Concurrent Multiscale Topology Optimization of Coated Structures Infilled With Multiple Self‐Connected Microstructures

ABSTRACT Compared to those coated structures optimized with periodic and uniform microstructures, considering multiple lattice‐infilling microstructures can effectively enlarge the design freedom of coated structures with better structural performance achieved. This paper presents a concurrent multiscale topology optimization method for coated structures infilled with multiple self‐connected microstructures, which involves a new density‐based extended two‐step filtering procedure. Using various filtered density fields, the outer coating and the distribution of multiple microstructural blocks of coated structures can be simultaneously distinguished by relying on a single macroscale design variable field. In particular, the construction of coated structures with multiple infilling microstructures and the multi‐material interpolation model are demonstrated under the framework of the ordered solid isotropic material with penalization (SIMP) method. At the microscale, topologies of microstructures are described by the density model and optimized using the homogenization method. To conveniently ensure the connectivity between different microstructural configurations, the designable connective region (DCR) method is introduced into the proposed approach to achieve the self‐connected property of optimized lattice microstructures. The effectiveness of the proposed method is proved through several numerical examples, with discussions on the influences of different coating thicknesses, different volume fractions, etc. Eventually, the manufacturability of optimized structures at two scales is also illustrated by using the additive manufacturing (AM) technique, which further validates the applicability of the proposed approach.