Topology optimization on two-dimensional manifolds
Topology optimization on two-dimensional manifolds
复制标题
二维流形的拓扑优化
DOI：
10.1016/j.cma.2020.112937
复制
发表时间：
2020
影响因子：
7.2
通讯作者：
Korvink Jan G.
中科院分区：
文献类型：
--
作者：
Deng Yongbo;Liu Zhenyu;Korvink Jan G.
本文针对二阶偏微分方程描述的现象提出了一般二维流形的拓扑优化，其中材料插值是通过材料分布方法实现的。当在二维流形上定义物理场时，材料插值是在用于描述物理场分布的偏微分方程中的材料参数上实现的。当物理场定义在三维域上，其边界条件定义在对应于该三维域的表面或界面的二维流形上时，材料密度用于制定物理场偏微分方程的混合边界条件，并实现两种不同边界类型之间的惩罚。基于二维流形的同胚性质，数值试验中包括典型的二维流形，例如球体、环面、莫比乌斯带和克莱因瓶，用于演示这种拓扑优化方法解决流体力学、传热学和电磁学的设计问题。
This paper presents topology optimization on general two-dimensional manifolds for phenomena described by second-order partial differential equations, where the material interpolation is implemented by using the material distribution method. When a physical field is defined on a two-dimensional manifold, the material interpolation is implemented on a material parameter in the partial differential equation used to describe the distribution of the physical field. When the physical field is defined on a three-dimensional domain with its boundary conditions defined on a two-dimensional manifold corresponding a surface or an interface of this three-dimensional domain, the material density is used to formulate a mixed boundary condition of the partial differential equation for the physical field and implement the penalization between two different boundary types. Based on the homeomorphic property of two-dimensional manifolds, typical two-dimensional manifolds, e.g., sphere, torus, Möbius strip and Klein bottle, are included in the numerical tests, which are used to demonstrate this topology optimization approach for the design problems of fluidic mechanics, heat transfer and electromagnetics.