拓扑相关热载荷作用下稳态热传导结构拓扑优化  

Topology Optimization of Steady-state Heat Conduction Problems with Design-dependent Heat Loads

作　　者：张晖[1] 刘书田[1] 张雄 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116024 [2]韩国科学技术院,大田305701

出　　处：《中国机械工程》2009年第11期1339-1343,共5页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(10572030,10721062);国家重点基础研究发展计划资助项目(2006CB601205);教育部新世纪优秀人才支持计划资助项目(NCET-04-0272)

摘　　要：针对热源随结构形式变化的稳态结构热传导拓扑优化问题,提出了以温度方差为目标函数来评价设计域内温度分布的均匀程度的方法,同时考虑结构内热源引起的热载荷的拓扑相关性,以高热导率材料的体积用量为约束建立了拓扑优化模型。采用正则化的Heaviside函数建立了材料插值模型,获得了清晰的0/1拓扑。数值算例验证了所提出的目标函数以及采用的求解方法的合理性与有效性。Topology optimization of steady- state heat conduction problems with topology-dependent heat sources was studied herein. The nodal temperature variance in the design region was proposed as the objective function to estimate the extent of the uniformity of temperature distribution and the total volume of high heat conductive material was used as the constraint. The design- dependent heat loads derived from the heat source density were taken into consideration in the optimization. The regularized Heaviside function was adopted to relate the material density to the material heat property and the discrete 0/1 design was obtained. Several numerical examples demonstrate the validity of the proposed objective function and the optimization method.

关 键 词：拓扑优化 热传导 拓扑相关载荷 Heaviside函数 

分 类 号：O39[理学—工程力学]