Multiscale topological design of coated structures with layer-wise bi-material lattice infill for minimum dynamic compliance

In this paper, a novel multiscale topological design strategy for coated structures infilled with layer-wise bi-material lattice microstructures is presented, where the objective is to minimize the dynamic compliance of the macrostructure under time-harmonic excitation frequency. The optimization of bi-material microstructures is concurrently performed with the topological design of the macrostructure to fully consider the interaction of structural evolution between the two scales. At the macroscale, the material distribution for the macrostructure is optimized using the velocity field-based level set method, which inherits the implicit geometrical representation, and smooth structural boundaries can be obtained. Due to the signed distance property, the thickness of the outer coating is able to be well-maintained during the iteration. As for the microscale, the density method is chosen to conduct topology optimization of lattice microstructures. The lattice infill for coated structures is designed to be layer-wise by dividing it uniformly (or near-uniformly) into different layers, and each layer is composed of periodic and uniform bi-material microstructures, which can enlarge the design space and generate various microscale structural patterns to better resist the vibration response. The sensitivity analysis for the dynamic compliance with respect to the design variables at different scales is carefully performed and the influences of the number of divided layers, excitation frequency, coating thickness, damping coefficients, element meshes, static constraint, and division direction for the lattice infill on the optimized macroscale and microscale structures are studied by several numerical examples. Moreover, a body-fitted mesh for a Computer-Aided Design (CAD) model is constructed and the finite element analysis results further verify the effectiveness of the proposed approach.