Fiber Bundle Topology Optimization for Surface Flows

Yongbo Deng ¹Weihong Zhang ²Jihong Zhu ²Yingjie Xu ²Jan G Korvink³

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作者信息

1. State Key Laboratory of Applied Optics,Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences,Changchun 130033,China
2. State IJR Center of Aerospace Design and Additive Manufacturing,Northwestern Polytechnical University,Xi'an 710072,China
3. Institute of Microstructure Technology(IMT),Karlsruhe Institute of Technology(KIT),Hermann-von-Helmholtzplatz 1,76344 Eggenstein-Leopoldshafen,Germany
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Abstract

This paper presents a topology optimization approach for the surface flows on variable design domains.Via this approach,the matching between the pattern of a surface flow and the 2-manifold used to define the pattern can be optimized,where the 2-manifold is implicitly defined on another fixed 2-manifold named as the base manifold.The fiber bundle topology optimization approach is developed based on the description of the topological structure of the surface flow by using the differential geometry concept of the fiber bundle.The material distribution method is used to achieve the evolution of the pattern of the surface flow.The evolution of the implicit 2-manifold is realized via a homeomorphous map.The design variable of the pattern of the surface flow and that of the implicit 2-mani-fold are regularized by two sequentially implemented surface-PDE filters.The two surface-PDE filters are coupled,because they are defined on the implicit 2-manifold and base manifold,respectively.The surface Navier-Stokes equa-tions,defined on the implicit 2-manifold,are used to describe the surface flow.The fiber bundle topology optimiza-tion problem is analyzed using the continuous adjoint method implemented on the first-order Sobolev space.Several numerical examples have been provided to demonstrate this approach,where the combination of the viscous dis-sipation and pressure drop is used as the design objective.

Key words

Fiber bundle/Topology optimization/2-manifold/Surface flow/Material distribution method/Porous medium model

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基金项目

EU2020 FET grant(TiSuMR)

EU2020 FET grant(737043)

DFG(KO 1883/20-1 Metacoils)

German Excellence Intitiative(EXC 2082)

VirtMat initiative"Virtual Materials Design"Supported by National Natural Science Foundation of China(51875545)

Innovation Grant of Changchun Institute of Optics,Fine Mechanics and Physics(CIOMP)()

CAS Project for Young Scientists in Basic Research of China(YSBR-066)

Science and Technology Development Program of Jilin Province of China(SKL202302020)

出版年

2024

中国机械工程学报

中国机械工程学会

中国机械工程学报

CSTPCD

影响因子：0.765

ISSN：1000-9345

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