随机变量下的热传导结构拓扑优化设计

研究具有随机变量的稳态热传导结构在散热弱度约束下的拓扑优化设计问题．建立了以单元相对导热系数为设计变量，导热材料体积极小化为目标函数，满足散热弱度可靠性指标为约束条件的稳态热传导结构的拓扑优化设计数学模型．基于随机因子法，利用代数综合法推导出散热弱度的数字特征的计算表达式．采用渐进结构优化方法(Evolutionary Structural Optimization，ESO)求解，并利用过滤技术消除优化过程中的数值不稳定性现象．通过两个算例验证文中模型及求解策略、方法的合理性和有效性．

Topology optimization design of heat conduction structures with random variables

Topology optimization design of a heat conduction structure with random variables under dissipation of heat transport potential capacity constraint is discussed. The mathematical model of topology optimization, based on the probabilistic reliability index with dissipation of heat transport potential capacity constraint, is constructed. The total volume of heat conductive material is to be minimized and the relative thermal conductivity of elements is regarded as the design variable here. The computational expressions for numerical characteristics of dissipation of heat transport potential capacity based on the random factor method are presented. Evolutionary structural optimization method is used in optimization. A filtering technique is employed to eliminate numerical instabilities in process of topology optimization. Two numerical examples are presented to demonstrate the feasibility and effectiveness of the optimal model and the solution.