Discussion of Objective Functions in Heat Conduction Topology Optimization

China Mechanical Engineering ›› 2011, Vol. 22 ›› Issue (9): 1112-1117,1122.

Previous Articles Next Articles

Discussion of Objective Functions in Heat Conduction Topology Optimization

Qiao Heting;Zhang Yongcun;Liu Shutian

State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian,Liaoning,116023

Online:2011-05-10 Published:2011-05-17
Supported by:

National Natural Science Foundation of China（No. 10721062，10902019，90816025）;

National Program on Key Basic Research Project (973 Program)（No. 2006CB601205）;
National Science and Technology Major Project ( No. 2009ZX4014-034)

散热结构拓扑优化目标函数的讨论

乔赫廷;张永存;刘书田

大连理工大学工业装备结构分析国家重点实验室,大连,116023

基金资助:
国家自然科学基金资助项目(10721062，10902019，90816025)；国家重点基础研究发展计划(973计划)资助项目(2006CB601205)；大连理工大学人才启动经费项目；国家科技重大专项(2009ZX4014-034)
National Natural Science Foundation of China（No. 10721062，10902019，90816025）;

National Program on Key Basic Research Project (973 Program)（No. 2006CB601205）;
National Science and Technology Major Project ( No. 2009ZX4014-034)

Abstract

Abstract:

Using geometric average temperature as a good approximation for the maximum temperature which was proposed as the objective function into heat conduction topology optimization model, and a new design model was developed for heat conduction topology optimization. Sensitivity of the new objective function was derived by using the adjoint method. By comparing the maximum temperature, the maximum temperature gradient, and the nodal temperature with the design results respectively, the differences among these three models as well as their scopes of application were discussed through theory and numerical analyses.

Key words: topology optimization, dissipation of heat transport potential capacity, temperature variance, the geometric average temperature, finite element

摘要：

将几何平均温度作为最高温度的近似引入到散热结构拓扑优化中,建立了新的散热结构拓扑优化模型，采用伴随法推导了与该函数对应的灵敏度分析列式，并通过比较最高温度、最大温度梯度以及温度方差(衡量温度场均匀程度的指标)等特征指标来研究基于几何平均温度的优化模型与两个传统优化模型在散热结构拓扑优化设计中的差异以及各自适用的设计范围。

关键词:

拓扑优化, 散热弱度, 温度方差, 几何平均温度, 有限元



CLC Number:

O302
O39

JIAO He-Ting, ZHANG Yong-Cun, LIU Shu-Tian.

Discussion of Objective Functions in Heat Conduction Topology Optimization

[J]. China Mechanical Engineering, 2011, 22(9): 1112-1117,1122.

乔赫廷, 张永存, 刘书田.

散热结构拓扑优化目标函数的讨论

[J]. 中国机械工程, 2011, 22(9): 1112-1117,1122.

