关键词: 功能梯度, 周期性的, 拓扑优化, 热传导, 散热弱度

Abstract: 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. 

Key words:  , functional gradient, periodic, topology optimization, heat conduction, dissipation of heat potential capacity