关键词: 拓扑优化, 多材料, 梯度点阵, 热力耦合, 数据驱动

Abstract: This paper presents a topology optimization method for the design of thermoelastic multi-configuration gradient lattice structures. Specifically, the structure is assumed to consist of several spatially varying lattice substructures. Two design variables are considered for each substructure, a quasi-discrete variable that determines its spatial topological layout and a continuous density variable that determines its material usage. For lattice substructures with predefined geomet-ric topology, a series of samples of lattice substructures with fixed configuration and variable density are obtained by varying their feature sizes, and static condensation is performed to reduce the number of degrees of freedom, building the corresponding data-driven interpolation model to explicitly correlate the density variable with its thermoelastic equivalent behavior. Furthermore, a multi-material interpolation model for quasi-discrete lattice selection variables is constructed to realize the hybrid layout design of multi-configuration lattice substructures. The numerical example re-sults show that the design method is able to utilize the gradient lattice structures to balance the mechanical defor-mation caused by temperature loading, which in turn effectively enhances the thermal-mechanical coupled load carry-ing capacity of the structure. Moreover, since the gradient lattice structure is modeled based on the substructure meth-od, the geometrical configuration and thermoelastic properties of the whole structure and the lattice structures are cou-pled; compared with the design method based on the homogenization theory, the design scheme in this paper does not require additional geometrical post-processing, and the performance deviation between design and fabrication can be effectively avoided.

Key words: topology optimization, multi-material, gradient lattice, thermo-mechanical coupling, data-driven