References

[1]郝云刚[1],刘玲[2].电子设备的热设计[J].兵工自动化,2010(2):49-50.
[2]Bendsoe M P. Topology Optimization Theory Methods and Applications[M]. 2nd ed. Berlin: Springer, 2003.
[3]Gao T,Zhang W H,Zhu J H,et al. Topology Optimization of Heat Conduction Problem Involving Design- dependent Heat Load Effect[J]. Finite Elements in Analysis and Design, 2008,44 (14) : 805- 813.
[4]Gersborg-- Hansen A, Bendsoe M, Sigmund O. Topology Optimization of Heat Conduction Problems Using the Finite Volume Method[J].Structural and Muhidisciplinary Optimization, 2005, 31 (4) : 251 - 259.
[5]Ha S, Cho S. Topological Shape Optimization of Heat Conduction Problems Using Level Set Approach[J ]. Numerical Heat Transfer, Part R: Fundamentals, 2005,48 ( 1 ) : 67-88.
[6]Li Q,Steven G P,Querin O M,et al. Shape and Topology Design for Heat Conduction by Evolutionary Structural Optimization[J]. International Journal of Heat and Mass Transfer,1999,42(17):3361-3371.
[7]Li Q,Steven G P,Xie Y M,et at. Evolutionary Topology Optimization for Temperature Reduction of Heat Conducting Fields[J]. International Journal of Heat and Mass Transfer,2004,47(23):5071-5083.
[8]Marczak J Topology Optimization and Boundary Elements--a Preliminary Implementation for Linear Heat Transfer [J]. Engineering Analysis with Boundary Elements, 2007,31 (9) : 793-802.
[9]Sluzalec A, Kleiber M. Shape Sensitivity Analysis for Nonlinear Steadystate Heat Conduction Problems[J]. International Journal of Heat and Mass Transfer,1996,39(12) :2609-2613.
[10]Zhang Y,Liu S. Design of Conducting Paths Based on Topology Optimization [J].Heat and Mass Transfer, 2008,44(10) : 1217-1227.
[11]Zhuang C, Xiong Z, Ding H. A Level Set Method for Topology Optimization of Heat Conduction Problem under Multiple Load Cases[J]. Computer Methods in Applied Mechanics and Engineering, 2007,196 (4/6) : 1074-1084.
[12]蒋良杰[1],熊蔡华[1].基于SIMP方法的散热结构拓扑优化设计[J].机电一体化,2006,12(6):14-16.
[13]李家春[1,3],叶邦彦[1],汤勇[1],管琪明[2],刘伟[1].基于密度法的热传导结构拓扑优化准则算法[J].华南理工大学学报：自然科学版,2006,34(2):27-32.
[14]刘书田[1],贺丹[1].渐进密度AESO方法及其在热传导结构拓扑优化中的应用[J].计算力学学报,2009,26(2):151-156.
[15]龙凯[1],左正兴[1].稳态热传导下的连续体结构拓扑优化[J].中国机械工程,2007,18(24):2939-2943.
[16]左孔天[1],陈立平[1],张云清[1],王书亭[1].用拓扑优化方法进行热传导散热体的结构优化设计[J].机械工程学报,2005,41(4):13-16.
[17]贾海朋.结构与柔性机构拓扑优化[D].大连理工大学,2004:
[18]夏再忠,过增元.用生命演化过程模拟导热优化[J].自然科学进展：国家重点实验室通讯,2001,11(8):845-852.
[19]过增元,程新广,夏再忠.最小热量传递势容耗散原理及其在导热优化中的应用[J].科学通报,2003,48(1):21-25.
[20]程雪涛[1],徐向华[1],梁新刚[1].温度场与温度梯度场的均匀化[J].中国科学：E辑,2009(10):1730-1735. 3
[21]张晖[1],刘书田[1],张雄[2].拓扑相关热载荷作用下稳态热传导结构拓扑优化[J].中国机械工程,2009(11):1339-1343.
[22]Sigmund O. Materials with Prescribed Constitutive Parameters: an Inverse Homogenization Problem [J]. International Journal of Solids and Structures, 1994,31(17) :2313-2329.
[23]Mlejnek H P,Schirrmaeher R. An Engineer's Approach to Optimal Material Distribution and Shape Finding[J].Computer Methods in Applied Mechanics and Engineering, 1993,106(1/2) : 1-26.
[24]张永存[1],刘书田[1].最优传热结构设计问题的数学模型[J].自然科学进展,2008,18(6):680-685.
[25]Sigmund O, Petersson J. Numerical Instabilities in Topology Optimization.. a Survey on Procedures Dealing with Checkerboards, Mesh-- dependencies and Local Minima[J]. Structural and Multidiseiplinary Optimization, 1998,16 ( 1 ) : 68-75.
[26]Sigmund O. On the Design of Compliant Mechanisms Using Topology Optimization[J]. Mechanics of Structures and Machines, 1997,25(4) : 493-524.
[27]Krister S. The Method of Moving Asymptotes-- a New Method for Structural Optimization[J]. International Journal for Numerical Methods in Engineering, 1987,24(2) :359-373.

Discussion of Objective Functions in Heat Conduction Topology Optimization

散热结构拓扑优化目标函数的讨论

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 1

Recommended Articles

Metrics