Multiscale topology optimization of anisotropic multilayer periodic structures based on the isogeometric analysis method

A multiscale topology optimization model of anisotropic multilayer periodic structures (MPS) is proposed using the isogeometric analysis (IGA) method. The integrative design of multiscale structures was realized in two stages: the distribution optimization of multilayer periodic materials, which determines the types, distribution, and volume fraction of microstructures, and parallel topology optimization, which optimizes the macrostructure and various microstructures simultaneously. To implement the multilayer periodic constraint, the relative density and sensitivity of the IGA control points were equally redistributed. The correctness and advantages of the proposed model were confirmed by comparing its results with those obtained using finite element methods, and the optimal IGA microstructures displayed smoother boundaries. In addition, the multiscale MPS of the cantilever was 3D printed, confirming the practicality of the proposed model. The influences of the regularization scheme, multilayer periodic constraints, and Poisson's ratio factor on the results of the multiscale multilayer periodic optimization were explored, and recommendations for proper values of these parameters were provided to enhance the structural stiffness.