Filters in topology optimization
Filters in topology optimization
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DOI：
10.1002/nme.116
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发表时间：
2001-03-30
影响因子：
2.9
通讯作者：
Bourdin, B
中科院分区：
文献类型：
--
作者：
Bourdin, B
本文研究了最小顺应性拓扑优化问题的一个改进（“过滤”）版本。用卷积算子的均值对密度场进行正则化，取代了材料性质对其逐点密度的直接依赖。在这种情况下，有可能确定解决办法的存在。此外，还可以得到有限元近似的收敛性。通过一些数值实验说明了这一点。“滤波”技术也被证明可以处理拓扑优化中的两个重要数值问题，棋盘和网格相关设计。版权所有John Wiley & Sons， Ltd。
In this article, a modified ('filtered') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator. In this setting it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The 'filtering' technique is also shown to cope with two important numerical problems in topology optimization, checkerboards and mesh dependent designs. Copyright (C) 2001 John Wiley & Sons, Ltd.