多工况稳态热传导下的连续体拓扑优化

Topological Optimization of Continuum Structure for Heat Conduction under Multiple Loading Cases

针对多工况拓扑优化问题,提出了多工况加权单约束拓扑优化模型。基于独立联系映射法,实现了多工况稳态热传导下的连续体拓扑优化设计。根据拓扑优化模型,分析了多工况拓扑优化"病态载荷"现象产生的原因,提出了初始结构总热能判定依据,通过对载荷工况系数的适当调整来消除"病态载荷"现象。通过数值算例,对不同优化模型下的拓扑优化结果进行分析比较。结果表明,独立连续映射法和多工况加权单约束模型在处理多工况稳态热传导拓扑优化问题中具有可行性和有效性。

The mathematical model of topological optimization of continuum structure for heat conduction under multiple loading cases was established by using independent continuous mapping （ICM） method. In the mathematical model, weighting heat energy corresponding to different loading cases was taken as the single constraint considering all effects of multiple loading cases. Based on analysis of the phenomenon of ＂ill-condition loading＂, heat energy for initial structure was taken as criterion for ＂ill-condition loading＂ problem and adjusting weighting factors of small-loading cases were proposed to overcome this problem. Some numerical examples were provided and results were discussed under different mathematical models. Results show the feasibility and validity of the proposed method and model.