周期性多材料结构稳态热传导拓扑优化设计

提出一种考虑周期性约束的多材料结构稳态热传导拓扑优化设计方法。针对多材料结构，提出基于有序有理近似材料属性模型（ordered rational approximation of material properties，Ordered-RAMP）的多材料插值模型。以结构散热弱度最小化为目标函数，体积为约束条件，将设计区域划分为有限个相同的子多材料区域。通过重新分配单元散热弱度基值，实现周期性几何约束，借助优化准则法推导设计变量的迭代格式。通过典型2D与3D数值算例，分析不同子区域个数对宏观结构与微观子区域多材料拓扑构型的影响。结果表明:所提方法可实现面向多材料结构的周期性微观构型设计，且各材料分布合理边界清晰，具有良好的稳健性；当子区域个数不同时，均可得到具有周期性的拓扑构型，且所获拓扑形式具有差异性。

MULTI-MATERIAL TOPOLOGY OPTIMIZATION OF STEADY-STATE HEAT CONDUCTION STRUCTURE UNDER PERIODIC CONSTRAINT

A multi-material topology optimization design for periodic constraint steady-state heat conduction is proposed. The ordered rational approximation of material properties(Ordered-RAMP) based a multi-material interpolation model is constructed. The design domain is divided into finite identical multi-subregion material structures, involving the minimum thermal compliance and volume constraint condition. By redistributing the element base value of the thermal compliance, the periodic constraint is implemented, and the iterative format of the design variables is derived by an optimization criterion method. Through 2 D and 3 D examples, the effects of the number of subregions are researched on the optimal multi-material topologies of the macroscopic and microscopic sburegions. The results show that: the proposed method excellently realizes the robustness design of the periodic microstructure of a multi-material structure with a reasonable distribution and a distinct boundary;and the topological configuration of periodic structures exhibits different characteristics to some extent.