摘要为实现传热和振动条件下连续体结构的拓扑优化设计，以结构散热弱度最小化和动态特征值最大化加权函数为目标，建立传热和振动条件下连续体结构的多目标拓扑优化模型，实现了相应的算法和算例。方法中采用Rational Approximation of Material Properties(RAMP)方法对密度进行惩罚，利用优化准则法控制设计目标与材料分布，以敏度过滤技术抑制棋盘格效应，通过归一化目标函数有效地避免了不同性质目标函数的量级差异。通过算例，获得了热-振权重系数对结构拓扑构型和目标函数(宏观结构的散热弱度和基频)的影响规律，算例结果表明了该方法的有效性。
Abstract：For thermal and vibrational design problems, taking the minimum dissipation of heat transport potential capacity and the maximum fundamental frequency as the objectives, a thermal and vibrational collaborative optimization model for the continuum structure was developed and corresponding numerical experiments were carried out. In the model, Rational Approximation of Material Properties (RAMP) was adopted to ensure clear topologies, the design objective and material distribution were controlled by optimization criteria method and the checkerboard influence was eliminated by a sensitivity filter method. To improve the smoothness of the objective function and avoid the singularity of numerical computation, the weighted objection function is normalized. Based on the numerical experiments, effects of the weight coefficient of the thermal and vibrational optimization on the topology configuration and objective values (the dissipation of heat transport potential capacity and fundamental frequency) were investigated and the results indicated that the proposed method is effective.
刘远东 莫军 尹益辉 徐兵. 考虑热振特性的连续体结构拓扑优化设计[J]. 振动与冲击, 2016, 35(17): 113-116.
Liu Yuandong Mo Jun Yin Yihui Xu Bin. Topology Optimization for Continuum Structure Consideration of Thermal and Vibrational Performances. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(17): 113-116.
1. 周克民,李俊峰,李霞.结构拓扑优化研究方法综述[J].力学进展，2005,35(1):69-76
Zhou Kemin, Li Junfeng, Li Xia. A review on topology optimization of structures [J]. Advances in mechanics, 2005,35(1):69-76
2. 罗震,陈立平等. 连续体结构拓扑优化设计[J].力学进展,2004,34(4):463-476
Luo Zhen, Chen Liping. Topological optimization design for continuum structures [J]. Advances in mechanics, 2004,34(4):463-476
3. Mathieu-Potvin F, Gosselin L. Optimal conduction pathways for a heat generating body: A comparison exercise [J]. International Journal of Heat Mass Transfer, 2007, 50(5-16):2996-3006
4. Li Q, Steven GP, Xie YM, et al. Evolutionary topology optimization for temperature reduction of heat conducting fields [J]. International Journal of Heat and Mass Transfer, 2004, 47(23):5071-5083
5. Gersborg-Hansen A, Bendsoe MP, Sigmund O. Topology optimization of heat conduction problems using the finite volume method [J]. Structural and Multidisciplinary Optimization, 2006, 31(4):251-259
6. Zhang Y, Liu S. Design of conducting paths based on topology optimization [J]. Heat and Mass Transfer, 2008, 44(10):1217-1227
7. Li Q, Steven GP, Xie YM. Displacement minimization of thermo-elastic structures by evolutionary thickness design [J].Computer Methods in Applied Mechanics Engineering, 1999(3-4), 179:361-378
8. Cho S, Choi JY. Efficient topology optimization of thermo elasticity problems using coupled field adjoint sensitivity analysis method [J]. Finite Elements in Analysis and Design, 2005, 41(51):1481-1495
9. 左孔天, 赵雨东, 陈立平.传热结构的多目标拓扑优化设计研究[J].计算力学学报, 2007, 24(5):620-627
Zuo Kongtian, Zhao Yudong, Chen Liping. Study on multiple objective topology optimization of thermal conductive structure [J]. Chines journal of computational mechanics,2007,24(5) :620-627
10 Zhang WH , Yang JG, Xu XJ, etal. Topology optimization of thermoelastic structures: mean compliance minimization or elastic strain energy minimization [J] Structural and Multidisciplinary Optimization, 2014, 49(3):417-429
11 Yang XW, Li YM. Topology optimization to minimize the dynamic compliance of a bi-material plate in a thermal environment [J]. Structural and Multidisciplinary Optimization, 2013, 47(3):399-408
12 Yang XW, Li YM. Structural topology optimization on dynamic compliance at resonance frequency in thermal environments [J]. Structural and Multidisciplinary Optimization, 2014, 49(1):81-91
13 Sigmund O. Morphology-based black and white filters for topology optimization[J]. Struct Multidisc Optim, 2007,33 (4-5):401-424
14 刘远东. 材料/结构一体化静动力学多目标优化设计和两尺度实验研究[D],绵阳,2007
Liu YD. Static and dynamic multi-objective design optimization based on integrated design of materials and structure and two-scale experimental research. Phd Thesis, Mianyang, 2012(in Chinese)
15 Bendsoe MP, Sigmund O. Topology optimization theory, methods and application. Berlin: Springer, 2003:71-75
