基于极小曲面的元器件散热优化模拟  

Simulation and optimization of components heat conduction problem based on minimal surface

作　　者：张俊顶 王远弟[1] 张鹏[2] 马非[2] ZHANG Junding;WANG Yuandi;ZHANG Peng;MA Fei(College of Sciences,Shanghai University,Shanghai 200444,China;Institute of Refrigeration and Cryogenics,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海大学理学院,上海200444 [2]上海交通大学制冷与低温工程研究所,上海200240

出　　处：《应用数学与计算数学学报》2018年第4期995-1010,共16页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11471207)

摘　　要：对"体点"导热优化问题中高导热系数材料的最优分布问题,以全局平均温度最低为优化目标,提出并证明了高导热系数材料最优分布时的曲面面积极小化原则,即将全局平均温度最低时高导热系数材料的最优分布与温度场曲面面积达到最小做对应,利用该原则进行数值模拟得出高导热材料的区域最优布置,计算结果说明了该方法的合理有效性.最后,用本文提出的方法和仿生优化方法数值计算了不同条件下高导热系数材料的最优分布,并对比分析了两者在不同条件下的传热优化效果.The optimal distribution of the high thermal conductivity material in the volume-to-point(VP)problem is studied in this paper.By minimizing the mean temperature of the area using the high thermal conductivity material,we propose and prove the area minimization principle to solve the VP problem,that is,the surface of the temperature field has the minimum area when the mean temperature is minimized.Based on the new principle,the optimal distribution of the high thermal conductivity material is obtained.The results of the numerical simulations illustrate that the new method is very effective for solving the VP problem.Then,we compare the optimal distributions of the high thermal conductivity material,which are got by the new method and by the bionic optimization in different filling ratios and different ratios of the thermal conductivity.The analyses of the results are also presented.

关 键 词：导热优化 极小曲面 平均值定理 

分 类 号：O29[理学—应用数学]