北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (6): 1042-1048.doi: 10.13700/j.bh.1001-5965.2014.0401

• 论文 • 上一篇    下一篇

基于SIMP法的周期性传热材料拓扑优化

贾娇1, 程伟1, 龙凯2   

  1. 1. 北京航空航天大学 航空科学与工程学院, 北京 100191;
    2. 华北电力大学 新能源电力系统国家重点实验室, 北京 102206
  • 收稿日期:2014-07-03 出版日期:2015-06-20 发布日期:2015-07-30
  • 通讯作者: 程伟(1961—),男,河北保定人,教授,cheng_wei@buaa.edu.cn,主要研究方向为结构动力学、微振动测试及分析、参数辨识等. E-mail:cheng_wei@buaa.edu.cn
  • 作者简介:贾娇(1984—),女,内蒙古鄂尔多斯人,博士研究生,jiajiao_2012@163.com
  • 基金资助:
    国家自然科学基金 (11202078)

Topology optimization for periodic thermal conductive material using SIMP method

JIA Jiao1, CHENG Wei1, LONG Kai2   

  1. 1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    2. State Key Laboratory for Alternate Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China
  • Received:2014-07-03 Online:2015-06-20 Published:2015-07-30

摘要: 为了实现基于宏观热传导条件的周期性材料微结构设计,建立了基于固体各向同性材料惩罚法的周期性结构拓扑优化模型.模型以体积比为约束,散热弱度最小为优化目标.为了满足周期性约束,将设计域划分为若干相同子区域,并重新分配散热弱度.基于偏微分方程的图像处理方式可以有效地消除棋盘格和网格依赖性现象.讨论并分析了不同子区域个数及不同载荷工况对拓扑优化构型的影响.数值实验结果表明:周期性结构的建模方式可以实现基于宏观稳态热传导条件的周期性材料微结构设计.子区域个数不同时,优化得到不同的微结构构型,这反映了尺寸效应对材料设计的影响.当子区域个数不断增加时,优化结果逐渐趋向收敛于均匀化方法对应的极限值.

关键词: 拓扑优化, 周期性结构, 尺寸效应, 材料设计, 稳态热传导

Abstract: In order to obtain periodic material microstructure under macroscopic thermal conduction condition, the optimal topological model of periodic structure was built by solid isotropic material with penalization (SIMP) method. The volume fraction was referred as constraint and minimized thermal compliance was taken as optimization objective in this model. To satisfy the periodic constraint, the designable domain was divided into a certain number of identical unit cells and the thermal compliance was reallocated. The filtered variable implicitly as a solution of a partial differential equation (PDE) was applied to eliminate the checkerboard patterns and mesh-dependence problems efficiently. The optimal topological configurations were analyzed and compared with different numbers of unit cells and different load cases. The numerical results indicate that proposed periodic model is valid in design of periodic material microstructure with macroscopic steady state thermal conduction condition. Microstructure configurations are different when number of unit cells changes and it reflects the influences of size effect to periodic material design. With an increasing number of unit cells, the optimal results gradually converge to the results using homogenization method.

Key words: topology optimization, periodic structure, size effect, material design, steady state thermal conduction

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