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. For each substructure， two design variables are considered： a quasi-discrete variable， which determines its spatial topological layout； a continuous density variable， which determines its material usage. For the lattice substructures with predefined geometric topology， a series of samples of lattice substructures with fixed configuration and variable density are obtained by varying their feature sizes， and static condensation of the substructures is performed to reduce the number of degrees of freedom. On this basis， the corresponding data-driven interpolation model is built to explicitly correlate the density variable with the thermoelastic equivalent constitutive behavior of the lattice substructure. Furthermore， to realize the hybrid layout design of multi-configuration lattice substructures， a multi-material interpolation model for quasi-discrete lattice selection variables is constructed. The numerical example results show that the design method is able to utilize the gradient lattice structures to balance the mechanical deformation caused by temperature loading， which in turn effectively enhances the thermo-mechanical load carrying capacity of the structure. Moreover， since the gradient lattice structure is modeled based on the substructure method， the geometrical configuration and thermoelastic properties of the whole structure and the lattice structures are coupled. Compared with the design method based on the homogenization theory， the design scheme proposed in this paper does not require additional geometric post-processing， effectively avoiding the performance deviation between design and fabrication.

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