution demonstrates the method’s capability for attaining a prescribed displacement in response to temperature gradients