Self-connected multi-domain topology optimization of structures with multiple dissimilar microstructures

Multi-domain topology optimization allows the design of lattice structures with multiple dissimilar microstructures. However, how to handle the connectivity issue between the dissimilar microstructures is a very important and difficult topic. In this paper, a self-connected material interpolation is proposed to handle the topology optimization of structures with multiple dissimilar-but-connected microstructures. Due to this interpolation, the material in the interface domains between the dissimilar microstructures can be separately defined, which enables us to carefully design the material of interface to guarantee good connectivity. An advantage of this way is that the connectivity requirement is only considered for these microstructures in the small interface domain while other microstructures can be freely designed in the remaining relatively much bigger design domain. In this paper, the connectivity requirement is realized by simply using a non-design solid domain in the interface microstructures. Based on the proposed interpolation, a two-scale multi-objective optimization formulation is proposed for concurrently designing the topologies and the lattice materials. In addition to the traditional mechanical performance, a geometric feature, i.e., the mass of the interface, is also taken as an objective in this method to control the material usage of interface. Several examples with parameterized lattice microstructures are provided to illustrate the effectiveness of the proposed method.