Filters in topology optimization

TLDR

The paper studies a filtered version of the minimum compliance topology optimization problem. The authors replace the direct density–property dependence with a convolution‑based regularization of the density field. The filtered formulation guarantees existence of solutions, finite‑element convergence, and effectively eliminates checkerboard and mesh‑dependent artifacts, as demonstrated by numerical experiments. © 2001 John Wiley & Sons, Ltd.

Abstract

Abstract 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 © 2001 John Wiley & Sons, Ltd.