传热结构摄动敏度分析及动态拓扑优化

Perturbation Sensitivity Analysis and Dynamic Topology Optimization for Heat Transfer Structures

针对传热强化拓扑优化过程中新形成的孔洞边界对拓扑优化影响的问题,研究了考虑孔洞影响的拓扑导数分析技术,并提出了优化过程中对新形成孔洞边界进行处理的自适应动态边界处理方法。应用Lebesgue微分理论,基于域摄动敏度分析和局部极限定律,推导了Poisson方程控制系统在三类边界条件下不同目标函数的拓扑导数计算公式;最后通过数值分析实例验证了采用该方法直接设计高效换热器的可行性和有效性。

Aimed at the effects of the generated new hole boundaries on the topology optimization in the processes of heat transfer enhancement topology optimization, a topological derivative analysis with respect to the new holes was studied ？ and an adaptive dynamic boundary treatment method was proposed for the new boundaries in the optimization processes. By using Lebesgue differential theory, based on the domain perturbation technique and local limit law？ the topological derivative formulas with different objective functions subjected to three kinds of boundary conditions were derived for the control system of Poisson equation. Finally,a number of numerical examples were presented to demon-strate the feasibility and effectiveness of the proposed method for designing the efficient heat exchangers.