稳态热传导结构非概率可靠性拓扑优化设计

摘要

Topology optimization design of a steady-state heat conduction structure with interval parameters under constraint of dissipation of heat potential capacity was studied.The topology optimization model of the heat conduction structure with interval parameter was constructed based on the constraint of non-probabilistic reliability for dissipation of heat potential capacity.The total volume of heat conductive material was minimized and the relative thermal conductivities of elements were regarded as the design variables here.The computational expressions of numerical characteristics of dissipation of heat potential capacity based on the interval factor method were derived.The evolutionary structural optimization method was used in the optimization.A filtering technique was employed to eliminate numerical instabilities in the process of topology optimization.The numerical examples were presented to demonstrate the feasibility and effectiveness of the optimal model and solving approach.%研究具有区间参数的稳态热传导结构在散热弱度非概率可靠性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，满足散热弱度非概率可靠性为约束条件的稳态热传导结构的拓扑优化设计数学模型。基于区间因子法，推导出散热弱度的均值及离差的计算表达式。采用渐进结构优化法的求解策略与方法，并利用过滤技术消除优化过程中的数值不稳定性现象。通过算例验证所述模型及求解策略、方法的合理性和有效性。