基于ordered-EAMP模型的多材料传热结构拓扑优化

基于多材料变密度拓扑优化方法提出了一种密度指数函数插值的有序多材料性能近似(ordered exponential approximation of material properties,ordered-EAMP)模型,数学性质以及算例表明,与传统的SIMP/RAMP插值相比,该模型具有计算稳定,收敛速度快,优化结构灰度单元少的特点。在优化准则(OC)法求解变密度拓扑优化模型时,构造了一种适用于多材料的密度过滤格式,算例表明:可以有效减少灰度单元,且降低了优化的目标函数值。运用MATLAB-ANSYS联合优化,实现三类热边界条件下复杂热环境的多材料传热结构拓扑优化。相比于高热传导系数的单材料结构,多材料传热拓扑优化结构由于各种热传导系数材料的优化分布,结构的传热势容耗散更小,算例4中对比分析降低了20.3%,传热效率更高。 

Multi-material topology optimization for heat transfer structure based on ordered-EAMP model

A density-based ordered-EAMP (exponential approximation of material properties) interpolation model was presented to solve topology optimization problems of multi-material heat transfer structure.Compared with the classical SIMP/RAMP, the numerical examples showed that the proposed interpolation had the characteristics of stable calculation, fast convergence and less gray units of optimized structure. A density filtering scheme for multi-material was constructed in the iterative formula for solving the optimization model based on the optimization criterion (OC) method. The example showed that the scheme can effectively reduce the gray units and the value of optimal objective function. The MATLAB-ANSYS combined calculation was used to achieve the topology optimization of multi-material heat transfer structure in complex thermal environment under three kinds of thermal boundary conditions. The results showed that compared with the structure of single material with large coefficient of conductivity, the multi-material heat transfer topology optimization structure corresponded to the optimal distribution of various heat conduction coefficient materials, which was characterized by smaller dissipation of heat, the dissipation was reduced by 20.3% in numerical example 4, and the heat transfer efficiency was higher.