Topology Optimization of Heat Transfer Structures Under Gaussian Moving Heat Source Transient Effects
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摘要: 针对热源位置随时间发生变化的结构热传导问题，考虑Gauss移动热源进行瞬态热传导拓扑优化设计. 分别以整个时间历程内传热结构散热弱度最小化与区域温度最大值最小化为设计目标，体积分数为约束条件，采用伴随变量法推导目标函数与约束条件的敏度信息，借助移动渐进线法更新设计变量，研究了不同Gauss热源移动路径与移动速度对拓扑优化结果的影响. 结果表明，瞬态拓扑结构相较于稳态结果具有明显时变性，同时最佳传热构型受到热源加热时间和移动速度及路径的多重影响.Abstract: For the structural heat transfer problem with heat sources moving with time, the Gaussian moving heat sources were considered for transient heat transfer topology optimization design. The design objectives are to minimize the total heat dissipation of the structure over the entire time history and to minimize the maximum temperature in particular regions, with the volume fraction as the constraint. Sensitivity information for the objectives and constraints was derived with the adjoint variable method, and design variables were updated with the moving asymptote method. The effects of different Gaussian heat source paths and speeds on the topology optimization results were studied. The numerical results indicate that, the transient topology structure exhibits pronounced time-varying characteristics compared to the steady-state results. Moreover, the optimal heat dissipation configuration depends on multiple factors, including the heating time, the path and the speed of the moving heat source.
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图 3 Gauss热源热流密度及模拟路径
Figure 3. The Gaussian heat source heat flux density and the simulation path
图 4 Gaussian热源移动过程仿真
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 4. Simulation of the Gaussian heat source movement process
图 6 稳态热传导与瞬态热传导的拓扑优化结果
Figure 6. Topologiy optimization results of steady-state and transient-state heat transfer
图 7 稳态热传导与移动热源不同速度的优化结果
Figure 7. Topologiy optimization results of steady-state heat conduction and moving heat source at different speeds
图 8 不同热源速度下的目标函数随迭代步数变化曲线
Figure 8. The objective function curves with the number of iteration steps
图 11 S形路径移动热源的拓扑构型
Figure 11. Topological configurations of the S-shaped path moving heat source
表 1 不同热源拓扑优化结果
Table 1. Results of different heat source topology optimizations
表 2 材料体积占比不同下拓扑优化结果
Table 2. Topology optimization results under different volume proportions of materials
表 3 Gauss移动热源不同移动范围的拓扑构型
Table 3. Topology optimization results of the Gaussian heat sources with different moving ranges
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