Multi-objective concurrent isogeometric topology optimization of multiscale structures

Multiscale structures require excellent multiphysical properties to withstand the loads in various complex engineering fields. In this study, a concurrent isogeometric topology optimization method is proposed to design multiscale structures with high thermal conductivity and low mechanical compliance. First, the mathematical description model of multi-objective topology optimization for multiscale structures is constructed, and a single-objective concurrent isogeometric topology optimization formulation for mechanical and thermal compliance is proposed. Then, by combining the isogeometric analysis method, the material interpolation model and decoupled sensitivity analysis scheme of the objective function are established on macro and micro scales. The solid isotropic material with penalization method is employed to update iteratively the macro and microstructure topologies simultaneously. Finally, the feasibility and advantages of the proposed approach are illustrated by several 2D and 3D numerical examples with different volume fractions, while the effects of volume fraction and different boundary conditions on the final configuration and multi-objective performance of the multiscale structure are explored. Results show that the isogeometric concurrent design of multiscale structures through multi-objective optimization can produce better multi-objective performance compared with a single-scale one.