Multiscale concurrent topology optimization for structures with multiple lattice materials considering interface connectivity

Ensuring connection between different lattice materials is a very aspect of topic in multiscale concurrent topology optimization methods. This paper presents a novel approach to design structures that comprise multiple lattice substructures. This paper presents a novel approach to design structures that comprise multiple lattice substructures. The connectivity between these lattice substructures is improved by dedicating a connective microstructure and by enforcing similarity of the boundaries of the connective microstructure and the other base lattice substructures. First, a connective region is predefined for all microstructures. Next, solid elements in these regions are extracted and assembled into a connector. Then, two inequality constraints are introduced to retain topologies of the connective region in the connective microstructure and the connector that are consistent. Finally, due to the uncertainty of the final use of interfacial materials, a multiobjective optimization approach is developed to minimize both compliance and material use. The topology of all microstructures, the macrostructure and the connector are concurrently optimized. The two inequality constraints are only considered in the interfacial material microstructure. Other base lattice substructures are optimized without considering connectivity, thus allowing the method to have greater design space. On the macroscale, a multiple lattice materials interpolation model is defined to describe the distribution of different lattice materials and their interfaces. The numerical homogenization method bridges between the scales and evaluates the equivalent properties of the microstructure. Several 2D and 3D numerical examples are given to illustrate the effectiveness of our method.