Multi-Scale Topology Optimization of Multi-Material Structures with Controllable Geometric Complexity - Applications to Heat Transfer Problems

This paper presents a topology optimization method to design assemblies of periodic cellular materials with controllable geometric complexity. The framework is based on a novel multi-scale and multi-material design model in which the structure, the layout of the material subdomains, and their micro-structures are optimized concurrently. To allow a tight control over its geometrical complexity, the layout at the macro-scale is described by level-set fields, parameterized by geometric primitives. The micro-scale geometry is represented through a density approach. A nonlinear programming algorithm drives the optimization process using design sensitivities computed by the discrete adjoint method. The proposed design framework is studied with heat transfer problems. Practical design problems, such as a heat sink and a thermal storage unit with phase change are discussed. The macro-scale analysis model relies on a generalized transient diffusion equation. At the micro-scale, homogenization is used to compute equivalent material properties. The numerical examples show that the optimized multi-scale multi-material layouts outperform the corresponding mono-scale structures while maintaining geometric simplicity at the macro-scale level.