Multiscale concurrent topology optimization of hierarchal multi-morphology lattice structures

This paper proposes a multiscale concurrent topology optimization method for design of hierarchal multi-morphology lattice structures (HMMLSs), which features in the Kriging metamodel assisted Uniform Multiphase Materials Interpolation (KUMMI) model and the sigmoid function (SF) based hybrid transition strategy. Specifically, level set functions are adopted to model hierarchal lattice unit cells (LUCs). Then LUCs with different morphology are treated as distinct lattice materials (LMs) and the SF-based hybrid transition strategy is employed to realize smooth transition between multi-morphology LUCs. Besides, Kriging metamodels are constructed to predict the equivalent properties of LUCs efficiently so that the topology optimization of HMMLSs can be achieved with an affordable computational cost. Two kinds of design variables are involved in the topology optimization of HMMLSs, where discrete variables indicate the categories of lattice materials and continuous variables determine the relative densities of lattice microstructures. The proposed KUMMI model can couple the two kinds of design variables dexterously to realize concurrent optimization of relative densities of LUCs, and distribution regions and percentages of different LMs within HMMLSs. Several numerical examples are presented to demonstrate the effectiveness and applicability of the proposed method. Results indicate the optimized HMMLSs exhibit rational distribution of hierarchal multi-morphology LUCs, hence achieving superior structural performance.