周期性功能梯度结构稳态热传导拓扑优化设计

提出了一种考虑周期性约束的功能梯度结构稳态热传导拓扑优化设计方法。建立了基于变密度理论的固体各向同性微结构惩罚（SIMP）模型的周期性功能梯度拓扑优化模型。以整体结构散热弱度最小化为目标函数、体积分数为约束条件进行宏观拓扑优化，提取了最优构型中各预设梯度层的体积分数；通过重新分配单元散热弱度，实现了梯度层周期性约束设置。借助基于偏微分方程的灵敏度过滤方法消除数值不稳定问题，并采用移动渐近线法对设计变量进行了迭代更新。通过2D和3D数值算例分析了全局周期以及周期性分层梯度设置下，不同离散单元和子区域个数对宏观结构和微观构型的影响规律。研究结果表明：所提方法能够实现周期性约束下功能梯度结构的拓扑优化设计，不同子区域个数条件下均能获得清晰的周期性功能梯度结构且所获得的结构具有良好的散热性能。

Steady-state Heat Conduction Topology Optimization Design for Periodic Functional Gradient Structures

A topology optimization design method of steady-state heat conduction for functional gradient structures was proposed considering periodic constraints. The periodic functional gradient topology optimization model was established based on the variable density theory of solid isotropic microstructure with penalization（SIMP）. The macroscopic topology optimization was performed with the minimization of dissipation of heat potential capacity for the overall structures as the objective function and the volume fraction as the constraint， and the volume fraction of each preset gradient layer was extracted in the optimal configuration. The dissipation of heat potential capacity for units was redistributed to achieve the gradient layer periodic constraint. The numerical instability was eliminated with the application of sensitivity filtering method based on partial differential equation， and the design variables were iteratively updated by using the method of moving asymptotes. Through 2D and 3D numerical examples， the influences of the number of discrete units and sub-regions on the macro-structures and micro-configurations were analyzed under the global periods and the periodic layered gradient settings. The results show that the proposed method is able to achieve the optimal design of the functional gradient topology with periodic constraints. The clear periodic functional gradient structures may be obtained under different numbers of sub-regions, and the obtained structures have excellent heat dissipation performance.