Filters in topology optimization based on Helmholtz-type differential equations
Filters in topology optimization based on Helmholtz-type differential equations
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DOI：
10.1002/nme.3072
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发表时间：
2011-05-13
影响因子：
2.9
通讯作者：
Sigmund, O.
中科院分区：
文献类型：
--
作者：
Lazarov, B. S.;Sigmund, O.
本文的目的是应用亥姆霍兹型偏微分方程作为替代标准密度过滤拓扑优化问题。以前，这种方法已成功地应用为灵敏度滤波器。拓扑优化中常用的滤波技术需要得到相邻单元的信息，而这对于精细网格或复杂区域和几何形状是很难获得的。在并行计算中，当设计域被分解为多个不重叠的分区时，问题的复杂性进一步增加。从相邻子域获取信息是一个昂贵的操作。建议的过滤器技术只需要必要的有限元离散化的问题的网格信息。其主要思想是将过滤变量隐式定义为具有齐次Neumann边界条件的Helmholtz型微分方程的解。滤波器的性能证明了各种二维和三维拓扑优化问题的线性弹性，解决了串行和并行计算机。版权所有（C）2010约翰威利父子有限公司
The aim of this paper is to apply a Helmholtz-type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology optimization require information about the neighbor cells, which is difficult to obtain for fine meshes or complex domains and geometries. The complexity of the problem increases further in parallel computing, when the design domain is decomposed into multiple non-overlapping partitions. Obtaining information from the neighbor subdomains is an expensive operation. The proposed filter technique requires only mesh information necessary for the finite element discretization of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz-type differential equation with homogeneous Neumann boundary conditions. The properties of the filter are demonstrated for various 2D and 3D topology optimization problems in linear elasticity, solved on serial and parallel computers. Copyright (C) 2010 John Wiley & Sons, Ltd.